Implement Vector3::MinElement

CMakeLists.txt

@@ -4,13 +4,10 @@ PROJECT(J3ML
         LANGUAGES CXX
 )
 
-
 if (PROJECT_SOURCE_DIR STREQUAL PROJECT_BINARY_DIR)
     message(FATAL_ERROR "In-source builds are not allowed")
 endif()
 
-
-
 set(CMAKE_CXX_STANDARD 20)
 #set(CMAKE_POSITION_INDEPENDENT_CODE ON)
 if (WIN32)
@@ -32,7 +29,7 @@ file(GLOB_RECURSE J3ML_SRC     "src/J3ML/*.c" "src/J3ML/*.cpp")
 include_directories("include")
 
 add_library(J3ML SHARED ${J3ML_SRC}
-        src/J3ML/LinearAlgebra/AxisAngle.cpp)
+        include/J3ML/Geometry/Common.h)
 set_target_properties(J3ML PROPERTIES LINKER_LANGUAGE CXX)
 
 install(TARGETS ${PROJECT_NAME} DESTINATION lib/${PROJECT_NAME})

include/J3ML/Algorithm/DifferentialSolvers.h

@@ -0,0 +1,42 @@
+//
+// Created by dawsh on 2/8/24.
+//
+
+namespace J3ML::Algorithm
+{
+    /// Implementations for a variety of Differential Equation Solving algorithms
+    namespace Solvers
+    {
+
+        // Consider a differential equation
+        // dy/dx = (x + y + xy)
+        float eq(float x, float y)
+        {
+            return (x + y + x*y);
+        }
+
+        // Accelleration = Velocity / Time
+        // Velocity = Position / Time
+        // Position = Vector3
+
+        //
+
+        float euler(float x0, float y, float h, float x)
+        {
+            float temp = -0.f;
+            // Iterating till the point at which we need approximation
+            while (x0 < x) {
+                temp = y;
+                y = y + h * eq(x0, y);
+                x0 = x0 + h;
+            }
+            return y;
+        }
+
+        class EulerMethodSolver {};
+        class SemiImplicitEulerMethodSolver {};
+        class GaussSeidelMethodSolver {};
+        class GradientDescentSolver {};
+        class VerletIntegrationSolver {};
+    }
+}

include/J3ML/Algorithm/RNG.h

@@ -0,0 +1,99 @@
+#pragma once
+
+
+#include "J3ML/J3ML.h"
+
+namespace J3ML::Algorithm
+{
+/** @brief A linear congruential random number generator.
+
+	Uses D.H. Lehmer's Linear Congruential Method (1949) for generating random numbers.
+	Supports both Multiplicative Congruential Method (increment==0) and
+	Mixed Congruential Method (increment!=0)
+	It is perhaps the simplest and fastest method to generate pseudo-random numbers on
+	a computer. Per default uses the values for Minimal Standard LCG.
+	http://en.wikipedia.org/wiki/Linear_congruential_generator
+	http://www.math.rutgers.edu/~greenfie/currentcourses/sem090/pdfstuff/jp.pdf
+
+	Pros:
+	<ul>
+	    <li> Easy to implement.
+	    <li> Fast.
+	</ul>
+
+	Cons:
+	<ul>
+	    <li> NOT safe for cryptography because of the easily calculatable sequential
+	        correlation between successive calls. A case study:
+	        http://www.cigital.com/papers/download/developer_gambling.php
+
+	    <li> Tends to have less random low-order bits (compared to the high-order bits)
+	         Thus, NEVER do something like this:
+
+	           u32 numBetween1And10 = 1 + LCGRand.Int() % 10;
+
+	         Instead, take into account EVERY bit of the generated number, like this:
+
+	           u32 numBetween1And10 = 1 + (int)(10.0 * (double)LCGRand.Int()
+	                                                      /(LCGRand.Max()+1.0));
+	         or simply
+
+	           u32 numBetween1And10 = LCGRand.Float(1.f, 10.f);
+	</ul> */
+
+
+    class RNG {
+    public:
+        /// Initializes the generator from the current system clock.
+        RNG();
+        RNG(u32 seed, u32 multiplier = 69621,
+            u32 increment = 0, u32 modulus = 0x7FFFFFFF) // 2^31 - 1
+        {
+            Seed(seed, multiplier, increment, modulus);
+        }
+        /// Reinitializes the generator to the new settings.
+        void Seed(u32 seed, u32 multiplier, u32 increment, u32 modulus = 0x7FFFFFFF);
+        /// Returns a random integer picked uniformly in the range [0, MaxInt()]
+        u32 Int();
+        /// Returns the biggest number the generator can yield. [modulus - 1]
+        u32 MaxInt() const { return modulus - 1;}
+        /// Returns a random integer picked uniformly in the range [0, 2^32-1].
+        /// @note The configurable modulus and increment are not used by this function, but are always increment == 0, modulus=2^32
+        u32 IntFast();
+        /// Returns a random integer picked uniformly in the range [a, b]
+        /// @param a Lower bound, inclusive.
+        /// @param b Upper bound, inclusive.
+        /// @return A random integer picked uniformly in the range [a, b]
+        int Int(int a, int b);
+
+        /// Returns a random float picked uniformly in the range [0, 1].
+        float Float();
+
+        /// Returns a random float picked uniformly in the range [0, 1].
+        /// @note this is much slower than Float()! Prefer that function if possible.
+        float Float01Incl();
+
+        /// Returns a random float picked uniformly in the range ]-1, 1[.
+        /// @note This function has one more bit of randomness compared to Float(), but has a theoretical bias
+        /// towards 0.0, since floating point has two representations for 0 (+0, and -0).
+        float FloatNeg1_1();
+
+        /// Returns a random float picked uniformly in the range [a, b[.
+        /// @param a Lower bound, inclusive.
+        /// @param b Upper bound, exclusive.
+        /// @return A random float picked uniformly in the range [a, b[
+        /// @note This function is slower than RNG::FloatIncl(). If you don't care about the open/closed interval, prefer that function.
+        float Float(float a, float b);
+
+        /// Returns a random float picked uniformly in the range [a, b].
+        /// @param a Lower bound, inclusive.
+        /// @param b Upper bound, inclusive.
+        /// @return A random float picked uniformly in the range [a, b]
+        float FloatIncl(float a, float b);
+
+        u32 multiplier;
+        u32 increment;
+        u32 modulus;
+        u32 lastNumber;
+    };
+}

include/J3ML/Algorithm/Spring.h

@@ -0,0 +1,21 @@
+//
+// Created by dawsh on 2/8/24.
+//
+
+namespace J3ML::Algorithm
+{
+    // Numerical model of a "Spring" object
+    // Simulates any oscillating system i.e. a mass suspended from a spring.
+    class Spring
+    {
+        float Dampening;
+        float Stiffness;
+        float Goal;
+        float RestLength = 1.f;
+
+        bool Overdamped() const;
+        bool Undamped() const;
+        bool Underdamped() const;
+        bool CriticallyDamped() const;
+    };
+}

include/J3ML/Geometry.h

@@ -1,66 +1,22 @@
-#include <J3ML/LinearAlgebra/Vector3.h>
+#include <J3ML/LinearAlgebra.h>
 
 #pragma once
 
-namespace Geometry {
-    using Point2D = LinearAlgebra::Vector2;
+#include <J3ML/Geometry/AABB2D.h>
+#include <J3ML/Geometry/Plane.h>
+#include <J3ML/Geometry/Sphere.h>
+#include <J3ML/Geometry/LineSegment.h>
+#include <J3ML/Geometry/Frustum.h>
+#include <J3ML/Geometry/OBB.h>
+#include <J3ML/Geometry/Capsule.h>
+#include <J3ML/Geometry/AABB.h>
+#include <J3ML/Geometry/Polyhedron.h>
+#include <J3ML/Geometry/QuadTree.h>
+#include <J3ML/Geometry/Ray.h>
+#include <J3ML/Geometry/Shape.h>
+#include <J3ML/Geometry/Sphere.h>
+#include <J3ML/Geometry/Triangle.h>
+#include <J3ML/Geometry/Triangle2D.h>
+#include <J3ML/Geometry/TriangleMesh.h>
 
-    class LineSegment2D
-    {
-        Point2D A;
-        Point2D B;
-    };
-
-    class Rectangle; //AABB2D;
-    class OBB2D;
-    class Line2D;
-    class Ray2D;
-    class Triangle2D;
-    class Polygon2D;
-
-    struct IntersectionResult2D {
-
-    };
-
-    bool Intersects2D(LineSegment2D seg, Rectangle rect);
-    IntersectionResult2D GetIntersection2D(LineSegment2D seg, Rectangle rect);
-
-
-
-    
-
-    using Point3D = LinearAlgebra::Vector3;
-
-    // A 3D axis-aligned bounding box
-    // This data structure can be used to represent coarse bounds of objects, in situations where detailed triangle-level
-    // computations can be avoided. In physics systems, bounding boxes are used as an efficient early-out test for geometry
-    // intersection queries.
-    // the 'Axis-aligned' part in the name means that the local axes of this bounding box are restricted to align with the
-    // axes of the world space coordinate system. This makes computation involving AABB's very fast, since AABB's cannot
-    // be arbitrarily oriented in the space with respect to each other.
-    // If you need to represent a box in 3D space with arbitrary orientation, see the class OBB. */
-    class AABB;
-    class Capsule;
-    class Line;
-    class LineSegment
-    {
-        Point3D A;
-        Point3D B;
-    };
-    class Ray
-    {
-        Point3D Origin;
-        Point3D Direction;
-    };
-
-    class OBB;
-    class Frustum;
-    class Plane;
-    class Polygon;
-    class Polyhedron;
-    class QuadTree;
-    class OctTree;
-    class Sphere;
-    class Triangle;
-    class TriangleMesh;
-}
+using namespace J3ML::Geometry;

include/J3ML/Geometry/AABB.h

@@ -0,0 +1,149 @@
+#pragma once
+
+#include <J3ML/LinearAlgebra.h>
+#include <J3ML/Geometry/Common.h>
+#include <J3ML/Geometry/Shape.h>
+
+// TODO: Fix circular include between AABB and OBB
+
+namespace J3ML::Geometry
+{
+    using namespace J3ML::LinearAlgebra;
+    // A 3D axis-aligned bounding box
+    // This data structure can be used to represent coarse bounds of objects, in situations where detailed triangle-level
+    // computations can be avoided. In physics systems, bounding boxes are used as an efficient early-out test for geometry
+    // intersection queries.
+    // the 'Axis-aligned' part in the name means that the local axes of this bounding box are restricted to align with the
+    // axes of the world space coordinate system. This makes computation involving AABB's very fast, since AABB's cannot
+    // be arbitrarily oriented in the space with respect to each other.
+    // If you need to represent a box in 3D space with arbitrary orientation, see the class OBB. */
+
+    class AABB : public Shape {
+    public:
+        Vector3 minPoint;
+        Vector3 maxPoint;
+
+        AABB();
+
+        AABB(const Vector3& min, const Vector3& max);
+
+        static int NumFaces() { return 6; }
+
+        static int NumEdges() { return 12; }
+
+        static int NumVertices() { return 8; }
+
+        static AABB FromCenterAndSize(const Vector3 &center, const Vector3 &size);
+
+        float MinX() const;
+
+        float MinY() const;
+
+        float MinZ() const;
+
+        float MaxX() const;
+
+        float MaxY() const;
+
+        float MaxZ() const;
+
+        /// Returns the smallest sphere that contains this AABB.
+        /// This function computes the minimal volume sphere that contains all the points inside this AABB
+        Sphere MinimalEnclosingSphere() const;
+
+        Vector3 HalfSize() const;
+
+        /// Returns the largest sphere that can fit inside this AABB
+        /// This function computes the largest sphere that can fit inside this AABB.
+        Sphere MaximalContainedSphere() const;
+
+        bool IsFinite() const;
+
+        Vector3 Centroid() const;
+
+        Vector3 Size() const;
+
+        // Quickly returns an arbitrary point inside this AABB
+        Vector3 AnyPointFast() const;
+
+        Vector3 PointInside(float x, float y, float z) const;
+
+        // Returns an edge of this AABB
+        LineSegment Edge(int edgeIndex) const;
+
+        Vector3 CornerPoint(int cornerIndex) const;
+
+        Vector3 ExtremePoint(const Vector3 &direction) const;
+
+        Vector3 ExtremePoint(const Vector3 &direction, float &projectionDistance);
+
+        Vector3 PointOnEdge(int edgeIndex, float u) const;
+
+        Vector3 FaceCenterPoint(int faceIndex) const;
+
+        Vector3 FacePoint(int faceIndex, float u, float v) const;
+
+        Vector3 FaceNormal(int faceIndex) const;
+
+        Plane FacePlane(int faceIndex) const;
+
+        static AABB MinimalEnclosingAABB(const Vector3 *pointArray, int numPoints);
+        float GetVolume() const;
+        float GetSurfaceArea() const;
+        Vector3 GetClosestPoint(const Vector3& point) const;
+        Vector3 GetRandomPointInside();
+        Vector3 GetRandomPointOnSurface();
+        Vector3 GetRandomPointOnEdge();
+        Vector3 GetRandomCornerPoint();
+        AABB Translated(const Vector3& offset) const;
+        AABB TransformAABB(const Matrix3x3& transform);
+        AABB TransformAABB(const Matrix4x4& transform);
+        AABB TransformAABB(const Quaternion& transform);
+        OBB Transform(const Matrix3x3& transform);
+        OBB Transform(const Matrix4x4& transform);
+        OBB Transform(const Quaternion& transform);
+        bool Contains(const Vector3& point) const;
+        bool Contains(const LineSegment& lineSegment) const;
+        bool Contains(const AABB& aabb) const;
+        bool Contains(const OBB& obb) const;
+        bool Contains(const Sphere& sphere) const;
+        bool Contains(const Triangle& triange) const;
+        bool Contains(const Polygon& polygon) const;
+        bool Contains(const Frustum& frustum) const;
+        bool Contains(const Polyhedron& polyhedron) const;
+        bool Contains(const Capsule& capsule) const;
+        // Tests whether this AABB and the given object intersect.
+        bool Intersects(const Ray& ray, float dNear, float dFar) const;
+        bool Intersects(const Capsule& capsule) const;
+        bool Intersects(const Triangle& triangle) const;
+        bool Intersects(const Polygon& polygon) const;
+        bool Intersects(const Frustum& frustum) const;
+        bool Intersects(const Polyhedron& polyhedron) const;
+        TriangleMesh Triangulate(int numFacesX, int numFacesY, int numFacesZ, bool ccwIsFrontFacing) const;
+        AABB Intersection(const AABB& rhs) const;
+        bool IntersectLineAABB(const Vector3& linePos, const Vector3& lineDir, float tNear, float tFar) const;
+
+
+        void SetFrom(const Vector3 *pVector3, int i);
+
+        void SetFromCenterAndSize(const Vector3 &center, const Vector3 &size);
+
+        void SetFrom(const OBB &obb);
+
+        void SetFrom(const Sphere &s);
+
+        Vector3 GetRandomPointInside() const;
+
+        void SetNegativeInfinity();
+
+        void Enclose(const Vector3 &point);
+
+        void Enclose(const Vector3 &aabbMinPt, const Vector3 &aabbMaxPt);
+
+        void Enclose(const LineSegment &lineSegment);
+
+        void Enclose(const OBB &obb);
+
+        bool TestAxis(const Vector3& axis, const Vector3& v0, const Vector3& v1, const Vector3& v2) const;
+    };
+}

include/J3ML/Geometry/AABB2D.h

@@ -0,0 +1,54 @@
+#pragma once
+
+#include <J3ML/LinearAlgebra/Vector2.h>
+#include "Shape.h"
+
+namespace J3ML::Geometry
+{
+    using LinearAlgebra::Vector2;
+    // CaveGame AABB
+    class AABB2D : public Shape2D
+    {
+    public:
+
+        Vector2 minPoint;
+        Vector2 maxPoint;
+        AABB2D() {}
+        AABB2D(const Vector2& min, const Vector2& max):
+        minPoint(min), maxPoint(max)
+        {}
+
+        float Width() const;
+        float Height() const;
+
+        float DistanceSq(const Vector2& pt) const;
+
+        void SetNegativeInfinity();
+
+        void Enclose(const Vector2& point);
+
+        bool Intersects(const AABB2D& rhs) const;
+
+        bool Contains(const AABB2D& rhs) const;
+
+        bool Contains(const Vector2& pt) const;
+
+        bool Contains(int x, int y) const;
+
+        bool IsDegenerate() const;
+
+        bool HasNegativeVolume() const;
+
+        bool IsFinite() const;
+
+        Vector2 PosInside(const Vector2 &normalizedPos) const;
+
+        Vector2 ToNormalizedLocalSpace(const Vector2 &pt) const;
+
+
+        AABB2D operator+(const Vector2& pt) const;
+
+        AABB2D operator-(const Vector2& pt) const;
+
+    };
+}

include/J3ML/Geometry/Capsule.h

@@ -0,0 +1,28 @@
+#pragma once
+
+#include "LineSegment.h"
+#include "Shape.h"
+#include <J3ML/LinearAlgebra/Vector3.h>
+
+namespace J3ML::Geometry
+{
+    using namespace LinearAlgebra;
+    class Capsule : public Shape
+    {
+        // Specifies the two inner points of this capsule
+        LineSegment l;
+        // Specifies the radius of this capsule
+        float r;
+
+        Capsule();
+        Capsule(const LineSegment& endPoints, float radius);
+        Capsule(const Vector3& bottomPt, const Vector3& topPt, float radius);
+        bool IsDegenerate() const;
+        float Height() const;
+        float Diameter() const;
+        Vector3 Bottom() const;
+        Vector3 Center() const;
+        Vector3 Centroid() const;
+        Vector3 ExtremePoint(const Vector3& direction);
+    };
+}

include/J3ML/Geometry/Common.h

@@ -0,0 +1,30 @@
+#pragma once
+
+
+// Forward declarations for classes that include each other
+namespace J3ML::Geometry
+{
+    class Shape;
+    class AABB2D;
+    class AABB;
+    class Capsule;
+    class Frustum;
+    class LineSegment;
+    class OBB;
+    class Plane;
+    class Polygon;
+    class Polyhedron;
+    template<typename T> class QuadTree;
+    class Ray;
+    class Shape;
+    class Sphere;
+    class Triangle;
+    class Triangle2D;
+    class TriangleMesh;
+}
+
+// Methods required by Geometry types
+namespace J3ML::Geometry
+{
+
+}

include/J3ML/Geometry/Frustum.h

@@ -0,0 +1,43 @@
+//
+// Created by dawsh on 1/25/24.
+//
+#pragma once
+
+#include "Plane.h"
+#include "Shape.h"
+#include <J3ML/LinearAlgebra/CoordinateFrame.h>
+
+namespace J3ML::Geometry
+{
+
+    using J3ML::LinearAlgebra::CoordinateFrame;
+
+    enum class FrustumType
+    {
+        Invalid,
+        /// Set the Frustum type to this value to define the orthographic projection formula. In orthographic projection,
+        /// 3D images are projected onto a 2D plane essentially by flattening the object along one direction (the plane normal).
+        /// The size of the projected images appear the same independent of their distance to the camera, and distant objects will
+        /// not appear smaller. The shape of the Frustum is identical to an oriented bounding box (OBB).
+        Orthographic,
+        /// Set the Frustum type to this value to use the perspective projection formula. With perspective projection, the 2D
+        /// image is formed by projecting 3D points towards a single point (the eye point/tip) of the Frustum, and computing the
+        /// point of intersection of the line of the projection and the near plane of the Frustum.
+        /// This corresponds to the optics in the real-world, and objects become smaller as they move to the distance.
+        /// The shape of the Frustum is a rectangular pyramid capped from the tip.
+        Perspective
+    };
+
+    class Frustum : public Shape {
+    public:
+        Plane TopFace;
+        Plane BottomFace;
+        Plane RightFace;
+        Plane LeftFace;
+        Plane FarFace;
+        Plane NearFace;
+        static Frustum CreateFrustumFromCamera(const CoordinateFrame& cam, float aspect, float fovY, float zNear, float zFar);
+    };
+
+
+}

include/J3ML/Geometry/LineSegment.h

@@ -0,0 +1,16 @@
+#pragma once
+
+#include <J3ML/LinearAlgebra/Vector3.h>
+
+namespace J3ML::Geometry
+{
+    using LinearAlgebra::Vector3;
+    class LineSegment
+    {
+    public:
+        LineSegment();
+        LineSegment(const Vector3& a, const Vector3& b);
+        Vector3 A;
+        Vector3 B;
+    };
+}

include/J3ML/Geometry/OBB.h

@@ -0,0 +1,90 @@
+#pragma once
+
+#include <J3ML/Geometry/Common.h>
+#include <J3ML/Geometry/AABB.h>
+#include <J3ML/Geometry/Polyhedron.h>
+
+
+namespace J3ML::Geometry {
+    /// A 3D arbitrarily oriented bounding box
+    // This data structure represents a box in 3D space. The local axes of this box can be arbitrarily oriented/rotated
+    // with respect to the global world coordinate system. This allows OBBs to more tightly bound objects than AABBs do,
+    // which always align with the world space axes. This flexibility has the drawback that the geometry tests and operations
+    // involving OBBs are more costly, and representing an OBB in memory takes more space (15 floats vs 6 floats)
+    class OBB : public Shape
+    {
+    public:
+        // The center position of this OBB
+        Vector3 pos;
+        // Stores half-sizes to x, y, and z directions in the local space of this OBB.
+        Vector3 r;
+        // Specifies normalized direction vectors for the local axes
+        Vector3 axis[3];
+
+        /// Default constructor that does not initialize any member values.
+        OBB() {}
+        // Constructs an OBB by explicitly initializing all member values
+        OBB(const Vector3& pos, const Vector3& radii, const Vector3& axis0, const Vector3& axis1, const Vector3& axis2);
+        OBB(const AABB& aabb);
+        inline static int NumFaces() { return 6;  }
+        inline static int NumEdges() { return 12; }
+        inline static int NumVertices() { return 8; }
+
+        Polyhedron ToPolyhedron() const;
+        //PBVolume<6> ToPBVolume() const;
+        AABB MinimalEnclosingAABB() const
+        {
+            AABB aabb;
+            aabb.SetFrom(*this);
+            return aabb;
+        }
+
+        Sphere MinimalEnclosingSphere() const;
+        Sphere MaximalContainedSphere() const;
+        Vector3 Size() const;
+        Vector3 HalfSize() const;
+        Vector3 Diagonal() const;
+        Vector3 HalfDiagonal() const;
+        void Transform(const Matrix3x3& transform);
+        void Transform(const Matrix4x4& transform);
+        bool IsFinite() const;
+        bool IsDegenerate() const;
+        Vector3 CenterPoint() const;
+        Vector3 Centroid() const;
+
+        Vector3 AnyPointFast() const;
+
+        float Volume() const;
+        float SurfaceArea() const;
+        Geometry::LineSegment Edge(int edgeIndex) const;
+        Vector3 CornerPoint(int cornerIndex) const;
+
+        Vector3 PointInside(float x, float y, float z) const;
+        Vector3 PointInside(const Vector3& pt) const;
+
+        void ProjectToAxis(const Vector3 &direction, float &outMin, float &outMax) const;
+
+        int UniqueFaceNormals(Vector3 *out) const;
+
+        int UniqueEdgeDirections(Vector3 *out) const;
+
+        Vector3 PointOnEdge(int edgeIndex, float u) const;
+
+        Vector3 FaceCenterPoint(int faceIndex) const;
+
+        void GetCornerPoints(Vector3 *outPointArray) const;
+
+        void GetFacePlanes(Plane *outPlaneArray) const;
+
+        Plane FacePlane(int faceIndex) const;
+
+        void ExtremePointsAlongDirection(const Vector3 &dir, const Vector3 *pointArray, int numPoints, int &idxSmallest,
+                                         int &idxLargest, float &smallestD, float &largestD);
+
+        Vector3 FacePoint(int faceIndex, float u, float v) const;
+
+        Vector3 ExtremePoint(const Vector3 &direction, float &projectionDistance) const;
+
+        Vector3 ExtremePoint(const Vector3 &direction) const;
+    };
+}

include/J3ML/Geometry/Plane.h

@@ -0,0 +1,20 @@
+#pragma once
+#include <J3ML/LinearAlgebra/Vector3.h>
+#include "Shape.h"
+
+
+namespace J3ML::Geometry
+{
+    using J3ML::LinearAlgebra::Vector3;
+
+    class Plane : public Shape
+    {
+    public:
+        Plane() : Shape() {}
+        Plane(const Vector3& pos, const Vector3& norm)
+        : Shape(), Position(pos), Normal(norm) {}
+        Vector3 Position;
+        Vector3 Normal;
+        float distance = 0.f;
+    };
+}

include/J3ML/Geometry/Polygon.h

@@ -0,0 +1,12 @@
+#pragma once
+
+#include "Shape.h"
+
+namespace J3ML::Geometry {
+    class Polygon : public Shape
+    {
+    public:
+    protected:
+    private:
+    };
+}

include/J3ML/Geometry/Polyhedron.h

@@ -0,0 +1,37 @@
+#pragma once
+
+#include <J3ML/Geometry/Shape.h>
+#include <vector>
+#include <J3ML/LinearAlgebra/Vector3.h>
+
+namespace J3ML::Geometry
+{
+    using namespace J3ML::LinearAlgebra;
+
+    // Represents a three-dimensional closed geometric solid defined by flat polygonal faces.
+    class Polyhedron : public Shape
+    {
+    public:
+        // Stores a list of indices of a single face of a Polygon
+        struct Face
+        {
+            // Specifies the indices of the corner vertices of the polyhedron.
+            // Indices point to the polyhedron vertex array.
+            // The face vertices should all lie on the same plane.
+            // The positive direction of the plane (the direction the face outwards normal points)
+            // is the one where the vertices are wound in counter-clockwise order.
+            std::vector<int> v;
+
+            // Reverses the winding order of this face. This has the effect of reversing the direction
+            // the normal of this face points to.
+            void FlipWindingOrder();
+
+        };
+
+        // Specifies the vertices of this polyhedron.
+        std::vector<Vector3> v;
+
+    protected:
+    private:
+    };
+}

include/J3ML/Geometry/QuadTree.h

@@ -0,0 +1,369 @@
+#pragma once
+
+#include <vector>
+#include <cstdint>
+#include <J3ML/LinearAlgebra/Vector2.h>
+#include "AABB2D.h"
+
+namespace J3ML::Geometry {
+
+
+    using LinearAlgebra::Vector2;
+
+    template<typename T>
+    class QuadTree {
+        /// A fixed split rule for all QuadTrees: A QuadTree leaf node is only ever split if the leaf contains at least this many objects.
+        /// Leaves containing fewer than this many objects are always kept as leaves until the object count is exceeded.
+        constexpr static const int minQuadTreeNodeObjectCount = 16;
+
+        /// A fixed split limit rule for all QuadTrees: If the QuadTree node side length is smaller than this, the node will
+        /// never be split again into smaller subnodes. This provides a hard limit safety net for infinite/extra long recursion
+        /// in case multiple identical overlapping objects are placed into the tree.
+        constexpr static const float minQuadTreeQuadrantSize = 0.05f;
+
+    public:
+        struct Node {
+            Node *parent;
+            uint32_t childIndex;
+            std::vector<T> objects;
+
+            Vector2 center;
+            Vector2 radius;
+
+            bool IsLeaf() const { return childIndex == 0xFFFFFFFF; }
+
+            uint32_t TopLeftChildIndex() const { return childIndex; }
+
+            uint32_t TopRightChildIndex() const { return childIndex + 1; }
+
+            uint32_t BottomLeftChildIndex() const { return childIndex + 2; }
+
+            uint32_t BottomRightChildIndex() const { return childIndex + 3; }
+
+            /// This assumes that the QuadTree contains unique objects and never duplicates
+            void Remove(const T &object) {
+                for (size_t i = 0; i < objects.size(); ++i) {
+                    if (objects[i] == object) {
+                        AssociateQuadTreeNode(object,
+                                              0); // Mark in the object that it has been removed from the QuadTree.
+                        std::swap(objects[i], objects.back());
+                        objects.pop_back();
+                        return;
+                    }
+                }
+            }
+
+            AABB2D ComputeAABB() {}
+
+            float DistanceSq(const Vector2 &point) const {
+                Vector2 centered = point - center;
+                Vector2 closestPoint = centered.Clamp(-radius, radius);
+                return closestPoint.DistanceSq(centered);
+            }
+
+        };
+
+        // Helper struct used when traversing through the tree
+        struct TraversalStackItem {
+            Node *node;
+        };
+
+        QuadTree() :
+                rootNodeIndex(-1),
+                boundingAABB(Vector2(0, 0), Vector2(0, 0)) {
+            // TODO: currently storing persistent raw pointers to this array outside the array
+            nodes.reserve(200000);
+        }
+
+        /// Removes all nodes and objects in this tree and reintializes the tree to a single root node.
+        void Clear(const Vector2 &minXY = Vector2(-1, -1), const Vector2 &maxXY = Vector2(1, 1));
+
+        /// Places the given object onto the proper (leaf) node of the tree. After placing, if the leaf split rule is
+        /// satisfied, subdivides the leaf node into 4 subquadrants and reassings the objects to the new leaves.
+        void Add(const T &object);
+
+        /// Removes the given object from this tree.
+        /// To call this function, you must define a function QuadTree<T>::Node *GetQuadTreeNode(const T& object)
+        /// which returns the node of this quadtree where the object resides in.
+        void Remove(const T &object);
+
+        /// @return The bounding rectangle for the whole tree.
+        /// @note This bounding rectangle does not tightly bound the objects themselves, only the root node of the tree.
+        AABB2D BoundingAABB() const { return boundingAABB; }
+
+        /// @return The topmost node in the tree.
+        Node *Root();
+
+        const Node *Root() const;
+
+        /// Returns the total number of nodes (all nodes, i.e. inner nodes + leaves) in the tree.
+        /// Runs in constant time.
+        int NumNodes() const;
+
+        /// Returns the total number of leaf nodes in the tree.
+        /// @warning Runs in time linear 'O(n)' to the number of nodes in the tree.
+        int NumLeaves() const;
+
+        /// Returns the total number of inner nodes in the tree.
+        /// @warning Runs in time linear 'O(n)' to the number of nodes in the tree.
+        int NumInnerNodes() const;
+
+        /// Returns the total number of objects stored in the tree.
+        /// @warning Runs in time linear 'O(n)' to the number of nodes in the tree.
+        int NumObjects() const;
+
+        /// Returns the maximum height of the whole tree (the path from the root to the farthest leaf node).
+        int TreeHeight() const;
+
+        /// Returns the height of the subtree rooted at 'node'.
+        int TreeHeight(const Node *node) const;
+
+        /// Performs an AABB intersection query in this Quadtreee, and calls the given callback function for each non-empty
+        /// node of the tree which intersects the given AABB.
+        /** @param aabb The axis-aligned bounding box to intersect this QuadTree with.
+            @param callback A function or a function object of prototype
+                bool callbackFunction(QuadTree<T> &tree, const AABB2D &queryAABB, QuadTree<T>::Node &node);
+            If the callback function returns true, the execution of the query is stopped and this function immediately
+            returns afterwards. If the callback function returns false, the execution of the query continues. */
+        template<typename Func>
+        inline void AABBQuery(const AABB2D &aabb, Func &callback);
+
+        /// Finds all object pairs inside the given AABB which have colliding AABBs. For each such pair, calls the
+        /// specified callback function.
+        template<typename Func>
+        inline void CollidingPairsQuery(const AABB2D &aabb, Func &callback);
+
+        /// Performs various consistency checks on the given node. Use only for debugging purposes.
+        void DebugSanityCheckNode(Node *n);
+
+    private:
+        void Add(const T &object, Node *n);
+
+        /// Allocates a sequential 4-tuple of QuadtreeNodes, contiguous in memory.
+        int AllocateNodeGroup(Node *parent);
+
+        void SplitLeaf(Node *leaf);
+
+        std::vector<Node> nodes;
+        int rootNodeIndex;
+        AABB2D boundingAABB;
+
+        void GrowRootTopLeft();
+
+        void GrowRootTopRight();
+
+        void GrowRootBottomLeft();
+
+        void GrowRootBottomRight();
+
+        void GrowImpl(int quadrantForRoot);
+    };
+
+    // NOTE: Keep members defined here. Template-parameterized classes
+    // can't be split across header and implementation files
+    // but the presence of the implementation file is a requirement
+
+
+    template<typename T>
+    void QuadTree<T>::Clear(const Vector2 &minXY, const Vector2 &maxXY) {
+        nodes.clear();
+
+        boundingAABB.minPoint = minXY;
+        boundingAABB.maxPoint = maxXY;
+
+        rootNodeIndex = AllocateNodeGroup(0);
+
+        Node *root = Root();
+        root->center = (minXY + maxXY) * 0.5f;
+        root->radius = maxXY - root->center;
+    }
+
+    template<typename T>
+    void QuadTree<T>::Add(const T &object) {
+        Node *n = Root();
+        AABB2D objectAABB = GetAABB2D(object);
+
+        // Ramen Noodle Bowls of nested if statements are generally bad practice
+        // Unfortunately, sometimes the problem domain makes this unavoidable
+
+        if (objectAABB.minPoint.x >= boundingAABB.minPoint.x) {
+            // object fits left.
+            if (objectAABB.maxPoint.x <= boundingAABB.maxPoint.x) {
+                // object fits left and right.
+                if (objectAABB.minPoint.y >= boundingAABB.minPoint.y) {
+                    // Object fits left, right, and top.
+                    if (objectAABB.maxPoint.y <= boundingAABB.maxPoint.y) {
+                        // Object fits the whole root AABB. Can safely add into the existing tree size.
+                        AddObject(object, n);
+                        return;
+                    } else {
+                        // Object fits left, right, and top, but not bottom.
+                        GrowRootBottomRight(); // Could grow bottom-left as well, wouldn't matter here.
+                    }
+                } else {
+                    // Object fits left and right, but not to top.
+                    GrowRootTopRight(); // Could grow top-left as well, wouldn't matter here.
+                }
+            } else {
+                // Object fits left, but not to right. We must grow right. Check whether to grow top or bottom;
+                if (objectAABB.minPoint.y < boundingAABB.minPoint.y)
+                    GrowRootTopRight();
+                else
+                    GrowRootBottomRight();
+            }
+        } else {
+            // We must grow left. Check whether to grow top or bottom.
+            if (objectAABB.minPoint.y < boundingAABB.minPoint.y)
+                GrowRootTopLeft();
+            else
+                GrowRootBottomLeft();
+        }
+        // Now that we have grown the tree root node, try adding again.
+        Add(object);
+    }
+
+    template<typename T>
+    void QuadTree<T>::Remove(const T &object) {
+        Node *n = GetQuadTreeNode(object);
+        if (n) {
+            n->Remove(object);
+        }
+    }
+
+    template<typename T>
+    void QuadTree<T>::Add(const T &object, Node *n) {
+        for (;;) {
+            // Traverse the QuadTree to decide which quad to place this object on.
+            float left = n->center.x - MinX(object); // If left > 0.f, then the object overlaps with the left quadrant.
+            float right = MaxX(object) - n->center.x; // If right > 0.f, then the object overlaps with the right quadrant.
+
+            float top = n->center.y - MinY(object); // If top > 0.f, then the object overlaps with the top quadrant
+            float bottom =
+                    MaxY(object) - n->center.y; // If bottom > 0.f, then the object overlaps with the bottom quadrant
+            float leftAndRight = std::min(left, right); // If > 0.f, then the object straddles left-right halves.
+            float topAndBottom = std::min(top, bottom); // If > 0.f, then the object straddles top-bottom halves.
+            float straddledEitherOne = std::max(leftAndRight,
+                                                topAndBottom); // If > 0.f, thne the object is in two or more quadrants.
+
+            // Note: It can happen that !left && !right, or !top && !bottom.
+            // but the if()s are setup below so that right/bottom is taken if no left/top, so that is ok.
+
+            // We must put the object onto this node if
+            // a) the object straddled the parent->child split lines.
+            // b) this object is a leaf
+            if (straddledEitherOne > 0.f) {
+                n->objects.push_back(object);
+                AssociateQuadTreeNode(object, n);
+                return;
+            }
+            if (n->IsLeaf()) {
+                n->objects.push_back(object);
+                AssociateQuadTreeNode(object, n);
+
+                if ((int) n->objects.size() > minQuadTreeNodeObjectCount &&
+                    std::min(n->radius.x, n->radius.y) >= minQuadTreeQuadrantSize) {
+                    SplitLeaf(n);
+                }
+
+                return;
+            }
+            if (left > 0.f) {
+                if (top > 0.f) {
+                    n = &nodes[n->TopLeftChildIndex()];
+                } else {
+                    n = &nodes[n->BottomLeftChildIndex()];
+                }
+            } else {
+                if (top > 0.f) {
+                    n = &nodes[n->TopRightChildIndex()];
+                } else {
+                    n = &nodes[n->BottomRightChildIndex()];
+                }
+            }
+        }
+    }
+
+    template<typename T>
+    typename QuadTree<T>::Node *QuadTree<T>::Root() {
+        return nodes.empty() ? 0 : &nodes[rootNodeIndex];
+    }
+
+    template<typename T>
+    const typename QuadTree<T>::Node *QuadTree<T>::Root() const {
+        return nodes.empty() ? 0 : &nodes[rootNodeIndex];
+    }
+
+    template <typename T>
+    int QuadTree<T>::AllocateNodeGroup(Node* parent) {
+        size_t oldCap = nodes.capacity();
+
+        int index = (int)nodes.size();
+        Node n;
+        n.parent = parent;
+        n.childIndex = 0xFFFFFFFF;
+        if (parent) {
+            n.radius = parent->radius * 0.5f;
+            n.center = parent->center - n.radius;
+        }
+
+        nodes.push_back(n);
+        if (parent)
+            n.center.x = parent->center.x + n.radius.x;
+        nodes.push_back(n);
+
+        if (parent) {
+            n.center.x = parent->center.x - n.radius.x;
+            n.center.y = parent->center.y + n.radius.y;
+        }
+
+        nodes.push_back(n);
+        if (parent)
+            n.center.x = parent->center.x + n.radius.x;
+        nodes.push_back(n);
+
+        return index;
+    }
+
+    template <typename T>
+    void QuadTree<T>::SplitLeaf(Node *leaf) {
+        leaf->childIndex = AllocateNodeGroup(leaf);
+
+        size_t i = 0;
+        while (i < leaf->objects.size()) {
+            const T& object = leaf->objects[i];
+
+            // Traverse the QuadTree to decide which quad to place this object into
+            float left = leaf->center.x - MinX(object);
+            float right = MaxX(object) - leaf->center;
+            float top = leaf->center.y - MinY(object);
+            float bottom = MaxY(object) - leaf->center.y;
+            float leftAndRight = std::min(left, right);
+            float topAndBottom = std::min(top, bottom);
+
+            float straddledEitherOne = std::max(leftAndRight, topAndBottom);
+
+            if (straddledEitherOne > 0.f) {
+                ++i;
+                continue;
+            }
+
+            if (left > 0.f) {
+                if (top > 0.f) {
+                    Add(object, &nodes[leaf->TopLeftChildIndex()]);
+                } else {
+                    Add(object, &nodes[leaf->BottomLeftChildIndex()]);
+                }
+            } else {
+                if (top > 0.f) {
+                    Add(object, &nodes[leaf->TopRightChildIndex()]);
+                } else {
+                    Add(object, &nodes[leaf->BottomRightChildIndex()]);
+                }
+            }
+
+            // Remove the object we added to a child from this node.
+            leaf->objects[i] = leaf->objects.back();
+            leaf->objects.pop_back();
+        }
+    }
+}

include/J3ML/Geometry/Ray.h

@@ -0,0 +1,60 @@
+//
+// Created by dawsh on 1/25/24.
+//
+
+#pragma once
+
+#include <J3ML/LinearAlgebra/Vector3.h>
+#include <vector>
+#include "TriangleMesh.h"
+#include "Frustum.h"
+#include "OBB.h"
+
+namespace J3ML::Geometry
+{
+    using J3ML::LinearAlgebra::Vector3;
+
+
+    // RaycastResult structure containing the first object the ray collides with,
+    // the surface intersection point,
+    // and the surface normal at the point of intersection.
+    struct RaycastResult
+    {
+        Vector3 Intersection;
+        Vector3 SurfaceNormal;
+        bool Hit;
+        Shape* Target;
+        static RaycastResult NoHit() { return {Vector3::NaN, Vector3::NaN, false, nullptr};}
+    };
+
+    // A ray in 3D space is a line that starts from an origin point and extends to infinity in one direction
+    class Ray
+    {
+    public:
+        // The position of this ray.
+        Vector3 Origin;
+        // The normalized direction vector of this ray.
+        // @note: For proper functionality, this direction vector needs to always be normalized
+        Vector3 Direction;
+        Ray() {}
+        Ray(const Vector3& pos, const Vector3& dir);
+        //explicit Ray(const Line& line);
+        explicit Ray(const LineSegment& lineSegment);
+        bool IsFinite() const;
+        Vector3 GetPoint(float distance) const;
+        RaycastResult Cast(const Triangle& target, float maxDistance = 99999999);
+        RaycastResult Cast(const Plane& target, float maxDistance = 99999999);
+        RaycastResult Cast(const AABB& target, float maxDistance = 99999999);
+        // https://gdbooks.gitbooks.io/3dcollisions/content/Chapter3/raycast_sphere.html
+        RaycastResult Cast(const Sphere& target, float maxDistance = 99999999);
+        RaycastResult Cast(const OBB& target, float maxDistance = 99999999);
+        RaycastResult Cast(const Capsule& target, float maxDistance = 99999999);
+        RaycastResult Cast(const Frustum& target, float maxDistance = 99999999);
+        RaycastResult Cast(const TriangleMesh& target, float maxDistance = 9999999);
+
+        // Returns a RaycastResult structure containing the first object the ray collides with,
+        // the surface intersection point,
+        // and the surface normal at the point of intersection.
+        RaycastResult Cast(std::vector<Shape> shapes, float maxDistance = 99999999);
+    };
+}

include/J3ML/Geometry/Shape.h

@@ -0,0 +1,26 @@
+#pragma once
+
+
+namespace J3ML::Geometry
+{
+    class GeometricPrimitive
+    {
+    public:
+    protected:
+    private:
+    };
+
+    class Shape
+    {
+    public:
+    protected:
+    private:
+    };
+
+    class Shape2D
+    {
+    public:
+    protected:
+    private:
+    };
+}

include/J3ML/Geometry/Sphere.h

@@ -0,0 +1,71 @@
+#pragma once
+
+#include <J3ML/Geometry.h>
+#include <J3ML/LinearAlgebra/Matrix3x3.h>
+#include <J3ML/LinearAlgebra/Matrix4x4.h>
+#include <J3ML/Geometry/LineSegment.h>
+#include <J3ML/Geometry/TriangleMesh.h>
+#include <J3ML/Geometry/Shape.h>
+
+namespace J3ML::Geometry
+{
+    using J3ML::LinearAlgebra::Matrix3x3;
+    using J3ML::LinearAlgebra::Matrix4x4;
+
+    // A mathematical representation of a 3-dimensional sphere
+    class Sphere : public Shape
+    {
+    public:
+        Vector3 Position;
+        float Radius;
+        Sphere() {}
+        Sphere(const Vector3& pos, float radius) : Position(pos), Radius(radius) {}
+        void Translate(const Vector3& offset)
+        {
+            Position = Position + offset;
+        }
+        void Transform(const Matrix3x3& transform)
+        {
+            Position = transform * Position;
+        }
+        void Transform(const Matrix4x4& transform)
+        {
+            Position = transform * Position;
+        }
+        inline float Cube(float inp) const
+        {
+            return inp*inp*inp;
+        }
+        float Volume() const
+        {
+            return 4.f * M_PI * Cube(Radius) / 3.f;
+        }
+        float SurfaceArea() const
+        {
+            return 4.f * M_PI * Cube(Radius) / 3.f;
+        }
+        bool IsFinite() const
+        {
+            return Position.IsFinite() && std::isfinite(Radius);
+        }
+        bool IsDegenerate()
+        {
+            return !(Radius > 0.f) || !Position.IsFinite();
+        }
+        bool Contains(const Vector3& point) const
+        {
+            return Position.DistanceSquared(point) <= Radius*Radius;
+        }
+        bool Contains(const Vector3& point, float epsilon) const
+        {
+            return Position.DistanceSquared(point) <= Radius*Radius + epsilon;
+        }
+        bool Contains(const LineSegment& lineseg)  const
+        {
+
+        }
+        TriangleMesh GenerateUVSphere() const {}
+        TriangleMesh GenerateIcososphere() const {}
+
+    };
+}

include/J3ML/Geometry/Triangle.h

@@ -0,0 +1,17 @@
+#pragma once
+
+namespace J3ML::Geometry
+{
+    class Triangle
+    {
+    public:
+        Vector3 V0;
+        Vector3 V1;
+        Vector3 V2;
+
+        bool Intersects(const AABB& aabb) const
+        {
+            return aabb.Intersects(*this);
+        }
+    };
+}

include/J3ML/Geometry/Triangle2D.h

@@ -0,0 +1,9 @@
+#pragma once
+
+
+namespace J3ML::Geometry
+{
+    class Triangle2D {
+    public:
+    };
+}

include/J3ML/Geometry/TriangleMesh.h

@@ -0,0 +1,9 @@
+#pragma once
+
+namespace J3ML::Geometry
+{
+    class TriangleMesh
+    {
+
+    };
+}

include/J3ML/J3ML.h

@@ -1,8 +1,241 @@
+#pragma once
+
+
+
 //
 // Created by josh on 12/25/2023.
 //
+#include <cstdint>
+#include <cmath>
+#include <stdfloat>
+#include <string>
+#include <cassert>
 
-#ifndef J3ML_J3ML_H
-#define J3ML_J3ML_H
+namespace J3ML::SizedIntegralTypes
+{
+    using u8 = uint8_t;
+    using u16 = uint16_t;
+    using u32 = uint32_t;
+    using u64 = uint64_t;
+    using u128 = __uint128_t;
 
-#endif //J3ML_J3ML_H
+    using s8 = int8_t;
+    using s16 = int16_t;
+    using s32 = int32_t;
+    using s64 = int64_t;
+    using s128 = __int128_t;
+}
+
+
+
+namespace J3ML::SizedFloatTypes
+{
+    using f32 = float;
+    using f64 = double;
+    using f128 = long double;
+
+}
+
+using namespace J3ML::SizedIntegralTypes;
+using namespace J3ML::SizedFloatTypes;
+
+namespace J3ML::Math
+{
+
+
+    // Coming soon: Units Namespace
+    // For Dimensional Analysis
+    /*
+    namespace Units
+    {
+
+        struct Unit {};
+
+        struct Meters : public Unit { };
+        struct ImperialInches : public Unit {};
+        struct Time : public Unit {};
+        struct Grams : public Unit {};
+
+
+        struct MetersPerSecond : public Unit {};
+
+
+        template <typename TUnit>
+        struct Quantity
+        {
+        public:
+
+            float Value;
+        };
+
+        struct Mass : public Quantity<Grams> {};
+        struct Length : public Quantity<Meters> { };
+
+        struct Velocity : public Quantity<MetersPerSecond>{ };
+
+        class MetrixPrefix
+        {
+        public:
+            std::string Prefix;
+            std::string Symbol;
+            int Power;
+            float InverseMultiply(float input) const
+            {
+                return std::pow(input, -Power);
+            }
+            float Multiply(float input) const
+            {
+                return std::pow(input, Power);
+            }
+
+        };
+        namespace Prefixes
+        {
+            static constexpr MetrixPrefix Tera {"tera", "T", 12};
+            static constexpr MetrixPrefix Giga {"giga", "G", 9};
+            static constexpr MetrixPrefix Mega {"mega", "M", 6};
+            static constexpr MetrixPrefix Kilo {"kilo", "k", 3};
+            static constexpr MetrixPrefix Hecto {"hecto", "h", 2};
+            static constexpr MetrixPrefix Deca {"deca", "da", 1};
+            static constexpr MetrixPrefix None {"", "", 0};
+            static constexpr MetrixPrefix Deci {"", "", 0};
+            static constexpr MetrixPrefix Centi {"", "", 0};
+            static constexpr MetrixPrefix Milli {"", "", 0};
+            static constexpr MetrixPrefix Micro {"", "", 0};
+            static constexpr MetrixPrefix Nano {"", "", 0};
+            static constexpr MetrixPrefix Pico {"", "", 0};
+        }
+
+        Length operator ""_meters(long double value)
+        {
+            return {(float)value};
+        }
+        Length operator ""_m(long double value)
+        {
+            return {(float)value};
+        }
+        constexpr Length operator ""_kilometers(long double value)
+        {
+            return Length {(float)value};
+        }
+        Length operator ""_km(long double value)
+        {
+            return {(float)value};
+        }
+        Length operator ""_centimeters(long double value)
+        {
+            return {(float)value};
+        }
+        Length operator ""_cm(long double value)
+        {
+            return {(float)value};
+        }
+
+        Length operator ""_millimeters(long double value)
+        {
+            return {(float)value};
+        }
+        Length operator ""_mm(long double value)
+        {
+            return {(float)value};
+        }
+
+        Velocity operator ""_mps(long double value)
+        {
+            return {(float)value};
+        }
+
+        Velocity operator ""_meters_per_second(long double value)
+        {
+            return {(float)value};
+        }
+
+        Velocity operator ""_kmps(long double value)
+        {
+            return {(float)value};
+        }
+    }*/
+
+
+#pragma region Constants
+    static const float Pi           = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679f;
+    static const float RecipSqrt2Pi = 0.3989422804014326779399460599343818684758586311649346576659258296706579258993018385012523339073069364f;
+    static const float GoldenRatio  = 1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911375f;
+#pragma endregion
+
+#pragma region Math Functions
+
+    inline float Radians(float degrees);
+    inline float Degrees(float radians);
+
+
+    struct NumberRange
+    {
+        float LowerBound;
+        float UpperBound;
+    };
+
+
+    float NormalizeToRange(float input, float fromLower, float fromUpper, float toLower, float toUpper);
+    float NormalizeToRange(float input, const NumberRange& from, const NumberRange& to);
+    // auto rotation_normalized = NormalizeToRange(inp, {0, 360}, {-1, 1});
+
+    inline float Lerp(float a, float b, float t);
+    /// Linearly interpolates from a to b, under the modulus mod.
+    /// This function takes evaluates a and b in the range [0, mod] and takes the shorter path to reach from a to b.
+    inline float LerpMod(float a, float b, float mod, float t);
+    /// Computes the lerp factor a and b have to be Lerp()ed to get x.
+    inline float InverseLerp(float a, float b, float x);
+    /// See http://msdn.microsoft.com/en-us/library/bb509665(v=VS.85).aspx
+    inline float Step(float y, float x);
+    /// See http://msdn.microsoft.com/en-us/library/bb509658(v=vs.85).aspx
+    inline float Ramp(float min, float max, float x);
+
+    inline float PingPongMod(float x, float mod);
+
+    inline float Sqrt(float x);
+    inline float FastSqrt(float x);
+    /// Returns 1/Sqrt(x). (The reciprocal of the square root of x)
+    inline float RSqrt(float x);
+
+    inline float FastRSqrt(float x);
+
+
+#pragma endregion
+
+
+    namespace BitTwiddling
+    {
+        /// Parses a string of form "011101010" to a u32
+        u32 BinaryStringToValue(const char* s);
+
+        /// Returns the number of 1's set in the given value.
+        inline int CountBitsSet(u32 value);
+    }
+
+    namespace Interp
+    {
+        inline float SmoothStart(float t);
+    }
+
+    struct Rotation
+    {
+    public:
+        Rotation();
+        Rotation(float value);
+        float valueInRadians;
+        float ValueInRadians() const;
+        float ValueInDegrees() const;
+        Rotation operator+(const Rotation& rhs);
+    };
+
+
+    Rotation operator ""_rad(long double rads);
+
+    Rotation operator ""_radians(long double rads);
+
+    Rotation operator ""_deg(long double rads);
+
+    Rotation operator ""_degrees(long double rads);
+
+}

include/J3ML/LinearAlgebra.h

@@ -1,76 +1,30 @@
+//// Dawsh Linear Algebra Library - Everything you need for 3D math
+/// @file LinearAlgebra.h
+/// @description Includes all LinearAlgebra classes and functions
+/// @author Josh O'Leary, William Tomasine II
+/// @copyright 2024 Redacted Software
+/// @license Unlicense - Public Domain
+/// @revision 1.3
+/// @edited 2024-02-26
+
 #pragma once
-#include <cstdint>
-#include <cmath>
-#include <cstdlib>
-#include <algorithm>
-#include <functional>
-
-
-namespace Math
-{
-    const float Pi = M_PI;
-    inline float Radians(float degrees) { return degrees * (Pi/180.f); }
-    inline float Degrees(float radians) { return radians * (180.f/Pi); }
-
-
-    struct NumberRange
-    {
-        float LowerBound;
-        float UpperBound;
-    };
-
-
-    float NormalizeToRange(float input, float fromLower, float fromUpper, float toLower, float toUpper);
-    float NormalizeToRange(float input, const NumberRange& from, const NumberRange& to);
-    // auto rotation_normalized = NormalizeToRange(inp, {0, 360}, {-1, 1});
-    inline float Lerp(float a, float b, float t);
-
-}
-
-
-// Dawsh Linear Algebra Library - Everything you need for 3D math
-namespace LinearAlgebra {
-    class Vector2; // A type representing a position in a 2-dimensional coordinate space.
-    class Vector3; // A type representing a position in a 3-dimensional coordinate space.
-    class Vector4; // A type representing a position in a 4-dimensional coordinate space.
-    class Angle2D; // Uses x,y components to represent a 2D rotation.
-    class EulerAngle; // Uses pitch,yaw,roll components to represent a 3D orientation.
-    class AxisAngle; //
-    class CoordinateFrame; //
-    class Matrix2x2;
-    class Matrix3x3;
-    class Matrix4x4;
-    class Transform2D;
-    class Transform3D;
-    class Quaternion;
-
-
-    using Position = Vector3;
-}
 
 // TODO: Enforce Style Consistency (Function Names use MicroSoft Case)
-
-// Note: Josh Linear Algebra Types are designed as Immutable Data Types
-// x, y, z, w, etc. values should not and can not be set directly.
-// rather, you just construct a new type and assign it.
-// This might sound ass-backwards for many object types.
-// But mathematically, a vector or matrix is defined by it's size, and values.
-// Changing the value of one axis fundamentally changes the definition of the vector/matrix.
-// So we enforce this conceptually at code level...
-// If you're wondering how it remains performant, it only heap-allocates a tiny space (4*n bytes for vectors) (4*n*m bytes for matrices)
-// Just Trust Me Bro - Josjh
-#define MUTABLE true // Toggle This For: Ugly math, ugly code, and an ugly genital infection!
-
-#if MUTABLE
-#define IMMUTABLE !MUTABLE
-#endif
-
-namespace LinearAlgebra
-{
+// TODO: Implement Templated Linear Algebra
 
 
+// Library Code //
 
+#include "J3ML/LinearAlgebra/Vector2.h"
+#include "J3ML/LinearAlgebra/Vector3.h"
+#include "J3ML/LinearAlgebra/Vector4.h"
+#include "J3ML/LinearAlgebra/Quaternion.h"
+#include "J3ML/LinearAlgebra/AxisAngle.h"
+#include "J3ML/LinearAlgebra/EulerAngle.h"
+#include "J3ML/LinearAlgebra/Matrix2x2.h"
+#include "J3ML/LinearAlgebra/Matrix3x3.h"
+#include "J3ML/LinearAlgebra/Matrix4x4.h"
+#include "J3ML/LinearAlgebra/Transform2D.h"
+#include "J3ML/LinearAlgebra/CoordinateFrame.h"
 
-
-
-}
+using namespace J3ML::LinearAlgebra;

include/J3ML/LinearAlgebra/Angle2D.h

@@ -1,10 +1,22 @@
 #pragma once
 
-#include <J3ML/LinearAlgebra.h>
 
-namespace LinearAlgebra {
+namespace J3ML::LinearAlgebra {
+
     class Angle2D {
     public:
+        float x;
+        float y;
+        Angle2D(Math::Rotation rads);
+        Angle2D(float X, float Y)
+        {
+            x = X;
+            y = Y;
+        }
 
+        bool operator==(const Angle2D& rhs) const {
+            return (this->x==rhs.x && this->y==rhs.y);
+        }
     };
+
 }

include/J3ML/LinearAlgebra/AxisAngle.h

@@ -1,9 +1,11 @@
 #pragma once
 
-#include <J3ML/LinearAlgebra.h>
+#include <J3ML/LinearAlgebra/EulerAngle.h>
+#include <J3ML/LinearAlgebra/Quaternion.h>
+#include <J3ML/LinearAlgebra/AxisAngle.h>
 #include <J3ML/LinearAlgebra/Vector3.h>
 
-namespace LinearAlgebra
+namespace J3ML::LinearAlgebra
 {
 
     /// Transitional datatype, not useful for internal representation of rotation
@@ -13,6 +15,12 @@ namespace LinearAlgebra
         float angle;
     public:
         AxisAngle();
-        AxisAngle(const Vector3& axis, float angle);
+
+        AxisAngle(const Vector3 &axis, float angle);
+
+        EulerAngle ToEulerAngleXYZ() const;
+
+        Quaternion ToQuaternion() const;
+        static AxisAngle FromEulerAngleXYZ(const EulerAngle&);
     };
 }

include/J3ML/LinearAlgebra/Common.h

@@ -0,0 +1,28 @@
+#pragma once
+
+// Forward Declarations for classes that include each other
+namespace J3ML::LinearAlgebra
+{
+    class Vector2; // A type representing a position in a 2-dimensional coordinate space.
+    class Vector3; // A type representing a position in a 3-dimensional coordinate space.
+    class Vector4; // A type representing a position in a 4-dimensional coordinate space.
+    class Angle2D; // Uses x,y components to represent a 2D rotation.
+    class EulerAngle; // Uses pitch,yaw,roll components to represent a 3D orientation.
+    class AxisAngle; //
+    class CoordinateFrame; //
+    class Matrix2x2;
+    class Matrix3x3;
+    class Matrix4x4;
+    class Transform2D;
+    class Transform3D;
+    class Quaternion;
+
+
+    using Position = Vector3;
+}
+
+// Methods required by LinearAlgebra types
+namespace J3ML::LinearAlgebra
+{
+
+}

include/J3ML/LinearAlgebra/CoordinateFrame.h

@@ -1,20 +1,17 @@
 #pragma once
 
-#include <J3ML/LinearAlgebra.h>
 
-namespace LinearAlgebra
+#include <J3ML/LinearAlgebra/Vector3.h>
+
+namespace J3ML::LinearAlgebra
 {
     /// The CFrame is fundamentally 4 vectors (position, forward, right, up vector)
     class CoordinateFrame
     {
-        Vector3 getPosition();
-        Vector3 getLookVector();
-        Vector3 getRightVector();
-        Vector3 getUpVector();
-        AxisAngle GetAxisAngle();
-        EulerAngle GetEulerAngleXYZ();
-        EulerAngle GetWorldAngleYZX();
+    public:
+        Vector3 Position;
+        Vector3 Front;
+        Vector3 Right;
+        Vector3 Up;
     };
-
-
 }

include/J3ML/LinearAlgebra/EulerAngle.h

@@ -1,8 +1,12 @@
 #pragma once
-#include <J3ML/LinearAlgebra.h>
-#include <J3ML/LinearAlgebra/Vector3.h>
 
-namespace LinearAlgebra {
+#include <J3ML/LinearAlgebra/Vector3.h>
+#include <J3ML/LinearAlgebra/Quaternion.h>
+#include <J3ML/LinearAlgebra/AxisAngle.h>
+
+namespace J3ML::LinearAlgebra {
+
+    class AxisAngle;
 
 // Essential Reading:
 // http://www.essentialmath.com/GDC2012/GDC2012_JMV_Rotations.pdf
@@ -11,8 +15,13 @@ public:
     EulerAngle();
     EulerAngle(float pitch, float yaw, float roll);
     EulerAngle(const Vector3& vec) : pitch(vec.x), yaw(vec.y), roll(vec.z) {}
-    static EulerAngle FromRadians(float radians);
-    static EulerAngle FromDegrees(float degrees);
+
+    AxisAngle ToAxisAngle() const;
+
+
+    explicit EulerAngle(const Quaternion& orientation);
+    explicit EulerAngle(const AxisAngle& orientation);
+
     /// TODO: Implement separate upper and lower bounds
     /// Preserves internal value of euler angles, normalizes and clamps the output.
     /// This does not solve gimbal lock!!!

include/J3ML/LinearAlgebra/Matrix.h

@@ -0,0 +1,66 @@
+#pragma once
+
+#include <cstddef>
+#include <cstdlib>
+#include <algorithm>
+#include "Vector.h"
+
+namespace J3ML::LinearAlgebra
+{
+
+
+    template <uint ROWS, uint COLS, typename T>
+    class Matrix
+    {
+        static constexpr uint Diag = std::min(ROWS, COLS);
+
+        using RowVector = Vector<ROWS, T>;
+        using ColVector = Vector<COLS, T>;
+        using DiagVector = Vector<Diag, T>;
+
+        enum { Rows = ROWS };
+        enum { Cols = COLS };
+
+        void AssertRowSize(uint rows)
+        {
+            assert(rows < Rows && "");
+        }
+        void AssertColumnSize(uint cols)
+        {
+            assert(cols < Cols && "");
+        }
+
+        RowVector GetRow(uint index) const;
+        ColVector GetColumn(uint index) const;
+        void SetRow(uint index, RowVector);
+        void SetColumn(uint index, ColVector);
+
+        RowVector &Row(uint index) const;
+        ColVector &Column(uint index) const;
+
+        const T At(uint row, uint col) const
+        {
+            AssertRowSize(row);
+            AssertColumnSize(col);
+
+            return elems[row][col];
+        }
+
+        T &At(uint row, uint col)
+        {
+            AssertRowSize(row);
+            AssertColumnSize(col);
+
+            return elems[row][col];
+        }
+
+        float* ptr();
+        const float* ptr() const;
+
+        float operator[](uint index) const;
+        float& operator[](uint index);
+
+    private:
+        T elems[ROWS][COLS];
+    };
+}

include/J3ML/LinearAlgebra/Matrix2x2.h

@@ -1,9 +1,9 @@
 #pragma once
 
-#include <J3ML/LinearAlgebra.h>
+
 #include <J3ML/LinearAlgebra/Vector2.h>
 
-namespace LinearAlgebra {
+namespace J3ML::LinearAlgebra {
     class Matrix2x2 {
     public:
         enum { Rows = 3 };
@@ -12,9 +12,27 @@ namespace LinearAlgebra {
         static const Matrix2x2 Identity;
         static const Matrix2x2 NaN;
 
+        Matrix2x2() {}
+        Matrix2x2(float val);
+        Matrix2x2(float m00, float m01, float m10, float m11);
+        Matrix2x2(const Vector2& r1, const Vector2& r2);
+        explicit Matrix2x2(const float *data);
+
         Vector2 GetRow(int index) const;
         Vector2 GetColumn(int index) const;
+
+        void SetRow(int i, const Vector2& row);
+        void SetColumn(int i, const Vector2& col);
+        void SetAt(int x, int y, float value);
+
         float At(int x, int y) const;
+        float &At(int x, int y);
+
+        float Determinant() const;
+        Matrix2x2 Inverse() const;
+        Matrix2x2 Transpose() const;
+
+        Vector2 Transform(const Vector2& rhs) const;
 
 
         Vector2 operator * (const Vector2& rhs) const;

include/J3ML/LinearAlgebra/Matrix3x3.h

@@ -1,11 +1,15 @@
 #pragma once
 
-#include <J3ML/LinearAlgebra.h>
+
 #include <J3ML/LinearAlgebra/Vector2.h>
 #include <J3ML/LinearAlgebra/Vector3.h>
 #include <J3ML/LinearAlgebra/Quaternion.h>
 
-namespace LinearAlgebra {
+namespace J3ML::LinearAlgebra {
+
+
+    class Quaternion;
+
     /// A 3-by-3 matrix for linear transformations of 3D geometry.
     /* This can represent any kind of linear transformations of 3D geometry, which include
      * rotation, scale, shear, mirroring, and orthographic projection.
@@ -36,6 +40,8 @@ namespace LinearAlgebra {
         Matrix3x3(float m00, float m01, float m02, float m10, float m11, float m12, float m20, float m21, float m22);
         Matrix3x3(const Vector3& r1, const Vector3& r2, const Vector3& r3);
         explicit Matrix3x3(const Quaternion& orientation);
+        explicit Matrix3x3(const float *data);
+
 
         static Matrix3x3 RotateX(float radians);
         static Matrix3x3 RotateY(float radians);
@@ -43,13 +49,24 @@ namespace LinearAlgebra {
 
         Vector3 GetRow(int index) const;
         Vector3 GetColumn(int index) const;
+
+        float &At(int row, int col);
         float At(int x, int y) const;
 
-        /// Creates a new M3x3 that rotates about the given axis by the given angle
-        static Matrix3x3 RotateAxisAngle(const Vector3& rhs);
+        void SetRotatePart(const Vector3& a, float angle);
 
+        /// Creates a new M3x3 that rotates about the given axis by the given angle
+        static Matrix3x3 RotateAxisAngle(const Vector3& axis, float angleRadians);
+
+        // TODO: Implement
         static Matrix3x3 RotateFromTo(const Vector3& source, const Vector3& direction);
 
+        void SetRow(int i, const Vector3 &vector3);
+        void SetColumn(int i, const Vector3& vector);
+        void SetAt(int x, int y, float value);
+
+        void Orthonormalize(int c0, int c1, int c2);
+
         static Matrix3x3 LookAt(const Vector3& forward, const Vector3& target, const Vector3& localUp, const Vector3& worldUp);
 
         static Matrix3x3 FromQuat(const Quaternion& orientation);
@@ -62,14 +79,14 @@ namespace LinearAlgebra {
         // Transforming a vector v using this matrix computes the vector
         // v' == M * v == R*S*v == (R * (S * v)) which means the scale operation
         // is applied to the vector first, followed by rotation, and finally translation
-        static Matrix3x3 FromRS(const Quaternion& rotate, const Matrix3x3& scale);
-        static Matrix3x3 FromRS(const Matrix3x3 &rotate, const Matrix3x3& scale);
+        static Matrix3x3 FromRS(const Quaternion& rotate, const Vector3& scale);
+        static Matrix3x3 FromRS(const Matrix3x3 &rotate, const Vector3& scale);
 
 
         /// Creates a new transformation matrix that scales by the given factors.
         // This matrix scales with respect to origin.
-        static Matrix3x3 Scale(float sx, float sy, float sz);
-        static Matrix3x3 Scale(const Matrix3x3& scale);
+        static Matrix3x3 FromScale(float sx, float sy, float sz);
+        static Matrix3x3 FromScale(const Vector3& scale);
 
         /// Returns the main diagonal.
         Vector3 Diagonal() const;
@@ -99,13 +116,15 @@ namespace LinearAlgebra {
         Matrix3x3 Transpose() const;
 
         // Transforms the given vectors by this matrix M, i.e. returns M * (x,y,z)
-
         Vector2 Transform(const Vector2& rhs) const;
         Vector3 Transform(const Vector3& rhs) const;
 
 
+        Matrix3x3 ScaleBy(const Vector3& rhs);
+        Vector3 GetScale() const;
+
+        Vector3 operator[](int row) const;
 
-        Vector3 operator[] (float index) const;
         Vector3 operator * (const Vector3& rhs) const;
         Matrix3x3 operator * (const Matrix3x3& rhs) const;
 

include/J3ML/LinearAlgebra/Matrix4x4.h

@@ -1,34 +1,256 @@
 #pragma once
 
-#include <J3ML/LinearAlgebra.h>
+#include <J3ML/LinearAlgebra/Common.h>
+
+#include <J3ML/LinearAlgebra/Matrix3x3.h>
+#include <J3ML/LinearAlgebra/Quaternion.h>
 
 
+#include <J3ML/LinearAlgebra/Vector4.h>
+#include <algorithm>
+
+namespace J3ML::LinearAlgebra {
 
-namespace LinearAlgebra {
     /// A 4-by-4 matrix for affine transformations and perspective projections of 3D geometry.
-/* This matrix can represent the most generic form of transformations for 3D objects,
- * including perspective projections, which a 4-by-3 cannot store,
- * and translations, which a 3-by-3 cannot represent.
- * The elements of this matrix are
- *  m_00, m_01, m_02, m_03
- *  m_10, m_11, m_12, m_13
- *  m_20, m_21, m_22, m_23,
- *  m_30, m_31, m_32, m_33
- *
- *  The element m_yx is the value on the row y and column x.
- *  You can access m_yx using the double-bracket notation m[y][x]
- */
+    /* This matrix can represent the most generic form of transformations for 3D objects,
+     * including perspective projections, which a 4-by-3 cannot store,
+     * and translations, which a 3-by-3 cannot represent.
+     * The elements of this matrix are
+     *  m_00, m_01, m_02, m_03
+     *  m_10, m_11, m_12, m_13
+     *  m_20, m_21, m_22, m_23,
+     *  m_30, m_31, m_32, m_33
+     *
+     *  The element m_yx is the value on the row y and column x.
+     *  You can access m_yx using the double-bracket notation m[y][x]
+     */
     class Matrix4x4 {
     public:
+        // TODO: Implement assertions to ensure matrix bounds are not violated!
+        enum { Rows = 4 };
+        enum { Cols = 4 };
+
+        /// A constant matrix that has zeroes in all its entries
         static const Matrix4x4 Zero;
+        /// A constant matrix that is the identity.
         static const Matrix4x4 Identity;
 
-        Vector3 GetTranslationComponent() const;
-        Matrix3x3 GetRotationComponent() const;
+        /// A compile-time constant float4x4 which has NaN in each element.
+        /// For this constant, each element has the value of quet NaN, or Not-A-Number.
+        /// Never compare a matrix to this value. Due to how IEEE floats work, "nan == nan" returns false!
+        static const Matrix4x4 NaN;
+
+        /// Creates a new float4x4 with uninitialized member values.
+        Matrix4x4() {}
+        Matrix4x4(float val);
+        /// Constructs this float4x4 to represent the same transformation as the given float3x3.
+        /** This function expands the last row and column of this matrix with the elements from the identity matrix. */
+        Matrix4x4(const Matrix3x3&);
+        explicit Matrix4x4(const float* data);
+
+        /// Constructs a new float4x4 by explicitly specifying all the matrix elements.
+        /// The elements are specified in row-major format, i.e. the first row first followed by the second and third row.
+        /// E.g. The element _10 denotes the scalar at second (index 1) row, first (index 0) column.
+        Matrix4x4(float m00, float m01, float m02, float m03,
+                  float m10, float m11, float m12, float m13,
+                  float m20, float m21, float m22, float m23,
+                  float m30, float m31, float m32, float m33);
+        /// Constructs the matrix by explicitly specifying the four column vectors.
+        /** @param col0 The first column. If this matrix represents a change-of-basis transformation, this parameter is the world-space
+            direction of the local X axis.
+            @param col1 The second column. If this matrix represents a change-of-basis transformation, this parameter is the world-space
+            direction of the local Y axis.
+            @param col2 The third column. If this matrix represents a change-of-basis transformation, this parameter is the world-space
+            direction of the local Z axis.
+            @param col3 The fourth column. If this matrix represents a change-of-basis transformation, this parameter is the world-space
+            position of the local space pivot. */
+        Matrix4x4(const Vector4& r1, const Vector4& r2, const Vector4& r3, const Vector4& r4);
+
+        explicit Matrix4x4(const Quaternion& orientation);
+
+        /// Constructs this float4x4 from the given quaternion and translation.
+        /// Logically, the translation occurs after the rotation has been performed.
+        Matrix4x4(const Quaternion& orientation, const Vector3 &translation);
+
+        /// Creates a LookAt matrix from a look-at direction vector.
+        /** A LookAt matrix is a rotation matrix that orients an object to face towards a specified target direction.
+            @param localForward Specifies the forward direction in the local space of the object. This is the direction
+                the model is facing at in its own local/object space, often +X (1,0,0), +Y (0,1,0) or +Z (0,0,1). The
+                vector to pass in here depends on the conventions you or your modeling software is using, and it is best
+                pick one convention for all your objects, and be consistent.
+                This input parameter must be a normalized vector.
+            @param targetDirection Specifies the desired world space direction the object should look at. This function
+                will compute a rotation matrix which will rotate the localForward vector to orient towards this targetDirection
+                vector. This input parameter must be a normalized vector.
+            @param localUp Specifies the up direction in the local space of the object. This is the up direction the model
+                was authored in, often +Y (0,1,0) or +Z (0,0,1). The vector to pass in here depends on the conventions you
+                or your modeling software is using, and it is best to pick one convention for all your objects, and be
+                consistent. This input parameter must be a normalized vector. This vector must be perpendicular to the
+                vector localForward, i.e. localForward.Dot(localUp) == 0.
+            @param worldUp Specifies the global up direction of the scene in world space. Simply rotating one vector to
+                coincide with another (localForward->targetDirection) would cause the up direction of the resulting
+                orientation to drift (e.g. the model could be looking at its target its head slanted sideways). To keep
+                the up direction straight, this function orients the localUp direction of the model to point towards the
+                specified worldUp direction (as closely as possible). The worldUp and targetDirection vectors cannot be
+                collinear, but they do not need to be perpendicular either.
+            @return A matrix that maps the given local space forward direction vector to point towards the given target
+                direction, and the given local up direction towards the given target world up direction. The returned
+                matrix M is orthonormal with a determinant of +1. For the matrix M it holds that
+                M * localForward = targetDirection, and M * localUp lies in the plane spanned by the vectors targetDirection
+                and worldUp.
+            @note The position of (the translation performed by) the resulting matrix will be set to (0,0,0), i.e. the object
+                will be placed to origin. Call SetTranslatePart() on the resulting matrix to set the position of the model.
+            @see RotateFromTo(). */
+        static Matrix4x4 LookAt(const Vector3& localFwd, const Vector3& targetDir, const Vector3& localUp, const Vector3& worldUp);
+
+        /// Returns the translation part.
+        /** The translation part is stored in the fourth column of this matrix.
+            This is equivalent to decomposing this matrix in the form M = T * M', i.e. this translation is applied last,
+            after applying rotation and scale. If this matrix represents a local->world space transformation for an object,
+            then this gives the world space position of the object.
+            @note This function assumes that this matrix does not contain projection (the fourth row of this matrix is [0 0 0 1]). */
+        Vector3 GetTranslatePart() const;
+        /// Returns the top-left 3x3 part of this matrix. This stores the rotation part of this matrix (if this matrix represents a rotation).
+        Matrix3x3 GetRotatePart() const;
+        void SetTranslatePart(float translateX, float translateY, float translateZ);
+        void SetTranslatePart(const Vector3& offset);
+        void SetRotatePart(const Quaternion& q);
+        void Set3x3Part(const Matrix3x3& r);
+
+        void SetRow(int row, const Vector3& rowVector, float m_r3);
+        void SetRow(int row, const Vector4& rowVector);
+        void SetRow(int row, float m_r0, float m_r1, float m_r2, float m_r3);
+
+        Vector4 GetRow(int index) const;
+        Vector4 GetColumn(int index) const;
+        Vector3 GetRow3(int index) const;
+        Vector3 GetColumn3(int index) const;
+
+        Vector3 GetScale() const
+        {
+
+        }
+        Matrix4x4 Scale(const Vector3&);
+
+        float &At(int row, int col);
+        float At(int x, int y) const;
+
+        template <typename T>
+        void Swap(T &a, T &b)
+        {
+            T temp = std::move(a);
+            a = std::move(b);
+            b = std::move(temp);
+        }
+
+
+        void SwapColumns(int col1, int col2);
+
+        /// Swaps two rows.
+        void SwapRows(int row1, int row2);
+        /// Swapsthe xyz-parts of two rows element-by-element
+        void SwapRows3(int row1, int row2);
+
+        void ScaleRow(int row, float scalar);
+        void ScaleRow3(int row, float scalar);
+        void ScaleColumn(int col, float scalar);
+        void ScaleColumn3(int col, float scalar);
+        /// Algorithm from Eric Lengyel's Mathematics for 3D Game Programming & Computer Graphics, 2nd Ed.
+        void Pivot();
+
+        /// Tests if this matrix does not contain any NaNs or infs.
+        /** @return Returns true if the entries of this float4x4 are all finite, and do not contain NaN or infs. */
+        bool IsFinite() const;
+
+        /// Tests if this matrix has an inverse.
+        /** @return Returns true if this matrix can be inverted, up to the given epsilon. */
+        bool IsInvertible(float epsilon = 1e-3f) const;
+
+        Vector4 Diagonal() const;
+        Vector3 Diagonal3() const;
+        /// Returns the local +X axis in world space.
+        /// This is the same as transforming the vector (1,0,0) by this matrix.
+        Vector3 WorldX() const;
+        /// Returns the local +Y axis in world space.
+        /// This is the same as transforming the vector (0,1,0) by this matrix.
+        Vector3 WorldY() const;
+        /// Returns the local +Z axis in world space.
+        /// This is the same as transforming the vector (0,0,1) by this matrix.
+        Vector3 WorldZ() const;
+
+        /// Accesses this structure as a float array.
+        /// @return A pointer to the upper-left element. The data is contiguous in memory.
+        /// ptr[0] gives the element [0][0], ptr[1] is [0][1], ptr[2] is [0][2].
+        /// ptr[4] == [1][0], ptr[5] == [1][1], ..., and finally, ptr[15] == [3][3].
+        float *ptr() { return &elems[0][0]; }
+        const float *ptr() const { return &elems[0][0]; }
+
+        float Determinant3x3() const;
+        /// Computes the determinant of this matrix.
+        // If the determinant is nonzero, this matrix is invertible.
+        float Determinant() const;
+
+        #define SKIPNUM(val, skip) (val >= skip ? (val+1) : val)
+
+        float Minor(int i, int j) const;
+
+        Matrix4x4 Inverse() const;
+
+        Matrix4x4 Transpose() const;
+
+        Vector2 Transform(float tx, float ty) const;
+        Vector2 Transform(const Vector2& rhs) const;
+
+
+        Vector3 Transform(float tx, float ty, float tz) const;
+        Vector3 Transform(const Vector3& rhs) const;
+
+        Vector4 Transform(float tx, float ty, float tz, float tw) const;
+        Vector4 Transform(const Vector4& rhs) const;
+
+
+        Matrix4x4 Translate(const Vector3& rhs) const;
+        static Matrix4x4 FromTranslation(const Vector3& rhs);
+
+
+        static Matrix4x4 D3DOrthoProjLH(float nearPlane, float farPlane, float hViewportSize, float vViewportSize);
+        static Matrix4x4 D3DOrthoProjRH(float nearPlane, float farPlane, float hViewportSize, float vViewportSize);
+        static Matrix4x4 D3DPerspProjLH(float nearPlane, float farPlane, float hViewportSize, float vViewportSize);
+        static Matrix4x4 D3DPerspProjRH(float nearPlane, float farPlane, float hViewportSize, float vViewportSize);
+
+        static Matrix4x4 OpenGLOrthoProjLH(float n, float f, float h, float v);
+        static Matrix4x4 OpenGLOrthoProjRH(float n, float f, float h, float v);
+        static Matrix4x4 OpenGLPerspProjLH(float n, float f, float h, float v);
+        static Matrix4x4 OpenGLPerspProjRH(float n, float f, float h, float v);
+
+        Vector4 operator[](int row);
+
+        Matrix4x4 operator-() const;
+        Matrix4x4 operator +(const Matrix4x4& rhs) const;
+        Matrix4x4 operator - (const Matrix4x4& rhs) const;
+
+        Matrix4x4 operator *(float scalar) const;
+        Matrix4x4 operator /(float scalar) const;
+
+
+
+        Vector2 operator * (const Vector2& rhs) const;
+        Vector3 operator * (const Vector3& rhs) const;
+        Vector4 operator * (const Vector4& rhs) const;
+
+        Matrix4x4 operator * (const Matrix3x3 &rhs) const;
+
+        Matrix4x4 operator +() const;
+
+        Matrix4x4 operator * (const Matrix4x4& rhs) const;
+
+        Matrix4x4 &operator = (const Matrix3x3& rhs);
+        Matrix4x4 &operator = (const Quaternion& rhs);
+        Matrix4x4 &operator = (const Matrix4x4& rhs) = default;
 
-        Vector4 GetRow() const;
-        Vector4 GetColumn() const;
     protected:
         float elems[4][4];
+
+
     };
 }

include/J3ML/LinearAlgebra/Quaternion.h

@@ -1,44 +1,70 @@
 #pragma once
 
-#include <J3ML/LinearAlgebra.h>
 
+
+
+#include <J3ML/LinearAlgebra/Matrix3x3.h>
+#include <J3ML/LinearAlgebra/Matrix4x4.h>
 #include <J3ML/LinearAlgebra/Vector4.h>
 #include <J3ML/LinearAlgebra/AxisAngle.h>
-#include <J3ML/LinearAlgebra/Matrix3x3.h>
+//#include <J3ML/LinearAlgebra/AxisAngle.h>
+#include <cmath>
 
-namespace LinearAlgebra
+
+
+namespace J3ML::LinearAlgebra
 {
-    class Quaternion : public Vector4
-    {
+
+    class Matrix3x3;
+
+    class Quaternion : public Vector4 {
     public:
         Quaternion();
-        Quaternion(const Quaternion& rhs) = default;
-        explicit Quaternion(const Matrix3x3& rotationMtrx);
-        explicit Quaternion(const Matrix4x4& rotationMtrx);
+
+        Quaternion(const Quaternion &rhs) = default;
+
+        explicit Quaternion(const Matrix3x3 &rotationMtrx);
+
+        explicit Quaternion(const Matrix4x4 &rotationMtrx);
+
         // @note The input data is not normalized after construction, this has to be done manually.
         Quaternion(float X, float Y, float Z, float W);
 
         // Constructs this quaternion by specifying a rotation axis and the amount of rotation to be performed about that axis
         // @param rotationAxis The normalized rotation axis to rotate about. If using Vector4 version of the constructor, the w component of this vector must be 0.
-        Quaternion(const Vector3& rotationAxis, float rotationAngleBetween) { SetFromAxisAngle(rotationAxis, rotationAngleBetween); }
-        Quaternion(const Vector4& rotationAxis, float rotationAngleBetween) { SetFromAxisAngle(rotationAxis, rotationAngleBetween); }
+        Quaternion(const Vector3 &rotationAxis, float rotationAngleBetween);
+
+        Quaternion(const Vector4 &rotationAxis, float rotationAngleBetween);
         //void Inverse();
 
         explicit Quaternion(Vector4 vector4);
 
         void SetFromAxisAngle(const Vector3 &vector3, float between);
+
         void SetFromAxisAngle(const Vector4 &vector4, float between);
 
         Quaternion Inverse() const;
+
         Quaternion Conjugate() const;
 
         //void Normalize();
         Vector3 GetWorldX() const;
+
         Vector3 GetWorldY() const;
+
         Vector3 GetWorldZ() const;
 
+        Vector3 GetAxis() const;
+
+        float GetAngle() const;
+
+
         Matrix3x3 ToMatrix3x3() const;
 
+        Matrix4x4 ToMatrix4x4() const;
+
+        Matrix4x4 ToMatrix4x4(const Vector3 &translation) const;
+
         Vector3 Transform(const Vector3& vec) const;
         Vector3 Transform(float X, float Y, float Z) const;
         // Note: We only transform the x,y,z components of 4D vectors, w is left untouched
@@ -57,7 +83,6 @@ namespace LinearAlgebra
         // TODO: Document (But do not override!) certain math functions that are the same for Vec4
         // TODO: Double Check which operations need to be overriden for correct behavior!
 
-
         // Multiplies two quaternions together.
         // The product q1 * q2 returns a quaternion that concatenates the two orientation rotations.
         // The rotation q2 is applied first before q1.
@@ -71,12 +96,12 @@ namespace LinearAlgebra
 
         // Divides a quaternion by another. Divison "a / b" results in a quaternion that rotates the orientation b to coincide with orientation of
         Quaternion operator / (const Quaternion& rhs) const;
-        Quaternion operator +(const Quaternion& rhs) const;
-        Quaternion operator +() const;
-        Quaternion operator -() const;
+        Quaternion operator + (const Quaternion& rhs) const;
+        Quaternion operator + () const;
+        Quaternion operator - () const;
         float Dot(const Quaternion &quaternion) const;
 
-        float Angle() const;
+        float Angle() const { return acos(w) * 2.f;}
 
         float AngleBetween(const Quaternion& target) const;
 

include/J3ML/LinearAlgebra/Transform2D.h

@@ -1,19 +1,40 @@
 #pragma once
 
-#include <J3ML/LinearAlgebra.h>
+
 #include <J3ML/LinearAlgebra/Matrix3x3.h>
 
-namespace LinearAlgebra {
+namespace J3ML::LinearAlgebra {
     class Transform2D {
     protected:
         Matrix3x3 transformation;
     public:
+
+        const static Transform2D Identity;
+        const static Transform2D FlipX;
+        const static Transform2D FlipY;
+
+        Transform2D(float rotation, const Vector2& pos);
+        Transform2D(float px, float py, float sx, float sy, float ox, float oy, float kx, float ky, float rotation)
+        {
+            transformation = Matrix3x3(px, py, rotation, sx, sy, ox, oy, kx, ky);
+        }
+        Transform2D(const Vector2& pos, const Vector2& scale, const Vector2& origin, const Vector2& skew, float rotation);
+        Transform2D(const Matrix3x3& transform);
         Transform2D Translate(const Vector2& offset) const;
         Transform2D Translate(float x, float y) const;
-        Transform2D Scale(float scale); // Perform Uniform Scale
-        Transform2D Scale(float x, float y); // Perform Nonunform Scale
+        Transform2D Scale(float scale);           // Perform Uniform Scale
+        Transform2D Scale(float x, float y);      // Perform Nonunform Scale
         Transform2D Scale(const Vector2& scales); // Perform Nonuniform Scale
         Transform2D Rotate();
+        Vector2 Transform(const Vector2& input) const;
+        Transform2D Inverse() const;
+        Transform2D AffineInverse() const;
+        float Determinant() const;
+        Vector2 GetOrigin() const;
+        float GetRotation() const;
+        Vector2 GetScale() const;
+        float GetSkew() const;
+        Transform2D OrthoNormalize();
     };
 }
 

include/J3ML/LinearAlgebra/Vector.h

@@ -0,0 +1,15 @@
+#pragma once
+
+
+#include <cstdlib>
+
+namespace J3ML::LinearAlgebra
+{
+    template <uint DIMS, typename T>
+    class Vector {
+    public:
+        enum { Dimensions = DIMS};
+        T elems[DIMS];
+    };
+
+}

include/J3ML/LinearAlgebra/Vector2.h

@@ -1,15 +1,26 @@
+#pragma clang diagnostic push
+#pragma ide diagnostic ignored "modernize-use-nodiscard"
 #pragma once
-#include <J3ML/LinearAlgebra.h>
+#include <J3ML/J3ML.h>
 #include <cstddef>
 
-namespace LinearAlgebra {
-    // A 2D (x, y) ordered pair.
+namespace J3ML::LinearAlgebra {
+    using namespace J3ML;
+
+    /// A 2D (x, y) ordered pair.
     class Vector2 {
     public:
-        // Default Constructor - Initializes values to zero
+
+        enum {Dimensions = 2};
+
+        /// Default Constructor - Initializes values to zero
         Vector2();
-        // Constructs a new Vector2 with the value (X, Y)
+        /// Constructs a new Vector2 with the value (X, Y)
         Vector2(float X, float Y);
+        /// Constructs this float2 from a C array, to the value (data[0], data[1]).
+        explicit Vector2(const float* data);
+        // Constructs a new Vector2 with the value {scalar, scalar}
+        explicit Vector2(float scalar);
         Vector2(const Vector2& rhs);   // Copy Constructor
         //Vector2(Vector2&&) = default;   // Move Constructor
 
@@ -19,19 +30,43 @@ namespace LinearAlgebra {
         static const Vector2 Down;
         static const Vector2 Right;
         static const Vector2 NaN;
+        static const Vector2 Infinity;
 
         float GetX() const;
         float GetY() const;
         void SetX(float newX);
         void SetY(float newY);
 
+        /// Casts this float2 to a C array.
+        /** This function does not allocate new memory or make a copy of this float2. This function simply
+		returns a C pointer view to this data structure. Use ptr()[0] to access the x component of this float2
+		and ptr()[1] to access the y component.
+		@note Since the returned pointer points to this class, do not dereference the pointer after this
+			float2 has been deleted. You should never store a copy of the returned pointer.
+		@note This function is provided for compatibility with other APIs which require raw C pointer access
+			to vectors. Avoid using this function in general, and instead always use the operator []
+			or the At() function to access the elements of this vector by index.
+		@return A pointer to the first float element of this class. The data is contiguous in memory.
+		@see operator [](), At(). */
+        float* ptr();
+        const float *ptr() const;
+
+        float operator[](std::size_t index) const;
+        float &operator[](std::size_t index);
+
+        const float At(std::size_t index) const;
+
+        float &At(std::size_t index);
+
+        Vector2 Abs() const;
+
         bool IsWithinMarginOfError(const Vector2& rhs, float margin=0.001f) const;
 
         bool IsNormalized(float epsilonSq = 1e-5f) const;
         bool IsZero(float epsilonSq = 1e-6f) const;
         bool IsPerpendicular(const Vector2& other, float epsilonSq=1e-5f) const;
 
-        float operator[](std::size_t index);
+
         bool operator == (const Vector2& rhs) const;
         bool operator != (const Vector2& rhs) const;
 
@@ -44,75 +79,98 @@ namespace LinearAlgebra {
         Vector2 Clamp(const Vector2& min, const Vector2& max) const;
         static Vector2 Clamp(const Vector2& min, const Vector2& middle, const Vector2& max);
 
-        // Returns the magnitude between the two vectors.
+        /// Returns the magnitude between the two vectors.
         float Distance(const Vector2& to) const;
         static float Distance(const Vector2& from, const Vector2& to);
 
+        float DistanceSq(const Vector2& to) const;
+        static float DistanceSq(const Vector2& from, const Vector2& to);
+
+        float MinElement() const;
+
+        float MaxElement() const;
+
         float Length() const;
         static float Length(const Vector2& of);
 
         float LengthSquared() const;
         static float LengthSquared(const Vector2& of);
 
-        // Returns the length of the vector, which is sqrt(x^2 + y^2)
+        /// Returns the length of the vector, which is sqrt(x^2 + y^2)
         float Magnitude() const;
         static float Magnitude(const Vector2& of);
 
-        // Returns a float value equal to the magnitudes of the two vectors multiplied together and then multiplied by the cosine of the angle between them.
-        // For normalized vectors, dot returns 1 if they point in exactly the same direction,
-        // -1 if they point in completely opposite directions, and 0 if the vectors are perpendicular.
+
+        bool IsFinite() const;
+        static bool IsFinite(const Vector2& v);
+
+        /// Returns a float value equal to the magnitudes of the two vectors multiplied together and then multiplied by the cosine of the angle between them.
+        /// For normalized vectors, dot returns 1 if they point in exactly the same direction,
+        /// -1 if they point in completely opposite directions, and 0 if the vectors are perpendicular.
         float Dot(const Vector2& rhs) const;
         static float Dot(const Vector2& lhs, const Vector2& rhs);
 
-        // Projects one vector onto another and returns the result. (IDK)
+        /// Projects one vector onto another and returns the result. (IDK)
         Vector2 Project(const Vector2& rhs) const;
-        // @see Project
+        /// @see Project
         static Vector2 Project(const Vector2& lhs, const Vector2& rhs);
 
-        // Returns a copy of this vector, resized to have a magnitude of 1, while preserving "direction"
+        /// Returns a copy of this vector, resized to have a magnitude of 1, while preserving "direction"
         Vector2 Normalize() const;
         static Vector2 Normalize(const Vector2& of);
 
-        // Linearly interpolates between two points.
-        // Interpolates between the points and b by the interpolant t.
-        // The parameter is (TODO: SHOULD BE!) clamped to the range[0, 1].
-        // This is most commonly used to find a point some fraction of the wy along a line between two endpoints (eg. to move an object gradually between those points).
+        /// Linearly interpolates between two points.
+        /// Interpolates between the points and b by the interpolant t.
+        /// The parameter is (TODO: SHOULD BE!) clamped to the range[0, 1].
+        /// This is most commonly used to find a point some fraction of the wy along a line between two endpoints (eg. to move an object gradually between those points).
         Vector2 Lerp(const Vector2& rhs, float alpha) const;
-        // @see Lerp
+        /// @see Lerp
         static Vector2 Lerp(const Vector2& lhs, const Vector2& rhs, float alpha);
-        // Note: Input vectors MUST be normalized first!
+        /// Note: Input vectors MUST be normalized first!
         float AngleBetween(const Vector2& rhs) const;
         static float AngleBetween(const Vector2& lhs, const Vector2& rhs);
 
-        // Adds two vectors.
+        /// Adds two vectors.
         Vector2 operator +(const Vector2& rhs) const;
         Vector2 Add(const Vector2& rhs) const;
         static Vector2 Add(const Vector2& lhs, const Vector2& rhs);
 
-        // Subtracts two vectors.
+        /// Subtracts two vectors.
         Vector2 operator -(const Vector2& rhs) const;
         Vector2 Sub(const Vector2& rhs) const;
         static Vector2 Sub(const Vector2& lhs, const Vector2& rhs);
 
-        // Multiplies this vector by a scalar value.
+        /// Multiplies this vector by a scalar value.
         Vector2 operator *(float rhs) const;
         Vector2 Mul(float scalar) const;
         static Vector2 Mul(const Vector2& lhs, float rhs);
 
-        // Divides this vector by a scalar.
+        /// Multiplies this vector by a vector, element-wise
+        /// @note Mathematically, the multiplication of two vectors is not defined in linear space structures,
+        ///	 but this function is provided here for syntactical convenience.
+        Vector2 operator *(const Vector2& rhs) const
+        {
+
+        }
+        Vector2 Mul(const Vector2& v) const;
+
+        /// Divides this vector by a scalar.
         Vector2 operator /(float rhs) const;
         Vector2 Div(float scalar) const;
         static Vector2 Div(const Vector2& lhs, float rhs);
 
-        // Unary operator +
+        /// Divides this vector by a vector, element-wise
+        /// @note Mathematically, the multiplication of two vectors is not defined in linear space structures,
+        /// but this function is provided here for syntactical convenience
+        Vector2 Div(const Vector2& v) const;
+
+        /// Unary operator +
         Vector2 operator +() const; // TODO: Implement
         Vector2 operator -() const;
-        // Assigns a vector to another
-
-
-
-        Vector2& operator+=(const Vector2& rhs); // Adds a vector to this vector, in-place.
-        Vector2& operator-=(const Vector2& rhs); // Subtracts a vector from this vector, in-place
+        /// Assigns a vector to another
+        Vector2 &operator =(const Vector2 &rhs);
+        Vector2& operator+=(const Vector2& rhs);
+        Vector2& operator-=(const Vector2& rhs);
         Vector2& operator*=(float scalar);
         Vector2& operator/=(float scalar);
 
@@ -121,4 +179,10 @@ namespace LinearAlgebra {
         float y = 0;
 
     };
-}
+
+    static Vector2 operator*(float lhs, const Vector2 &rhs)
+    {
+        return rhs * lhs;
+    }
+}
+#pragma clang diagnostic pop

include/J3ML/LinearAlgebra/Vector3.h

@@ -1,24 +1,26 @@
 #pragma once
 
+#include <J3ML/LinearAlgebra/Vector2.h>
 #include <J3ML/LinearAlgebra/Vector3.h>
 #include <cstddef>
 #include <cstdlib>
+#include <J3ML/LinearAlgebra/Angle2D.h>
 
-
-namespace LinearAlgebra {
+namespace J3ML::LinearAlgebra {
 
 // A 3D (x, y, z) ordered pair.
 class Vector3 {
 public:
 
+    enum {Dimensions = 3};
+
     // Default Constructor - Initializes to zero
     Vector3();
     // Constructs a new Vector3 with the value (X, Y, Z)
     Vector3(float X, float Y, float Z);
     Vector3(const Vector3& rhs); // Copy Constructor
     Vector3(Vector3&&) = default; // Move Constructor
-    Vector3& operator=(const Vector3& rhs);
-
+    explicit Vector3(const float* data);
 
     static const Vector3 Zero;
     static const Vector3 Up;
@@ -28,6 +30,24 @@ public:
     static const Vector3 Forward;
     static const Vector3 Backward;
     static const Vector3 NaN;
+    static const Vector3 Infinity;
+    static const Vector3 NegativeInfinity;
+
+    float* ptr();
+
+    static void Orthonormalize(Vector3& a, Vector3& b);
+
+    Vector3 Abs() const;
+
+
+    /// Returns the DirectionVector for a given angle.
+    static Vector3 Direction(const Vector3 &rhs) ;
+
+    static void Orthonormalize(Vector3& a, Vector3& b, Vector3& c);
+
+    bool AreOrthonormal(const Vector3& a, const Vector3& b, float epsilon);
+
+    Vector3 ProjectToNorm(const Vector3& direction) const;
 
     float GetX() const;
     float GetY() const;
@@ -42,9 +62,14 @@ public:
     bool IsPerpendicular(const Vector3& other, float epsilonSq=1e-5f) const;
 
     float operator[](std::size_t index) const;
+    float &operator[](std::size_t index);
     bool operator == (const Vector3& rhs) const;
     bool operator != (const Vector3& rhs) const;
 
+    bool IsFinite() const;
+    float MinElement() const;
+    static float MinElement(const Vector3& of);
+
     Vector3 Min(const Vector3& min) const;
     static Vector3 Min(const Vector3& lhs, const Vector3& rhs);
 
@@ -54,80 +79,102 @@ public:
     Vector3 Clamp(const Vector3& min, const Vector3& max) const;
     static Vector3 Clamp(const Vector3& min, const Vector3& input, const Vector3& max);
 
-    // Returns the magnitude between the two vectors.
+    /// Returns the magnitude between the two vectors.
     float Distance(const Vector3& to) const;
     static float Distance(const Vector3& from, const Vector3& to);
 
+    float DistanceSquared(const Vector3& to) const;
+    static float DistanceSquared(const Vector3& from, const Vector3& to);
+
     float Length() const;
     static float Length(const Vector3& of);
 
     float LengthSquared() const;
     static float LengthSquared(const Vector3& of);
 
-    // Returns the length of the vector, which is sqrt(x^2 + y^2 + z^2)
+    /// Returns the length of the vector, which is sqrt(x^2 + y^2 + z^2)
     float Magnitude() const;
     static float Magnitude(const Vector3& of);
 
-    // Returns a float value equal to the magnitudes of the two vectors multiplied together and then multiplied by the cosine of the angle between them.
-    // For normalized vectors, dot returns 1 if they point in exactly the same direction,
-    // -1 if they point in completely opposite directions, and 0 if the vectors are perpendicular.
+    /// Returns a float value equal to the magnitudes of the two vectors multiplied together and then multiplied by the cosine of the angle between them.
+    /// For normalized vectors, dot returns 1 if they point in exactly the same direction,
+    /// -1 if they point in completely opposite directions, and 0 if the vectors are perpendicular.
     float Dot(const Vector3& rhs) const;
     static float Dot(const Vector3& lhs, const Vector3& rhs);
 
-    // Projects one vector onto another and returns the result. (IDK)
+    /// Projects one vector onto another and returns the result. (IDK)
     Vector3 Project(const Vector3& rhs) const;
     static Vector3 Project(const Vector3& lhs, const Vector3& rhs);
 
-    // The cross product of two vectors results in a third vector which is perpendicular to the two input vectors.
-    // The result's magnitude is equal to the magnitudes of the two inputs multiplied together and then multiplied by the sine of the angle between the inputs.
+    /// The cross product of two vectors results in a third vector which is perpendicular to the two input vectors.
+    /// The result's magnitude is equal to the magnitudes of the two inputs multiplied together and then multiplied by the sine of the angle between the inputs.
     Vector3 Cross(const Vector3& rhs) const;
     static Vector3 Cross(const Vector3& lhs, const Vector3& rhs);
 
-    // Returns a copy of this vector, resized to have a magnitude of 1, while preserving "direction"
+    /// Returns a copy of this vector, resized to have a magnitude of 1, while preserving "direction"
     Vector3 Normalize() const;
     static Vector3 Normalize(const Vector3& targ);
 
-    // Linearly interpolates between two points.
-    // Interpolates between the points and b by the interpolant t.
-    // The parameter is (TODO: SHOULD BE!) clamped to the range[0, 1].
-    // This is most commonly used to find a point some fraction of the wy along a line between two endpoints (eg. to move an object gradually between those points).
+    /// Linearly interpolates between two points.
+    /// Interpolates between the points and b by the interpolant t.
+    /// The parameter is (TODO: SHOULD BE!) clamped to the range[0, 1].
+    /// This is most commonly used to find a point some fraction of the wy along a line between two endpoints (eg. to move an object gradually between those points).
     Vector3 Lerp(const Vector3& goal, float alpha) const;
     static Vector3 Lerp(const Vector3& lhs, const Vector3& rhs, float alpha);
 
 
-    float AngleBetween(const Vector3& rhs) const; // TODO: 3D Angle representation?
-    static float AngleBetween(const Vector3& lhs, const Vector3& rhs); // TODO: 3D Angle representation?
+    Angle2D AngleBetween(const Vector3& rhs) const;
+    static Angle2D AngleBetween(const Vector3& lhs, const Vector3& rhs);
 
     // Adds two vectors
     Vector3 operator+(const Vector3& rhs) const;
     Vector3 Add(const Vector3& rhs) const;
     static Vector3 Add(const Vector3& lhs, const Vector3& rhs);
 
-    // Subtracts two vectors
+    /// Subtracts two vectors
     Vector3 operator-(const Vector3& rhs) const;
     Vector3 Sub(const Vector3& rhs) const;
     static Vector3 Sub(const Vector3& lhs, const Vector3& rhs);
 
-    // Multiplies this vector by a scalar value
+    /// Multiplies this vector by a scalar value
     Vector3 operator*(float rhs) const;
     Vector3 Mul(float scalar) const;
     static Vector3 Mul(const Vector3& lhs, float rhs);
 
-    // Divides this vector by a scalar
+    /// Multiplies this vector by a vector, element-wise
+    /// @note Mathematically, the multiplication of two vectors is not defined in linear space structures,
+    ///	 but this function is provided here for syntactical convenience.
+    Vector3 Mul(const Vector3& rhs) const;
+
+    /// Divides this vector by a scalar
     Vector3 operator/(float rhs) const;
     Vector3 Div(float scalar) const;
     static Vector3 Div(const Vector3& lhs, float rhs);
 
-    // Unary + operator
+
+    /// Divides this vector by a vector, element-wise
+    /// @note Mathematically, the multiplication of two vectors is not defined in linear space structures,
+    /// but this function is provided here for syntactical convenience
+    Vector3 Div(const Vector3& v) const;
+
+    /// Unary + operator
     Vector3 operator+() const; // TODO: Implement
-    // Unary - operator (Negation)
+    /// Unary - operator (Negation)
     Vector3 operator-() const;
 
-
+    Vector3 &operator =(const Vector3& rhs);
+    Vector3& operator+=(const Vector3& rhs);
+    Vector3& operator-=(const Vector3& rhs);
+    Vector3& operator*=(float scalar);
+    Vector3& operator/=(float scalar);
 public:
      float x = 0;
      float y = 0;
      float z = 0;
-
 };
+
+    static Vector3 operator*(float lhs, const Vector3& rhs)
+    {
+        return rhs * lhs;
+    }
 }

include/J3ML/LinearAlgebra/Vector4.h

@@ -1,9 +1,9 @@
 #pragma once
 
-#include <J3ML/LinearAlgebra.h>
 
+#include <J3ML/LinearAlgebra/Vector3.h>
 
-namespace LinearAlgebra {
+namespace J3ML::LinearAlgebra {
     class Vector4 {
     public:
         // Default Constructor
@@ -16,6 +16,11 @@ namespace LinearAlgebra {
         Vector4(Vector4&& move) = default;
         Vector4& operator=(const Vector4& rhs);
 
+        float* ptr()
+        {
+            return &x;
+        }
+
         float GetX() const;
         float GetY() const;
         float GetZ() const;
@@ -81,6 +86,8 @@ namespace LinearAlgebra {
 
         Vector4 operator+() const; // Unary + Operator
         Vector4 operator-() const; // Unary - Operator (Negation)
+
+
     public:
 #if MUTABLE
         float x;

include/J3ML/Units.h

@@ -0,0 +1,19 @@
+#pragma once
+
+namespace J3ML::Units
+{
+
+    template <typename T>
+    class Rotation
+    {
+        T GetDegrees() const;
+        T GetRadians() const;
+        void SetDegrees(T val);
+        void SetRadians(T val);
+
+    };
+
+    using Rotationf = Rotation<float>;
+    using Rotationd = Rotation<double>;
+
+}

main.cpp

@@ -1,5 +1,6 @@
 #include <iostream>
-
+#include <J3ML/Geometry.h>
+#include <J3ML/J3ML.h>
 
 int main(int argc, char** argv)
 {

src/J3ML/Algorithm/RNG.cpp

@@ -0,0 +1,154 @@
+#include <J3ML/Algorithm/RNG.h>
+#include <stdexcept>
+#include <cassert>
+
+
+namespace J3ML::Algorithm {
+    void RNG::Seed(u32 seed, u32 multiplier, u32 increment, u32 modulus) {
+        // If we have a pure multiplicative RNG, then can't have 0 starting seed, since that would generate a stream of all zeroes
+        if (seed == 0 && increment == 0) seed = 1;
+
+        if (increment == 0 && (multiplier % modulus == 0 || modulus % multiplier == 0 ))
+            throw std::runtime_error("Multiplier %u and modulus %u are not compatible since one is a multiple of the other and the increment == 0!");
+
+        // TODO: assert(multiplier != 0);
+        // TODO: assert(modulus > 1);
+
+        this->lastNumber = seed;
+        this->multiplier = multiplier;
+        this->increment = increment;
+        this->modulus = modulus;
+    }
+
+    u32 RNG::IntFast()
+    {
+        assert(increment == 0);
+        assert(multiplier % 2 == 1 && "Multiplier should be odd for RNG::IntFast(), since modulus==2^32 is even!");
+        // The configurable modulus and increment are not used by this function.
+        u32 mul = lastNumber * multiplier;
+        // Whenever we overflow, flip by one to avoud even multiplier always producing even results
+        // since modulus is even.
+        lastNumber = mul + (mul <= lastNumber?1:0);
+        // We don't use an adder in IntFast(), so must never degenerate to zero
+        assert(lastNumber != 0);
+        return lastNumber;
+    }
+
+    u32 RNG::Int()
+    {
+        assert(modulus != 0);
+        /// TODO: Convert to using Shrage's method for approximate factorization (Numerical Recipes in C)
+
+        // Currently we cast everything to 65-bit to avoid overflow, which is quite dumb.
+
+        // Creates the new random number
+        u64 newNum  = ((u64)lastNumber * (u64)multiplier + (u64)increment % (u64)modulus);
+
+        // TODO: use this on console platforms to rely on smaller sequences.
+        // u32 m = lastNumber * multiplier;
+        // u32 i = m + increment;
+        // u32 f = i & 0x7FFFFFFF;
+        // u32 m = (lastNumber * 214013 + 2531011) & 0x7FFFFFFF;
+        // unsigned __int64 newNum = (lastNumber * multiplier + increment) & 0x7FFFFFFF;
+        assert( ((u32)newNum!=0 || increment != 0) && "RNG degenerated to producing a stream of zeroes!");
+        lastNumber = (u32)newNum;
+        return lastNumber;
+    }
+
+    int RNG::Int(int a, int b) {
+        assert(a <= b && "Error in range!");
+
+        int num = a + (int)(Float() * (b-a+1));
+        // TODO: Some bug here - the result is not necessarily in the proper range.
+        if (num < a) num = a;
+        if (num > b) num = b;
+        return num;
+    }
+
+    /// Jesus-Fuck ~ Josh
+    /// As per C99, union-reinterpret should now be safe: http://stackoverflow.com/questions/8511676/portable-data-reinterpretation
+    union FloatIntReinterpret
+    {
+        float f;
+        u32 i;
+    };
+
+    template <typename To, typename From>
+    union ReinterpretOp {
+        To to;
+        From from;
+    };
+
+    template <typename To, typename From>
+    To ReinterpretAs(From input)
+    {
+        ReinterpretOp<To, From> fi {};
+        fi.to = input;
+        return fi.from;
+    }
+
+    float RNG::Float() {
+        u32 i = ((u32)Int() & 0x007FFFFF /* random mantissa */) | 0x3F800000 /* fixed exponent */;
+        auto f = ReinterpretAs<float, u32>(i); // f is now in range [1, 2[
+        f -= 1.f; // Map to range [0, 1[
+        assert(f >= 0.f);
+        assert(f < 1.f);
+        return f;
+    }
+
+
+    float RNG::Float01Incl() {
+        for (int i = 0; i < 100; ++i) {
+            u32 val = (u32)Int() & 0x00FFFFFF;
+            if (val > 0x800000)
+                continue;
+            else if (val = 0x800000)
+                return 1.f;
+            else {
+                val |= 0x3F800000;
+                float f = ReinterpretAs<float, u32>(val) - 1.f;
+                assert(f >= 0.f);
+                assert(f <= 1.f);
+                return f;
+            }
+        }
+        return Float();
+    }
+
+    float RNG::FloatNeg1_1() {
+        u32 i = (u32) Int();
+        u32 one = ((i & 0x00800000) << 8) /* random sign bit */ | 0x3F800000; /* fixed exponent */
+        i = one | (i & 0x007FFFFF); // Random mantissa
+        float f = ReinterpretAs<float, u32>(i); // f is now in range ]-2, -1[ union [1, 2].
+        float fone = ReinterpretAs<float, u32>(one); // +/- 1, of same sign as f.
+        f -= fone;
+        assert(f > -1.f);
+        assert(f < 1.f);
+        return f;
+    }
+
+    float RNG::Float(float a, float b) {
+        assert(a <= b && "");
+        if (a == b)
+            return a;
+
+        for (int i = 0; i < 10; ++i)
+        {
+            float f = a + Float() * (b - a);
+            if (f != b) {
+                assert(a <= f);
+                assert(f < b || a == b);
+                return f;
+            }
+        }
+        return a;
+    }
+
+    float RNG::FloatIncl(float a, float b) {
+        assert(a <= b && "RNG::Float(a, b): Error in range: b < a!");
+        float f = a + Float() * (b - a);
+        assert( a <= f);
+        assert(f <= b);
+        return f;
+    }
+}

src/J3ML/Geometry/AABB.cpp

@@ -0,0 +1,408 @@
+#include <J3ML/Geometry/AABB.h>
+#include <cassert>
+#include <J3ML/Geometry/Plane.h>
+#include <J3ML/Geometry/Sphere.h>
+//#include <J3ML/Geometry/OBB.h>
+#include <J3ML/Geometry/LineSegment.h>
+#include <J3ML/Geometry/Triangle.h>
+#include <J3ML/Geometry/Polygon.h>
+#include <J3ML/Geometry/Frustum.h>
+#include <J3ML/Geometry/Capsule.h>
+#include <J3ML/Geometry/Ray.h>
+#include <J3ML/Geometry/TriangleMesh.h>
+#include <J3ML/Geometry/Polyhedron.h>
+
+namespace J3ML::Geometry {
+
+    AABB AABB::FromCenterAndSize(const J3ML::Geometry::Vector3 &center, const J3ML::Geometry::Vector3 &size) {
+        Vector3 halfSize =  size * 0.5f;
+        return AABB{center - halfSize, center + halfSize};
+    }
+
+    float AABB::MinX() const { return minPoint.x; }
+
+    float AABB::MinY() const { return minPoint.y; }
+
+    float AABB::MinZ() const { return minPoint.z; }
+
+    float AABB::MaxX() const { return maxPoint.x; }
+
+    float AABB::MaxY() const { return maxPoint.y; }
+
+    float AABB::MaxZ() const { return maxPoint.z; }
+
+    Sphere AABB::MinimalEnclosingSphere() const {
+        return Sphere(Centroid(), Size().Length()*0.5f);
+    }
+
+    Vector3 AABB::HalfSize() const {
+        return this->Size()/2.f;
+    }
+
+    Sphere AABB::MaximalContainedSphere() const {
+        Vector3 halfSize = HalfSize();
+        return Sphere(Centroid(), std::min(halfSize.x, std::min(halfSize.y, halfSize.z)));
+    }
+
+    bool AABB::IsFinite() const {
+        return minPoint.IsFinite() && maxPoint.IsFinite();
+    }
+
+    Vector3 AABB::Centroid() const {
+        return (minPoint+maxPoint) * 0.5f;
+    }
+
+    Vector3 AABB::Size() const {
+        return this->maxPoint - this->minPoint;
+    }
+
+    Vector3 AABB::PointInside(float x, float y, float z) const {
+        Vector3 d = maxPoint - minPoint;
+        return minPoint + d.Mul({x, y, z});
+    }
+
+    LineSegment AABB::Edge(int edgeIndex) const {
+        switch(edgeIndex)
+        {
+            default:
+            case 0: return LineSegment(minPoint, {minPoint.x, minPoint.y, maxPoint.z});
+        }
+    }
+
+    Vector3 AABB::CornerPoint(int cornerIndex) const {
+        // TODO: assert(0 <= cornerIndex && cornerIndex <= 7)
+        switch(cornerIndex)
+        {
+            default:
+            case 0: return minPoint;
+            case 1: return {minPoint.x, minPoint.y, maxPoint.z};
+            case 2: return {minPoint.x, maxPoint.y, minPoint.z};
+            case 3: return {minPoint.x, maxPoint.y, maxPoint.z};
+            case 4: return {maxPoint.x, minPoint.y, minPoint.z};
+            case 5: return {maxPoint.x, minPoint.y, maxPoint.z};
+            case 6: return {maxPoint.x, maxPoint.y, minPoint.z};
+            case 7: return maxPoint;
+        }
+    }
+
+    Vector3 AABB::ExtremePoint(const Vector3 &direction) const {
+        return {direction.x >= 0.f ? maxPoint.x : minPoint.x,
+                direction.y >= 0.f ? maxPoint.y : minPoint.y,
+                direction.z >= 0.f ? maxPoint.z : minPoint.z};
+    }
+
+    Vector3 AABB::ExtremePoint(const Vector3 &direction, float &projectionDistance) {
+        auto extremePt = ExtremePoint(direction);
+        projectionDistance = extremePt.Dot(direction);
+        return extremePt;
+    }
+
+    Vector3 AABB::PointOnEdge(int edgeIndex, float u) const {
+        // TODO: assert(0 <= edgeIndex && edgeIndex <= 11);
+        // TODO: assert(0 <= u && u < 1.f);
+
+        auto d = maxPoint - minPoint;
+        switch(edgeIndex) {
+            default:
+            case 0: return {minPoint.x, minPoint.y, minPoint.z + u * d.z};
+            case 1: return {minPoint.x, maxPoint.y, minPoint.z + u * d.z};
+            case 2: return {maxPoint.x, minPoint.y, minPoint.z + u * d.z};
+            case 3: return {maxPoint.x, maxPoint.y, minPoint.z + u * d.z};
+
+            case 4: return {minPoint.x, minPoint.y + u * d.y, minPoint.z};
+            case 5: return {maxPoint.x, minPoint.y + u * d.y, minPoint.z};
+            case 6: return {minPoint.x, minPoint.y + u * d.y, maxPoint.z};
+            case 7: return {maxPoint.x, minPoint.y + u * d.y, maxPoint.z};
+
+            case 8: return {minPoint.x + u * d.x, minPoint.y, minPoint.z};
+            case 9: return {minPoint.x + u * d.x, minPoint.y, maxPoint.z};
+            case 10:return {minPoint.x + u * d.x, maxPoint.y, minPoint.z};
+            case 11:return {minPoint.x + u * d.x, maxPoint.y, maxPoint.z};
+        }
+    }
+
+    Vector3 AABB::FaceCenterPoint(int faceIndex) const {
+        // TODO: assert(0 <= faceIndex && faceIndex <= 5)
+        auto center = (minPoint + maxPoint) * 0.5f;
+        switch (faceIndex) {
+            default:
+            case 0: return {minPoint.x, center.y, center.z};
+            case 1: return {maxPoint.x, center.y, center.z};
+            case 2: return {center.x, minPoint.y, center.z};
+            case 3: return {center.x, maxPoint.y, center.z};
+            case 4: return {center.x, center.y, minPoint.z};
+            case 5: return {center.x, center.y, maxPoint.z};
+        }
+    }
+
+    Vector3 AABB::FacePoint(int faceIndex, float u, float v) const {
+        // TODO: assert(0 <= faceIndex && faceIndex <= 5);
+        // TODO: assert(0 <= u && u <= 1.f);
+        // TODO: assert(0 <= v && v <= 1.f);
+
+        auto d = maxPoint - minPoint;
+        switch(faceIndex)
+        {
+            default: // For release builds where assume() is disabled, return always the first option if out-of-bounds.
+            case 0: return {minPoint.x, minPoint.y + u * d.y, minPoint.z + v * d.z};
+            case 1: return {maxPoint.x, minPoint.y + u * d.y, minPoint.z + v * d.z};
+            case 2: return {minPoint.x + u * d.x, minPoint.y, minPoint.z + v * d.z};
+            case 3: return {minPoint.x + u * d.x, maxPoint.y, minPoint.z + v * d.z};
+            case 4: return {minPoint.x + u * d.x, minPoint.y + v * d.y, minPoint.z};
+            case 5: return {minPoint.x + u * d.x, minPoint.y + v * d.y, maxPoint.z};
+        }
+    }
+
+    Vector3 AABB::FaceNormal(int faceIndex) const {
+        // TODO: assert(0 <= faceIndex && faceIndex <= 5);
+        switch(faceIndex) {
+            default:
+            case 0: return {-1,  0,  0};
+            case 1: return { 1,  0,  0};
+            case 2: return { 0, -1,  0};
+            case 3: return { 0,  1,  0};
+            case 4: return { 0,  0, -1};
+            case 5: return { 0,  0,  1};
+        }
+    }
+
+    Plane AABB::FacePlane(int faceIndex) const {
+        // TODO: assert(0 <= faceIndex && faceIndex <= 5);
+        return Plane(FaceCenterPoint(faceIndex), FaceNormal(faceIndex));
+    }
+
+    AABB AABB::MinimalEnclosingAABB(const Vector3 *pointArray, int numPoints) {
+        AABB aabb;
+        aabb.SetFrom(pointArray, numPoints);
+        return aabb;
+    }
+
+    float AABB::GetVolume() const {
+        Vector3 sz = Size();
+        return sz.x * sz.y * sz.z;
+    }
+
+    float AABB::GetSurfaceArea() const {
+        Vector3 size = Size();
+        return 2.f * (size.x*size.y + size.x*size.z + size.y*size.z);
+    }
+
+    void AABB::SetFromCenterAndSize(const Vector3& center, const Vector3& size)
+    {
+
+    }
+
+
+    void AABB::SetFrom(const OBB& obb)
+    {
+
+    }
+
+    void AABB::SetFrom(const Sphere& s)
+    {
+
+    }
+
+    void AABB::SetFrom(const Vector3 *pointArray, int numPoints) {
+        assert(pointArray || numPoints == 0);
+        SetNegativeInfinity();
+        if (!pointArray)
+            return;
+        for (int i = 0; i < numPoints; ++i)
+            Enclose(pointArray[i]);
+    }
+
+    Vector3 AABB::GetRandomPointInside() const {
+
+    }
+
+    void AABB::SetNegativeInfinity() {
+        minPoint = Vector3::Infinity;
+        maxPoint = Vector3::NegativeInfinity;
+    }
+
+    void AABB::Enclose(const Vector3& point) {
+        minPoint = Vector3::Min(minPoint, point);
+        maxPoint = Vector3::Max(maxPoint, point);
+    }
+
+    void AABB::Enclose(const Vector3& aabbMinPt, const Vector3& aabbMaxPt)
+    {
+        minPoint = Vector3::Min(minPoint, aabbMinPt);
+        maxPoint = Vector3::Max(maxPoint, aabbMaxPt);
+    }
+
+    void AABB::Enclose(const LineSegment& lineSegment)
+    {
+       Enclose(Vector3::Min(lineSegment.A, lineSegment.B), Vector3::Max(lineSegment.A, lineSegment.B));
+    }
+
+    void AABB::Enclose(const OBB& obb)
+    {
+        Vector3 absAxis0 = obb.axis[0].Abs();
+        Vector3 absAxis1 = obb.axis[1].Abs();
+        Vector3 absAxis2 = obb.axis[2].Abs();
+        Vector3 d = obb.r.x * absAxis0 + obb.r.y * absAxis1 + obb.r.z * absAxis2;
+    }
+
+    Vector3 AABB::GetClosestPoint(const Vector3 &point) const {
+        Vector3 result = point;
+        if (point.x > this->maxPoint.x)
+            result.x = this->maxPoint.x;
+        else if (point.x < this->minPoint.x)
+            result.x = this->minPoint.x;
+        else
+            result.x = point.x;
+
+        if (point.y > this->maxPoint.y)
+            result.y = this->maxPoint.y;
+        else if (point.y < this->minPoint.y)
+            result.y = this->minPoint.y;
+        else
+            result.y = point.y;
+
+        if (point.z > this->maxPoint.z)
+            result.z = this->maxPoint.z;
+        else if (point.z < this->minPoint.z)
+            result.z = this->minPoint.z;
+        else
+            result.z = point.z;
+    }
+
+    AABB::AABB(const Vector3 &min, const Vector3 &max) : Shape(), minPoint(min), maxPoint(max)
+    {
+
+    }
+
+    AABB::AABB() : Shape() {}
+
+    float Max(float a, float b)
+    {
+        return std::max(a, b);
+    }
+    float Max(float a, float b, float c)
+    {
+        return std::max(a, std::max(b, c));
+    }
+
+    float Min(float a, float b, float c)
+    {
+        return std::min(a, std::min(b, c));
+    }
+
+    // Compute the face normals of the AABB, because the AABB is at center
+    // and (of course) axis aligned, we know it's normals are the X,Y,Z axes.
+    Vector3 u0 = Vector3(1.f, 0.f, 0.f);
+    Vector3 u1 = Vector3(0.f, 1.f, 0.f);
+    Vector3 u2 = Vector3(0.f, 0.f, 1.f);
+
+
+    bool AABB::TestAxis(const Vector3& axis, const Vector3& v0, const Vector3& v1, const Vector3& v2) const
+    {
+
+        Vector3 e = this->Size();
+
+        // Testing axis: axis_u0_f0
+        // Project all 3 vertices of the triangle onto the Separating axis
+        float p0 = Vector3::Dot(v0, axis);
+        float p1 = Vector3::Dot(v1, axis);
+        float p2 = Vector3::Dot(v2, axis);
+
+        // Project the AABB onto the separating axis
+        // We don't care about the end points of the projection
+        // just the length of the half-size of the AABB
+        // that is, we're only casting the extents onto the
+        // separating axis, not the AABB center. We don't
+        // need to cast the center, because we know that the
+        // AABB is at origin compared to the triangle!
+        float r = e.x * std::abs(Vector3::Dot(u0, axis)) +
+                  e.y * std::abs(Vector3::Dot(u1, axis)) +
+                  e.z * std::abs(Vector3::Dot(u2, axis));
+
+        // Now do the actual test, basically see if either of
+        // the most extreme of the triangle points intersects r
+        // You might need to write Min & Max functions that take 3 arguments
+        if (Max(Max(p0, p1, p2), Min(p0, p1, p2)) > r)
+        {
+            // This means BOTH of the points of the projected triangle
+            // are outside the projected half-length of the AABB
+            // Therefore the axis is separating and we can exit
+            return false;
+        }
+    }
+
+
+    bool AABB::Intersects(const Triangle &triangle) const {
+        // https://gdbooks.gitbooks.io/3dcollisions/content/Chapter4/aabb-triangle.html
+
+        Vector3 v0 = triangle.V0;
+        Vector3 v1 = triangle.V1;
+        Vector3 v2 = triangle.V2;
+
+        // Convert AABB to center-extentss form
+        Vector3 c = this->Centroid();
+        Vector3 e = this->Size();
+
+        // Translate the triangle as conceptually moving the AABB to origin
+        // This is the same as we did with the point in triangle test
+        v0 -= c;
+        v1 -= c;
+        v2 -= c;
+
+        // Compute the edge vectors of the triangle
+        // That is , get the lines between the points as vectors
+        Vector3 f0 = v1 - v0; // B - A
+        Vector3 f1 = v2 - v1; // C - B
+        Vector3 f2 = v0 - v2; // A - C
+
+        // There are a total of 13 axes to test!!!
+        // We first test against 9 axis, these axes are given by cross product combinations
+        // of the edges of the triangle and the edges of the AABB. You need to get an axis testing each of the 3 sides
+        // of the AABB against each of the 3 sides of the triangle. The result is 9 axes of separation.
+
+        // Compute the 9 axes
+        Vector3 axis_u0_f0 = Vector3::Cross(u0, f0);
+        Vector3 axis_u0_f1 = Vector3::Cross(u0, f1);
+        Vector3 axis_u0_f2 = Vector3::Cross(u0, f2);
+        Vector3 axis_u1_f0 = Vector3::Cross(u1, f0);
+        Vector3 axis_u1_f1 = Vector3::Cross(u1, f1);
+        Vector3 axis_u1_f2 = Vector3::Cross(u1, f2);
+        Vector3 axis_u2_f0 = Vector3::Cross(u1, f0);
+        Vector3 axis_u2_f1 = Vector3::Cross(u1, f1);
+        Vector3 axis_u2_f2 = Vector3::Cross(u1, f2);
+
+        if (TestAxis(axis_u0_f0, v0, v1, v2)) return true;
+        if (TestAxis(axis_u0_f1, v0, v1, v2)) return true;
+        if (TestAxis(axis_u0_f2, v0, v1, v2)) return true;
+        if (TestAxis(axis_u1_f0, v0, v1, v2)) return true;
+        if (TestAxis(axis_u1_f1, v0, v1, v2)) return true;
+        if (TestAxis(axis_u1_f2, v0, v1, v2)) return true;
+        if (TestAxis(axis_u2_f0, v0, v1, v2)) return true;
+        if (TestAxis(axis_u2_f1, v0, v1, v2)) return true;
+        if (TestAxis(axis_u2_f2, v0, v1, v2)) return true;
+
+        // Next we have 3 face normals from the AABB
+        // for these tests we are conceptually checking if the bounding box
+        // of the triangle intersects the bounding box of the AABB
+        // that is to say, the separating axis for all tests are axis aligned:
+        // axis1: (1, 0, 0), axis2: (0, 1, 0), axis3: (0, 0, 1)
+        // Do the SAT given the 3 primary axes of the AABB
+        // You already have two vectors for this: u0, u1, and u2
+
+        if (TestAxis(u0, v0, v1, v2)) return true;
+        if (TestAxis(u1, v0, v1, v2)) return true;
+        if (TestAxis(u2, v0, v1, v2)) return true;
+
+        // Finally we have one last axis to test, the face normal of the triangle
+        // We can get the normal of the triangle by crossing the first two line segments
+        Vector3 triangleNormal = Vector3::Cross(f0, f1);
+        if (TestAxis(triangleNormal, u0, u1, u2))
+            return true;
+
+        // Passed testing for all 13 separating axes that exist
+        return true;
+    }
+
+    Vector3 AABB::AnyPointFast() const { return minPoint;}
+
+}

src/J3ML/Geometry/AABB2D.cpp

@@ -0,0 +1,80 @@
+#include <J3ML/Geometry/AABB2D.h>
+
+namespace J3ML::Geometry
+{
+
+    float AABB2D::Width() const { return maxPoint.x - minPoint.x;  }
+
+    float AABB2D::Height() const { return maxPoint.y - minPoint.y; }
+
+    float AABB2D::DistanceSq(const Vector2 &pt) const {
+        Vector2 cp = pt.Clamp(minPoint, maxPoint);
+        return cp.DistanceSq(pt);
+    }
+
+    void AABB2D::SetNegativeInfinity() {
+        minPoint = Vector2::Infinity;
+        maxPoint = -Vector2::Infinity;
+    }
+
+    void AABB2D::Enclose(const Vector2 &point) {
+        minPoint = Vector2::Min(minPoint, point);
+        maxPoint = Vector2::Max(maxPoint, point);
+    }
+
+    bool AABB2D::Intersects(const AABB2D &rhs) const {
+        return maxPoint.x >= rhs.minPoint.x &&
+               maxPoint.y >= rhs.minPoint.y &&
+               rhs.maxPoint.x >= minPoint.x &&
+               rhs.maxPoint.y >= minPoint.y;
+    }
+
+    bool AABB2D::Contains(const AABB2D &rhs) const {
+        return rhs.minPoint.x >= minPoint.x && rhs.minPoint.y >= minPoint.y
+               && rhs.maxPoint.x <= maxPoint.x && rhs.maxPoint.y <= maxPoint.y;
+    }
+
+    bool AABB2D::Contains(const Vector2 &pt) const {
+        return pt.x >= minPoint.x && pt.y >= minPoint.y
+               && pt.x <= maxPoint.x && pt.y <= maxPoint.y;
+    }
+
+    bool AABB2D::Contains(int x, int y) const {
+        return x >= minPoint.x && y >= minPoint.y
+               && x <= maxPoint.x && y <= maxPoint.y;
+    }
+
+    bool AABB2D::IsDegenerate() const {
+        return minPoint.x >= maxPoint.x || minPoint.y >= maxPoint.y;
+    }
+
+    bool AABB2D::HasNegativeVolume() const {
+        return maxPoint.x < minPoint.x || maxPoint.y < minPoint.y;
+    }
+
+    bool AABB2D::IsFinite() const {
+        return minPoint.IsFinite() && maxPoint.IsFinite() && minPoint.MinElement() > -1e5f && maxPoint.MaxElement() < 1e5f;
+    }
+
+    Vector2 AABB2D::PosInside(const Vector2 &normalizedPos) const {
+        return minPoint + normalizedPos.Mul(maxPoint - minPoint);
+    }
+
+    Vector2 AABB2D::ToNormalizedLocalSpace(const Vector2 &pt) const {
+        return (pt - minPoint).Div(maxPoint - minPoint);
+    }
+
+    AABB2D AABB2D::operator+(const Vector2 &pt) const {
+        AABB2D a;
+        a.minPoint = minPoint + pt;
+        a.maxPoint = maxPoint + pt;
+        return a;
+    }
+
+    AABB2D AABB2D::operator-(const Vector2 &pt) const {
+        AABB2D a;
+        a.minPoint = minPoint - pt;
+        a.maxPoint = maxPoint - pt;
+        return a;
+    }
+}

src/J3ML/Geometry/Capsule.cpp

@@ -0,0 +1,7 @@
+#include <J3ML/Geometry/Capsule.h>
+
+namespace J3ML::Geometry
+{
+
+    Capsule::Capsule() : l() {}
+}

src/J3ML/Geometry/Frustum.cpp

@@ -0,0 +1,21 @@
+#include <J3ML/Geometry/Frustum.h>
+#include <cmath>
+
+namespace J3ML::Geometry
+{
+    Frustum Frustum::CreateFrustumFromCamera(const CoordinateFrame &cam, float aspect, float fovY, float zNear, float zFar) {
+        Frustum frustum;
+        const float halfVSide = zFar * tanf(fovY * 0.5f);
+        const float halfHSide = halfVSide * aspect;
+
+        const Vector3 frontMultFar = cam.Front * zFar;
+
+        frustum.NearFace  = Plane{cam.Position + cam.Front * zNear, cam.Front};
+        frustum.FarFace   = Plane{cam.Position + frontMultFar, -cam.Front};
+        frustum.RightFace = Plane{cam.Position, Vector3::Cross(frontMultFar - cam.Right * halfHSide, cam.Up)};
+        frustum.LeftFace  = Plane{cam.Position, Vector3::Cross(cam.Up, frontMultFar+cam.Right*halfHSide)};
+        frustum.TopFace   = Plane{cam.Position, Vector3::Cross(cam.Right, frontMultFar - cam.Up * halfVSide)};
+        frustum.BottomFace   = Plane{cam.Position, Vector3::Cross(frontMultFar + cam.Up * halfVSide, cam.Right)};
+        return frustum;
+    }
+}

src/J3ML/Geometry/LineSegment.cpp

@@ -0,0 +1,11 @@
+#include <J3ML/Geometry/LineSegment.h>
+
+namespace J3ML::Geometry {
+
+    LineSegment::LineSegment(const Vector3 &a, const Vector3 &b) : A(a), B(b)
+    {
+
+    }
+
+    LineSegment::LineSegment() {}
+}

src/J3ML/Geometry/OBB.cpp

@@ -0,0 +1,318 @@
+#include <J3ML/Geometry/Shape.h>
+#include <J3ML/Geometry/AABB.h>
+#include <J3ML/Geometry/LineSegment.h>
+#include <J3ML/Geometry/Polyhedron.h>
+#include <J3ML/Geometry/OBB.h>
+#include <J3ML/Geometry/Sphere.h>
+
+namespace J3ML::Geometry
+{
+
+    Polyhedron OBB::ToPolyhedron() const {
+        // Note to maintainer: This function is an exact copy of AABB::ToPolyhedron() and Frustum::ToPolyhedron()
+
+        Polyhedron p;
+        // populate the corners of this OBB
+        // this will be in the order 0: ---, 1: --+, 2: -+-, 3: -++, 4: +--, 5: +-+, 6: ++-, 7: +++
+        for (int i = 0; i < 8; ++i)
+        {
+            p.v.push_back(CornerPoint(i));
+        }
+
+        // generate the 6 faces of this OBB.
+        const int faces[6][4] =
+                {
+                        {0, 1, 3, 2}, // X-
+                        {4, 6, 7, 5}, // X+
+                        {0, 4, 5, 1}, // Y-
+                        {7, 6, 2, 3}, // Y+
+                        {0, 2, 6, 4}, // Z-
+                        {1, 5, 7, 3}  // Z+
+                };
+
+        for (int f = 0; f < 6; ++f)
+        {
+            Polyhedron::Face face;
+            for (int v = 0; v < 4; ++v)
+            {
+                face.v.push_back(faces[f][v]);
+            }
+            //p.f.push_back(face);
+        }
+        return p;
+    }
+
+    Sphere OBB::MinimalEnclosingSphere() const {
+        Sphere s;
+        s.Position = pos;
+        s.Radius = HalfDiagonal().Length();
+        return s;
+    }
+
+    Sphere OBB::MaximalContainedSphere() const {
+        Sphere s;
+        s.Position = pos;
+        s.Radius = r.MinElement();
+        return s;
+    }
+
+    bool OBB::IsFinite() const {
+        return pos.IsFinite() && r.IsFinite() && axis[0].IsFinite() && axis[1].IsFinite() && axis[2].IsFinite();
+    }
+
+    bool OBB::IsDegenerate() const
+    {
+        return !(r.x > 0.f && r.y > 0.f && r.z > 0.f);
+    }
+
+    Vector3 OBB::CenterPoint() const
+    {
+        return pos;
+    }
+
+    Vector3 OBB::PointInside(float x, float y, float z) const
+    {
+        assert(0.f <= x && x <= 1.f);
+        assert(0.f <= y && y <= 1.f);
+        assert(0.f <= z && z <= 1.f);
+
+        return pos + axis[0] * (2.f * r.x * x - r.x)
+                   + axis[1] * (2.f * r.y * y - r.y)
+                   + axis[2] * (2.f * r.z * z - r.z);
+    }
+
+    Vector3 OBB::PointInside(const Vector3& pt) const
+    {
+        return PointInside(pt.x, pt.y, pt.z);
+    }
+
+    LineSegment OBB::Edge(int edgeIndex) const
+    {
+        assert(0 <= edgeIndex && edgeIndex <= 11);
+
+        switch(edgeIndex)
+        {
+            default: // For release builds where Assert() is disabled, return always the first option if out-of-bounds
+            case 0: return LineSegment(CornerPoint(0), CornerPoint(1));
+            case 1: return LineSegment(CornerPoint(0), CornerPoint(2));
+            case 2: return LineSegment(CornerPoint(0), CornerPoint(4));
+            case 3: return LineSegment(CornerPoint(1), CornerPoint(3));
+            case 4: return LineSegment(CornerPoint(1), CornerPoint(5));
+            case 5: return LineSegment(CornerPoint(2), CornerPoint(3));
+            case 6: return LineSegment(CornerPoint(2), CornerPoint(6));
+            case 7: return LineSegment(CornerPoint(3), CornerPoint(7));
+            case 8: return LineSegment(CornerPoint(4), CornerPoint(5));
+            case 9: return LineSegment(CornerPoint(4), CornerPoint(6));
+            case 10: return LineSegment(CornerPoint(5), CornerPoint(7));
+            case 11: return LineSegment(CornerPoint(6), CornerPoint(7));
+        }
+    }
+
+    Vector3 OBB::CornerPoint(int cornerIndex) const
+    {
+        assert(0 <= cornerIndex && cornerIndex <= 7);
+        switch(cornerIndex)
+        {
+            default: // For release builds, return always the first option if out of bounds
+            case 0: return pos - r.x * axis[0] - r.y * axis[1] - r.z * axis[2];
+            case 1: return pos - r.x * axis[0] - r.y * axis[1] + r.z * axis[2];
+            case 2: return pos - r.x * axis[0] + r.y * axis[1] - r.z * axis[2];
+            case 3: return pos - r.x * axis[0] + r.y * axis[1] + r.z * axis[2];
+            case 4: return pos + r.x * axis[0] - r.y * axis[1] - r.z * axis[2];
+            case 5: return pos + r.x * axis[0] - r.y * axis[1] + r.z * axis[2];
+            case 6: return pos + r.x * axis[0] + r.y * axis[1] - r.z * axis[2];
+            case 7: return pos + r.x * axis[0] + r.y * axis[1] + r.z * axis[2];
+        }
+    }
+
+    Vector3 OBB::ExtremePoint(const Vector3& direction) const
+    {
+        Vector3 pt = pos;
+        pt += axis[0] * (Vector3::Dot(direction, axis[0]) >= 0.f ? r.x : -r.x);
+        pt += axis[1] * (Vector3::Dot(direction, axis[1]) >= 0.f ? r.y : -r.y);
+        pt += axis[2] * (Vector3::Dot(direction, axis[2]) >= 0.f ? r.z : -r.z);
+        return pt;
+    }
+
+    Vector3 OBB::ExtremePoint(const Vector3& direction, float &projectionDistance) const
+    {
+        Vector3 extremePoint = ExtremePoint(direction);
+        projectionDistance = extremePoint.Dot(direction);
+        return extremePoint;
+    }
+
+    void OBB::ProjectToAxis(const Vector3& direction, float& outMin, float& outMax) const
+    {
+        float x = std::abs(Vector3::Dot(direction, axis[0]) * r.x);
+        float y = std::abs(Vector3::Dot(direction, axis[1]) * r.y);
+        float z = std::abs(Vector3::Dot(direction, axis[2]) * r.z);
+        float pt = Vector3::Dot(direction, pos);
+        outMin = pt - x - y - z;
+        outMax = pt + x + y + z;
+    }
+
+    int OBB::UniqueFaceNormals(Vector3* out) const
+    {
+        out[0] = axis[0];
+        out[1] = axis[1];
+        out[2] = axis[2];
+        return 3;
+    }
+
+    int OBB::UniqueEdgeDirections(Vector3* out) const
+    {
+        out[0] = axis[0];
+        out[1] = axis[1];
+        out[2] = axis[2];
+        return 3;
+    }
+
+    Vector3 OBB::PointOnEdge(int edgeIndex, float u) const
+    {
+        assert(0 <= edgeIndex && edgeIndex <= 11);
+        assert(0 <= u && u <= 1.f);
+
+        edgeIndex = std::clamp(edgeIndex, 0, 11);
+        Vector3 d = axis[edgeIndex/4] * (2.f * u - 1.f) * r[edgeIndex/4];
+        switch(edgeIndex)
+        {
+            default:
+            case 0: return pos - r.y * axis[1] - r.z * axis[2] + d;
+            case 1: return pos - r.y * axis[1] + r.z * axis[2] + d;
+            case 2: return pos + r.y * axis[1] - r.z * axis[2] + d;
+            case 3: return pos + r.y * axis[1] + r.z * axis[2] + d;
+
+            case 4: return pos - r.x * axis[0] - r.z * axis[2] + d;
+            case 5: return pos - r.x * axis[0] + r.z * axis[2] + d;
+            case 6: return pos + r.x * axis[0] - r.z * axis[2] + d;
+            case 7: return pos + r.x * axis[0] + r.z * axis[2] + d;
+
+            case 8: return pos - r.x * axis[0] - r.y * axis[1] + d;
+            case 9: return pos - r.x * axis[0] + r.y * axis[1] + d;
+            case 10: return pos + r.x * axis[0] - r.y * axis[1] + d;
+            case 11: return pos + r.x * axis[0] + r.y * axis[1] + d;
+        }
+    }
+
+    Vector3 OBB::FaceCenterPoint(int faceIndex) const
+    {
+        assert(0 <= faceIndex && faceIndex <= 6);
+        switch(faceIndex)
+        {
+            default:
+            case 0: return pos - r.x * axis[0];
+            case 1: return pos + r.x * axis[0];
+            case 2: return pos - r.y * axis[1];
+            case 3: return pos + r.y * axis[1];
+            case 4: return pos - r.z * axis[2];
+            case 5: return pos + r.z * axis[2];
+        }
+    }
+
+    Vector3 OBB::FacePoint(int faceIndex, float u, float v) const
+    {
+        assert(0 <= faceIndex && faceIndex <= 5);
+        assert(0 <= u && u <= 1.f);
+        assert(0 <= v && v <= 1.f);
+
+        int uIdx = faceIndex/2;
+        int vIdx = (faceIndex/2 + 1) % 3;
+        Vector3 U = axis[uIdx] * (2.f * u - 1.f) * r[uIdx];
+        Vector3 V = axis[vIdx] * (2.f * v - 1.f) * r[vIdx];
+
+        switch(faceIndex)
+        {
+            default:
+            case 0: return pos - r.z * axis[2] + U + V;
+            case 1: return pos + r.z * axis[2] + U + V;
+            case 2: return pos - r.x * axis[0] + U + V;
+            case 3: return pos + r.x * axis[0] + U + V;
+            case 4: return pos - r.y * axis[1] + U + V;
+            case 5: return pos + r.y * axis[1] + U + V;
+        }
+    }
+
+    Plane OBB::FacePlane(int faceIndex) const
+    {
+        assert(0 <= faceIndex && faceIndex <= 5);
+        switch(faceIndex)
+        {
+            default:
+            case 0: return Plane(FaceCenterPoint(0), -axis[0]);
+            case 1: return Plane(FaceCenterPoint(1),  axis[0]);
+            case 2: return Plane(FaceCenterPoint(2), -axis[1]);
+            case 3: return Plane(FaceCenterPoint(3), axis[1]);
+            case 4: return Plane(FaceCenterPoint(4), -axis[2]);
+            case 5: return Plane(FaceCenterPoint(5), axis[2]);
+        }
+    }
+
+    void OBB::GetCornerPoints(Vector3 *outPointArray) const
+    {
+        assert(outPointArray);
+        for (int i = 0; i < 8; ++i)
+            outPointArray[i] = CornerPoint(i);
+    }
+
+    void OBB::GetFacePlanes(Plane *outPlaneArray) const
+    {
+        assert(outPlaneArray);
+        for (int i = 0; i < 6; ++i)
+            outPlaneArray[i] = FacePlane(i);
+    }
+
+    void OBB::ExtremePointsAlongDirection(const Vector3& dir, const Vector3* pointArray, int numPoints, int &idxSmallest, int &idxLargest, float &smallestD, float &largestD)
+    {
+        assert(pointArray || numPoints == 0);
+
+        idxSmallest = idxLargest = 0;
+
+        smallestD = INFINITY;
+        largestD = -INFINITY;
+
+        for (int i = 0; i < numPoints; ++i)
+        {
+            float d = Vector3::Dot(pointArray[i], dir);
+            if (d < smallestD)
+            {
+                smallestD = d;
+                idxSmallest = i;
+            }
+            if (d > largestD)
+            {
+                largestD = d;
+                idxLargest = i;
+            }
+        }
+    }
+
+    Vector3 OBB::Size() const {
+        return r * 2.f;
+    }
+
+    Vector3 OBB::HalfSize() const {
+        return r;
+    }
+
+    Vector3 OBB::Diagonal() const {
+        return 2.f * HalfDiagonal();
+    }
+
+    Vector3 OBB::HalfDiagonal() const {
+        return axis[0] * r[0] + axis[1] * r[1] + axis[2] * r[2];
+    }
+
+    float OBB::Volume() const {
+        Vector3 size = Size();
+        return size.x*size.y*size.z;
+    }
+
+    float OBB::SurfaceArea() const {
+        const Vector3 size = Size();
+        return 2.f * (size.x*size.y + size.x*size.z + size.y*size.z);
+    }
+
+
+
+
+}

src/J3ML/Geometry/Plane.cpp

@@ -0,0 +1 @@
+#include <J3ML/Geometry/Plane.h>

src/J3ML/Geometry/Polygon.cpp

@@ -0,0 +1,5 @@
+#include <J3ML/Geometry/Polygon.h>
+
+namespace Geometry {
+
+}

src/J3ML/Geometry/Polyhedron.cpp

@@ -0,0 +1,6 @@
+#include <J3ML/Geometry/Polyhedron.h>
+
+namespace Geometry
+{
+
+}

src/J3ML/Geometry/QuadTree.cpp

@@ -0,0 +1,6 @@
+#include <J3ML/Geometry/QuadTree.h>
+
+namespace Geometry
+{
+
+}

src/J3ML/Geometry/Ray.cpp

@@ -0,0 +1,126 @@
+#include <J3ML/Geometry/Ray.h>
+#include <J3ML/Geometry/Sphere.h>
+
+
+namespace J3ML::Geometry
+{
+    RaycastResult Ray::Cast(const Sphere &target, float maxDistance)
+    {
+        Vector3 p0 = this->Origin;
+        Vector3 d = this->Direction.Normalize();
+
+        Vector3 c = target.Position;
+        float r = target.Radius;
+
+        Vector3 e = c - p0;
+        // Using Length here would cause floating point error to creep in
+        float Esq = Vector3::LengthSquared(e);
+        float a = Vector3::Dot(e, d);
+        float b = std::sqrt(Esq - (a*a));
+        float f = std::sqrt((r*r) - (b*b));
+
+        float t = 0;
+        // No collision
+        if (r * r - Esq + a * a < 0.f)
+        {
+            t = -1;
+        } else if ( Esq < r*r) {
+            t = a + f;
+        } else
+        {
+            t = a - f;
+        }
+
+        // TODO: Verify this
+        Vector3 intersection = p0.Project(d*t);
+        Vector3 intersection_from_sphere_origin = (intersection - target.Position);
+
+        Vector3 normal = -intersection_from_sphere_origin.Normalize();
+
+        return RaycastResult{
+            intersection,
+            normal,
+            true,
+            (Shape *) &target
+        };
+    }
+
+    RaycastResult Ray::Cast(const AABB &target, float maxDistance) {
+        float t1 = (target.minPoint.x - Origin.x) / Direction.x;
+        float t2 = (target.maxPoint.x - Origin.x) / Direction.x;
+        float t3 = (target.minPoint.y - Origin.y) / Direction.y;
+        float t4 = (target.maxPoint.y - Origin.y) / Direction.y;
+        float t5 = (target.minPoint.z - Origin.z) / Direction.z;
+        float t6 = (target.maxPoint.z - Origin.z) / Direction.z;
+
+        float tmin = std::max( std::max( std::min(t1, t2), std::min(t3, t4)), std::min(t5, t6));
+        float tmax = std::min( std::min( std::max(t1, t2), std::max(t3, t4)), std::max(t5, t6));
+
+        // if tmax < 0, ray is intersecting aabb, but whole aabb is behind us.
+        if (tmax < 0)
+            return RaycastResult::NoHit();
+
+        // if tmin > tmax, ray doesn't intersect AABB
+        if (tmin > tmax)
+            return RaycastResult::NoHit();
+
+        float t = 0.f;
+
+        if (tmin < 0.f)
+            t = tmax;
+
+        t = tmin;
+
+        Vector3 p0 = this->Origin;
+        Vector3 d = this->Direction.Normalize();
+
+        // TODO: Verify this
+        Vector3 intersection = p0.Project(d*t);
+
+        // WTF: This algorithm is only valid for spheres!!!
+        // TODO: Calculate surfacenormal against rectangle
+        Vector3 intersection_from_sphere_origin = (intersection - target.Centroid());
+
+        Vector3 normal = -intersection_from_sphere_origin.Normalize();
+
+        return RaycastResult
+        {
+            intersection,
+            normal,
+            true,
+            (Shape*)&target
+        };
+    }
+
+    RaycastResult Ray::Cast(const Plane &target, float maxDistance) {
+        float nd = Vector3::Dot(Direction, target.Normal);
+        float pn = Vector3::Dot(Origin, target.Normal);
+
+        if (nd >= 0.f)
+            return RaycastResult::NoHit();
+
+        float t = (target.distance - pn) / nd;
+
+        Vector3 d = this->Direction.Normalize();
+
+        // TODO: verify this
+        Vector3 intersection = this->Origin.Project(d*t);
+
+        // TODO: flip the axis based on direction of incoming ray?
+        // Take dot product
+        Vector3 normal = target.Normal;
+
+        if (t >= 0.f)
+            return RaycastResult
+                    {
+                        intersection,
+                        normal,
+                        true,
+                        (Shape*) &target
+                    };
+
+        return RaycastResult::NoHit();
+    }
+}
+
+

src/J3ML/Geometry/Sphere.cpp

@@ -0,0 +1,6 @@
+#include <J3ML/Geometry/Sphere.h>
+
+namespace J3ML::Geometry
+{
+
+}

src/J3ML/Geometry/TriangleMesh.cpp

@@ -0,0 +1 @@
+#include <J3ML/Geometry/TriangleMesh.h>

src/J3ML/J3ML.cpp

@@ -0,0 +1,43 @@
+#include <J3ML/J3ML.h>
+
+
+namespace J3ML
+{
+
+    Math::Rotation Math::operator ""_degrees(long double rads) { return {Radians((float)rads)}; }
+
+    Math::Rotation Math::operator ""_deg(long double rads) { return {Radians((float)rads)}; }
+
+    Math::Rotation Math::operator ""_radians(long double rads) { return {(float)rads}; }
+
+    Math::Rotation Math::operator ""_rad(long double rads) { return {(float)rads}; }
+
+    float Math::FastRSqrt(float x) {
+        return 1.f / FastSqrt(x);
+    }
+
+    float Math::RSqrt(float x) {
+        return 1.f / Sqrt(x);
+    }
+
+    float Math::Radians(float degrees) { return degrees * (Pi/180.f); }
+
+    float Math::Degrees(float radians) { return radians * (180.f/Pi); }
+
+    Math::Rotation::Rotation() : valueInRadians(0) {}
+
+    Math::Rotation::Rotation(float value) : valueInRadians(value) {}
+
+    Math::Rotation Math::Rotation::operator+(const Math::Rotation &rhs) {
+        valueInRadians += rhs.valueInRadians;
+    }
+
+    float Math::Interp::SmoothStart(float t) {
+        assert(t >= 0.f && t <= 1.f);
+        return t*t;
+    }
+
+    int Math::BitTwiddling::CountBitsSet(u32 value) {
+
+    }
+}

src/J3ML/LinearAlgebra.cpp

@@ -1,4 +1,4 @@
-#include <J3ML/LinearAlgebra.h>
+#include "J3ML/LinearAlgebra.h"
 #include <cassert>
 
 namespace LinearAlgebra {

src/J3ML/LinearAlgebra/AxisAngle.cpp

@@ -1,8 +1,17 @@
 #include <J3ML/LinearAlgebra/AxisAngle.h>
-
-namespace LinearAlgebra {
+#include <J3ML/LinearAlgebra/Quaternion.h>
+namespace J3ML::LinearAlgebra {
 
     AxisAngle::AxisAngle() : axis(Vector3::Zero) {}
 
     AxisAngle::AxisAngle(const Vector3 &axis, float angle) : axis(axis), angle(angle) {}
+
+    Quaternion AxisAngle::ToQuaternion() const {
+        return {
+                axis.x * std::sin(angle/2),
+                axis.y * std::sin(angle/2),
+                axis.z * std::sin(angle/2),
+                std::cos(angle/2)
+        };
+    }
 }

src/J3ML/LinearAlgebra/EulerAngle.cpp

@@ -3,50 +3,49 @@
 #include <algorithm>
 
 
-#pragma region EulerAngle
-namespace LinearAlgebra {
-EulerAngle::EulerAngle(float pitch, float yaw, float roll): pitch(pitch), yaw(yaw), roll(roll)
-{}
+namespace J3ML::LinearAlgebra {
+    EulerAngle::EulerAngle(float pitch, float yaw, float roll): pitch(pitch), yaw(yaw), roll(roll)
+    {}
 
-float EulerAngle::GetPitch(float pitch_limit) const
-{ return std::clamp( std::remainderf(pitch,360.f), -pitch_limit, pitch_limit); }
+    float EulerAngle::GetPitch(float pitch_limit) const
+    { return std::clamp( std::remainderf(pitch,360.f), -pitch_limit, pitch_limit); }
 
-float EulerAngle::GetYaw(float yaw_limit) const
-{ return std::clamp(std::remainderf(yaw, 360.f), -yaw_limit, yaw_limit);   }
+    float EulerAngle::GetYaw(float yaw_limit) const
+    { return std::clamp(std::remainderf(yaw, 360.f), -yaw_limit, yaw_limit);   }
 
-float EulerAngle::GetRoll(float pitch_limit) const
-{ return std::clamp( std::remainderf(pitch,360.f), -pitch_limit, pitch_limit); }
+    float EulerAngle::GetRoll(float pitch_limit) const
+    { return std::clamp( std::remainderf(pitch,360.f), -pitch_limit, pitch_limit); }
 
-bool EulerAngle::operator==(const EulerAngle& a) const
-{
-    return (pitch == a.pitch) && (yaw == a.yaw) && (roll == a.roll);
-}
+    bool EulerAngle::operator==(const EulerAngle& a) const
+    {
+        return (pitch == a.pitch) && (yaw == a.yaw) && (roll == a.roll);
+    }
 
-void EulerAngle::clamp()
-{
-    if (this->pitch > 89.0f)
-        this->pitch = 89.0f;
-    if (this->pitch <= -89.0f)
-        this->pitch = -89.0f;
-    //TODO: Make this entirely seamless by getting the amount they rotated passed -180 and +180 by.
-    if (this->yaw <= -180.0f)
-        this->yaw = 180.0f;
-    if (this->yaw >= 180.01f)
-        this->yaw = -179.9f;
-    if (this->roll >= 360.0f)
-        this->roll = 0.0;
-    if (this->roll <= -360.0f)
-        this->roll = 0.0;
-}
+    void EulerAngle::clamp()
+    {
+        if (this->pitch > 89.0f)
+            this->pitch = 89.0f;
+        if (this->pitch <= -89.0f)
+            this->pitch = -89.0f;
+        //TODO: Make this entirely seamless by getting the amount they rotated passed -180 and +180 by.
+        if (this->yaw <= -180.0f)
+            this->yaw = 180.0f;
+        if (this->yaw >= 180.01f)
+            this->yaw = -179.9f;
+        if (this->roll >= 360.0f)
+            this->roll = 0.0;
+        if (this->roll <= -360.0f)
+            this->roll = 0.0;
+    }
 
-EulerAngle EulerAngle::movementAngle() const
-{
-    EulerAngle a;
-    a.pitch = (cos(Math::Radians(yaw)) * cos(Math::Radians(pitch)));
-    a.yaw = -sin(Math::Radians(pitch));
-    a.roll = (sin(Math::Radians(yaw)) * cos(Math::Radians(pitch)));
-    return a;
-}
+    EulerAngle EulerAngle::movementAngle() const
+    {
+        EulerAngle a;
+        a.pitch = (cos(Math::Radians(yaw)) * cos(Math::Radians(pitch)));
+        a.yaw = -sin(Math::Radians(pitch));
+        a.roll = (sin(Math::Radians(yaw)) * cos(Math::Radians(pitch)));
+        return a;
+    }
 
     EulerAngle::EulerAngle() : pitch(0), yaw(0), roll(0) {}
 }

src/J3ML/LinearAlgebra/Matrix2x2.cpp

@@ -1,6 +1,6 @@
 #include <J3ML/LinearAlgebra/Matrix2x2.h>
 
-namespace LinearAlgebra {
+namespace J3ML::LinearAlgebra {
 
     Vector2 Matrix2x2::GetRow(int index) const {
         float x = this->elems[index][0];
@@ -18,4 +18,8 @@ namespace LinearAlgebra {
     float Matrix2x2::At(int x, int y) const {
         return this->elems[x][y];
     }
+
+    float &Matrix2x2::At(int x, int y) {
+        return this->elems[x][y];
+    }
 }

src/J3ML/LinearAlgebra/Matrix3x3.cpp

@@ -1,7 +1,7 @@
 #include <J3ML/LinearAlgebra/Matrix3x3.h>
 #include <cmath>
 
-namespace LinearAlgebra {
+namespace J3ML::LinearAlgebra {
 
     const Matrix3x3 Matrix3x3::Zero = Matrix3x3(0, 0, 0, 0, 0, 0, 0, 0, 0);
     const Matrix3x3 Matrix3x3::Identity = Matrix3x3(1, 0, 0, 0, 1, 0, 0, 0, 1);
@@ -37,9 +37,14 @@ namespace LinearAlgebra {
         return {x, y, z};
     }
 
+
     float Matrix3x3::At(int x, int y) const {
         return this->elems[x][y];
+    }
 
+    void Matrix3x3::SetAt(int x, int y, float value)
+    {
+        this->elems[x][y] = value;
     }
 
     Vector3 Matrix3x3::operator*(const Vector3 &rhs) const {
@@ -175,5 +180,202 @@ namespace LinearAlgebra {
         };
     }
 
+    Quaternion Matrix3x3::ToQuat() const {
+        auto m00 = At(0,0);
+        auto m01 = At(0, 1);
+        auto m02 = At(0, 2);
+        auto m10 = At(1,0);
+        auto m11 = At(1, 1);
+        auto m12 = At(1, 2);
+        auto m20 = At(2,0);
+        auto m21 = At(2, 1);
+        auto m22 = At(2, 2);
+
+        auto w = std::sqrt(1.f + m00 + m11 + m22) / 2.f;
+        float w4 = (4.f * w);
+        return {
+                (m21 - m12) / w4,
+                (m02 - m20) / w4,
+                (m10 - m01) / w4,
+                w
+        };
+    }
+
+    void Matrix3x3::SetRotatePart(const Vector3 &a, float angle) {
+        float s = std::sin(angle);
+        float c = std::cos(angle);
+
+        const float c1 = 1.f - c;
+
+        elems[0][0] = c+c1*a.x*a.x;
+        elems[1][0] = c1*a.x*a.y+s*a.z;
+        elems[2][0] = c1*a.x*a.z-s*a.y;
+
+        elems[0][1] = c1*a.x*a.y-s*a.z;
+        elems[1][1] = c+c1*a.y*a.y;
+        elems[2][1] = c1*a.y*a.z+s*a.x;
+
+        elems[0][2] = c1*a.x*a.z+s*a.y;
+        elems[1][2] = c1*a.y*a.z-s*a.x;
+        elems[2][2] = c+c1*a.z*a.z;
+    }
+
+    Matrix3x3 Matrix3x3::RotateAxisAngle(const Vector3 &axis, float angleRadians) {
+        Matrix3x3 r;
+        r.SetRotatePart(axis, angleRadians);
+        return r;
+    }
+
+    void Matrix3x3::SetRow(int i, const Vector3 &vec) {
+        elems[i][0] = vec.x;
+        elems[i][1] = vec.y;
+        elems[i][2] = vec.z;
+    }
+
+    void Matrix3x3::SetColumn(int i, const Vector3& vec)
+    {
+        elems[0][i] = vec.x;
+        elems[1][i] = vec.y;
+        elems[2][i] = vec.z;
+    }
+
+    Matrix3x3
+    Matrix3x3::LookAt(const Vector3 &forward, const Vector3 &target, const Vector3 &localUp, const Vector3 &worldUp) {
+        // User must input proper normalized input direction vectors
+        // In the local space, the forward and up directions must be perpendicular to be well-formed.
+        // In the world space, the target direction and world up cannot be degenerate (co-linear)
+        // Generate the third basis vector in the local space;
+        Vector3 localRight = localUp.Cross(forward).Normalize();
+        // A. Now we have an orthonormal linear basis {localRight, localUp, forward} for the object local space.
+        // Generate the third basis vector for the world space
+        Vector3 worldRight = worldUp.Cross(target).Normalize();
+        // Since the input worldUp vector is not necessarily perpendicular to the target direction vector
+        // We need to compute the real world space up vector that the "head" of the object will point
+        // towards when the model is looking towards the desired target direction
+        Vector3 perpWorldUp = target.Cross(worldRight).Normalize();
+        // B. Now we have an orthonormal linear basis {worldRight, perpWorldUp, targetDirection } for the desired target orientation.
+        // We want to build a matrix M that performs the following mapping:
+        // 1. localRight must be mapped to worldRight.        (M * localRight = worldRight)
+        // 2. localUp must be mapped to perpWorldUp.          (M * localUp = perpWorldUp)
+        // 3. localForward must be mapped to targetDirection. (M * localForward = targetDirection)
+        // i.e. we want to map the basis A to basis B.
+
+        // This matrix M exists, and it is an orthonormal rotation matrix with a determinant of +1, because
+        // the bases A and B are orthonormal with the same handedness.
+
+        // Below, use the notation that (a,b,c) is a 3x3 matrix with a as its first column, b second, and c third.
+
+        // By algebraic manipulation, we can rewrite conditions 1, 2 and 3 in a matrix form:
+        //        M * (localRight, localUp, localForward) = (worldRight, perpWorldUp, targetDirection)
+        // or     M = (worldRight, perpWorldUp, targetDirection) * (localRight, localUp, localForward)^{-1}.
+        // or     M = m1 * m2, where
+
+        // m1 equals (worldRight, perpWorldUp, target):
+        Matrix3x3 m1(worldRight, perpWorldUp, target);
+
+        // and m2 equals (localRight, localUp, localForward)^{-1}:
+        Matrix3x3 m2;
+        m2.SetRow(0, localRight);
+        m2.SetRow(1, localUp);
+        m2.SetRow(2, forward);
+        // Above we used the shortcut that for an orthonormal matrix M, M^{-1} = M^T. So set the rows
+        // and not the columns to directly produce the transpose, i.e. the inverse of (localRight, localUp, localForward).
+
+        // Compute final M.
+        m2 = m1 * m2;
+
+        // And fix any numeric stability issues by re-orthonormalizing the result.
+        m2.Orthonormalize(0, 1, 2);
+        return m2;
+    }
+
+    Vector3 Matrix3x3::Diagonal() const {
+        return {elems[0][0],
+                elems[1][1],
+                elems[2][2]
+        };
+    }
+
+    float &Matrix3x3::At(int row, int col) {
+        return elems[row][col];
+    }
+
+    Vector3 Matrix3x3::WorldZ() const {
+        return GetColumn(2);
+    }
+
+    Vector3 Matrix3x3::WorldY() const {
+        return GetColumn(1);
+    }
+
+    Vector3 Matrix3x3::WorldX() const {
+        return GetColumn(0);
+    }
+
+    Matrix3x3 Matrix3x3::FromRS(const Quaternion &rotate, const Vector3 &scale) {
+        return Matrix3x3(rotate) * Matrix3x3::FromScale(scale);
+    }
+
+    Matrix3x3 Matrix3x3::FromRS(const Matrix3x3 &rotate, const Vector3 &scale) {
+        return rotate * Matrix3x3::FromScale(scale);
+    }
+
+    Matrix3x3 Matrix3x3::FromQuat(const Quaternion &orientation) {
+        return Matrix3x3(orientation);
+    }
+
+    Matrix3x3 Matrix3x3::ScaleBy(const Vector3 &rhs) {
+        return *this * FromScale(rhs);
+    }
+
+    Vector3 Matrix3x3::GetScale() const {
+        return Vector3(GetColumn(0).Length(), GetColumn(1).Length(), GetColumn(2).Length());
+    }
+
+    Vector3 Matrix3x3::operator[](int row) const {
+        return Vector3{elems[row][0], elems[row][1], elems[row][2]};
+    }
+
+    Matrix3x3 Matrix3x3::FromScale(const Vector3 &scale) {
+        Matrix3x3 m;
+        m.At(0,0) = scale.x;
+        m.At(1,1) = scale.y;
+        m.At(2,2) = scale.z;
+        return m;
+    }
+
+    Matrix3x3 Matrix3x3::FromScale(float sx, float sy, float sz) {
+        Matrix3x3 m;
+        m.At(0,0) = sx;
+        m.At(1,1) = sy;
+        m.At(2,2) = sz;
+        return m;
+    }
+
+    void Matrix3x3::Orthonormalize(int c0, int c1, int c2) {
+        Vector3 v0 = GetColumn(c0);
+        Vector3 v1 = GetColumn(c1);
+        Vector3 v2 = GetColumn(c2);
+        Vector3::Orthonormalize(v0, v1, v2);
+        SetColumn(c0, v0);
+        SetColumn(c1, v1);
+        SetColumn(c2, v2);
+    }
+
+    Matrix3x3::Matrix3x3(const float *data) {
+        assert(data);
+        At(0, 0) = data[0];
+        At(0, 1) = data[1];
+        At(0, 2) = data[2];
+
+        At(1, 0) = data[4];
+        At(1, 1) = data[5];
+        At(1, 2) = data[6];
+
+        At(2, 0) = data[8];
+        At(2, 1) = data[9];
+        At(2, 2) = data[10];
+    }
+
 }
 

src/J3ML/LinearAlgebra/Matrix4x4.cpp

@@ -1,5 +1,596 @@
 #include <J3ML/LinearAlgebra/Matrix4x4.h>
+#include <J3ML/LinearAlgebra/Vector4.h>
 
-namespace LinearAlgebra {
+namespace J3ML::LinearAlgebra {
+    const Matrix4x4 Matrix4x4::Zero = Matrix4x4(0.f);
+    const Matrix4x4 Matrix4x4::Identity = Matrix4x4({1,0,0,0}, {0,1,0,0}, {0,0,1,0}, {0,0,0,1});
+    const Matrix4x4 Matrix4x4::NaN = Matrix4x4(NAN);
 
+    Matrix4x4::Matrix4x4(const Vector4 &r1, const Vector4 &r2, const Vector4 &r3, const Vector4 &r4) {
+        this->elems[0][0] = r1.x;
+        this->elems[0][1] = r1.y;
+        this->elems[0][2] = r1.z;
+        this->elems[0][3] = r1.w;
+
+        this->elems[1][0] = r2.x;
+        this->elems[1][1] = r2.y;
+        this->elems[1][2] = r2.z;
+        this->elems[1][3] = r2.w;
+
+        this->elems[2][0] = r3.x;
+        this->elems[2][1] = r3.y;
+        this->elems[2][2] = r3.z;
+        this->elems[2][3] = r3.w;
+
+        this->elems[3][0] = r4.x;
+        this->elems[3][1] = r4.y;
+        this->elems[3][2] = r4.z;
+        this->elems[3][3] = r4.w;
+    }
+
+    Matrix4x4::Matrix4x4(float val) {
+        this->elems[0][0] = val;
+        this->elems[0][1] = val;
+        this->elems[0][2] = val;
+        this->elems[0][3] = val;
+
+        this->elems[1][0] = val;
+        this->elems[1][1] = val;
+        this->elems[1][2] = val;
+        this->elems[1][3] = val;
+
+        this->elems[2][0] = val;
+        this->elems[2][1] = val;
+        this->elems[2][2] = val;
+        this->elems[2][3] = val;
+
+        this->elems[3][0] = val;
+        this->elems[3][1] = val;
+        this->elems[3][2] = val;
+        this->elems[3][3] = val;
+    }
+
+    Matrix4x4::Matrix4x4(float m00, float m01, float m02, float m03, float m10, float m11, float m12, float m13,
+                         float m20, float m21, float m22, float m23, float m30, float m31, float m32, float m33) {
+        this->elems[0][0] = m00;
+        this->elems[0][1] = m01;
+        this->elems[0][2] = m02;
+        this->elems[0][3] = m03;
+
+        this->elems[1][0] = m10;
+        this->elems[1][1] = m11;
+        this->elems[1][2] = m12;
+        this->elems[1][3] = m13;
+
+        this->elems[2][0] = m20;
+        this->elems[2][1] = m21;
+        this->elems[2][2] = m22;
+        this->elems[2][3] = m23;
+
+        this->elems[3][0] = m30;
+        this->elems[3][1] = m31;
+        this->elems[3][2] = m32;
+        this->elems[3][3] = m33;
+
+    }
+
+    Matrix4x4::Matrix4x4(const Quaternion &orientation) {
+
+    }
+
+    void Matrix4x4::SetTranslatePart(float translateX, float translateY, float translateZ) {
+        elems[0][3] = translateX;
+        elems[1][3] = translateY;
+        elems[2][3] = translateZ;
+    }
+
+    void Matrix4x4::SetTranslatePart(const Vector3 &offset) {
+        elems[0][3] = offset.x;
+        elems[1][3] = offset.y;
+        elems[2][3] = offset.z;
+    }
+
+
+    void Matrix4x4::SetRotatePart(const Quaternion& q)
+    {
+        // See e.g. http://www.geometrictools.com/Documentation/LinearAlgebraicQuaternions.pdf .
+        const float x = q.x;
+        const float y = q.y;
+        const float z = q.z;
+        const float w = q.w;
+        elems[0][0] = 1 - 2*(y*y + z*z); elems[0][1] =     2*(x*y - z*w); elems[0][2] =     2*(x*z + y*w);
+        elems[1][0] =     2*(x*y + z*w); elems[1][1] = 1 - 2*(x*x + z*z); elems[1][2] =     2*(y*z - x*w);
+        elems[2][0] =     2*(x*z - y*w); elems[2][1] =     2*(y*z + x*w); elems[2][2] = 1 - 2*(x*x + y*y);
+    }
+
+    void Matrix4x4::Set3x3Part(const Matrix3x3& r)
+    {
+        At(0, 0) = r[0][0]; At(0, 1) = r[0][1]; At(0, 2) = r[0][2];
+        At(1, 0) = r[1][0]; At(1, 1) = r[1][1]; At(1, 2) = r[1][2];
+        At(2, 0) = r[2][0]; At(2, 1) = r[2][1]; At(2, 2) = r[2][2];
+    }
+
+
+
+    void Matrix4x4::SetRow(int row, const Vector3 &rowVector, float m_r3) {
+        SetRow(row, rowVector.x, rowVector.y, rowVector.z, m_r3);
+    }
+
+    void Matrix4x4::SetRow(int row, const Vector4 &rowVector) {
+        SetRow(row, rowVector.x, rowVector.y, rowVector.z, rowVector.w);
+    }
+
+    void Matrix4x4::SetRow(int row, float m_r0, float m_r1, float m_r2, float m_r3) {
+        elems[row][0] = m_r0;
+        elems[row][1] = m_r1;
+        elems[row][2] = m_r2;
+        elems[row][3] = m_r3;
+    }
+
+    Matrix4x4::Matrix4x4(const Quaternion &orientation, const Vector3 &translation) {
+        SetRotatePart(orientation);
+        SetTranslatePart(translation);
+        SetRow(3, 0, 0, 0, 1);
+    }
+
+    Matrix4x4 Matrix4x4::D3DOrthoProjLH(float n, float f, float h, float v) {
+        float p00 = 2.f / h; float p01 = 0;       float p02 = 0;           float p03 = 0.f;
+        float p10 = 0;       float p11 = 2.f / v; float p12 = 0;           float p13 = 0.f;
+        float p20 = 0;       float p21 = 0;       float p22 = 1.f / (f-n); float p23 = n / (n-f);
+        float p30 = 0;       float p31 = 0;       float p32 = 0.f;         float p33 = 1.f;
+
+        return {p00, p01, p02, p03, p10, p11, p12, p13, p20, p21, p22, p23, p30, p31, p32, p33};
+    }
+
+    /** This function generates an orthographic projection matrix that maps from
+	the Direct3D view space to the Direct3D normalized viewport space as follows:
+
+	In Direct3D view space, we assume that the camera is positioned at the origin (0,0,0).
+	The camera looks directly towards the positive Z axis (0,0,1).
+	The -X axis spans to the left of the screen, +X goes to the right.
+	-Y goes to the bottom of the screen, +Y goes to the top.
+
+	After the transformation, we're in the Direct3D normalized viewport space as follows:
+
+	(-1,-1,0) is the bottom-left corner of the viewport at the near plane.
+	(1,1,0) is the top-right corner of the viewport at the near plane.
+	(0,0,0) is the center point at the near plane.
+	Coordinates with z=1 are at the far plane.
+
+	Examples:
+		(0,0,n) maps to (0,0,0).
+		(0,0,f) maps to (0,0,1).
+		(-h/2, -v/2, n) maps to (-1, -1, 0).
+		(h/2, v/2, f) maps to (1, 1, 1).
+	*/
+    Matrix4x4 Matrix4x4::D3DOrthoProjRH(float n, float f, float h, float v)
+    {
+        // D3DOrthoProjLH and D3DOrthoProjRH differ from each other in that the third column is negated.
+        // This corresponds to LH = RH * In, where In is a diagonal matrix with elements [1 1 -1 1].
+        float p00 = 2.f / h; float p01 = 0;       float p02 = 0;           float p03 = 0.f;
+        float p10 = 0;       float p11 = 2.f / v; float p12 = 0;           float p13 = 0.f;
+        float p20 = 0;       float p21 = 0;       float p22 = 1.f / (n-f); float p23 = n / (n-f);
+        float p30 = 0;       float p31 = 0;       float p32 = 0.f;         float p33 = 1.f;
+    }
+
+    float Matrix4x4::At(int x, int y) const {
+        return elems[x][y];
+    }
+
+    Matrix4x4 Matrix4x4::operator*(const Matrix4x4 &rhs) const {
+
+        float r00 = At(0, 0) * rhs.At(0, 0) + At(0, 1) * rhs.At(1, 0) + At(0, 2) * rhs.At(2, 0) + At(0, 3) * rhs.At(3, 0);
+        float r01 = At(0, 0) * rhs.At(0, 1) + At(0, 1) * rhs.At(1, 1) + At(0, 2) * rhs.At(2, 1) + At(0, 3) * rhs.At(3, 1);
+        float r02 = At(0, 0) * rhs.At(0, 2) + At(0, 1) * rhs.At(1, 2) + At(0, 2) * rhs.At(2, 2) + At(0, 3) * rhs.At(3, 2);
+        float r03 = At(0, 0) * rhs.At(0, 3) + At(0, 1) * rhs.At(1, 3) + At(0, 2) * rhs.At(2, 3) + At(0, 3) * rhs.At(3, 3);
+
+        float r10 = At(1, 0) * rhs.At(0, 0) + At(1, 1) * rhs.At(1, 0) + At(1, 2) * rhs.At(2, 0) + At(1, 3) * rhs.At(3, 0);
+        float r11 = At(1, 0) * rhs.At(0, 1) + At(1, 1) * rhs.At(1, 1) + At(1, 2) * rhs.At(2, 1) + At(1, 3) * rhs.At(3, 1);
+        float r12 = At(1, 0) * rhs.At(0, 2) + At(1, 1) * rhs.At(1, 2) + At(1, 2) * rhs.At(2, 2) + At(1, 3) * rhs.At(3, 2);
+        float r13 = At(1, 0) * rhs.At(0, 3) + At(1, 1) * rhs.At(1, 3) + At(1, 2) * rhs.At(2, 3) + At(1, 3) * rhs.At(3, 3);
+
+        float r20 = At(2, 0) * rhs.At(0, 0) + At(2, 1) * rhs.At(1, 0) + At(2, 2) * rhs.At(2, 0) + At(2, 3) * rhs.At(3, 0);
+        float r21 = At(2, 0) * rhs.At(0, 1) + At(2, 1) * rhs.At(1, 1) + At(2, 2) * rhs.At(2, 1) + At(2, 3) * rhs.At(3, 1);
+        float r22 = At(2, 0) * rhs.At(0, 2) + At(2, 1) * rhs.At(1, 2) + At(2, 2) * rhs.At(2, 2) + At(2, 3) * rhs.At(3, 2);
+        float r23 = At(2, 0) * rhs.At(0, 3) + At(2, 1) * rhs.At(1, 3) + At(2, 2) * rhs.At(2, 3) + At(2, 3) * rhs.At(3, 3);
+
+        float r30 = At(3, 0) * rhs.At(0, 0) + At(3, 1) * rhs.At(1, 0) + At(3, 2) * rhs.At(2, 0) + At(3, 3) * rhs.At(3, 0);
+        float r31 = At(3, 0) * rhs.At(0, 1) + At(3, 1) * rhs.At(1, 1) + At(3, 2) * rhs.At(2, 1) + At(3, 3) * rhs.At(3, 1);
+        float r32 = At(3, 0) * rhs.At(0, 2) + At(3, 1) * rhs.At(1, 2) + At(3, 2) * rhs.At(2, 2) + At(3, 3) * rhs.At(3, 2);
+        float r33 = At(3, 0) * rhs.At(0, 3) + At(3, 1) * rhs.At(1, 3) + At(3, 2) * rhs.At(2, 3) + At(3, 3) * rhs.At(3, 3);
+        return {r00,r01,r02,r03, r10, r11, r12, r13, r20,r21,r22,r23, r30,r31,r32,r33};
+    }
+
+    Vector4 Matrix4x4::operator[](int row) {
+        return Vector4{elems[row][0], elems[row][1], elems[row][2], elems[row][3]};
+    }
+
+    Matrix4x4 Matrix4x4::operator*(const Matrix3x3 &rhs) const {
+        float r00 = At(0, 0) * rhs.At(0, 0) + At(0, 1) * rhs.At(1, 0) + At(0, 2) * rhs.At(2, 0);
+        float r01 = At(0, 0) * rhs.At(0, 1) + At(0, 1) * rhs.At(1, 1) + At(0, 2) * rhs.At(2, 1);
+        float r02 = At(0, 0) * rhs.At(0, 2) + At(0, 1) * rhs.At(1, 2) + At(0, 2) * rhs.At(2, 2);
+        float r03 = At(0, 3);
+
+        float r10 = At(1, 0) * rhs.At(0, 0) + At(1, 1) * rhs.At(1, 0) + At(1, 2) * rhs.At(2, 0);
+        float r11 = At(1, 0) * rhs.At(0, 1) + At(1, 1) * rhs.At(1, 1) + At(1, 2) * rhs.At(2, 1);
+        float r12 = At(1, 0) * rhs.At(0, 2) + At(1, 1) * rhs.At(1, 2) + At(1, 2) * rhs.At(2, 2);
+        float r13 = At(1, 3);
+
+        float r20 = At(2, 0) * rhs.At(0, 0) + At(2, 1) * rhs.At(1, 0) + At(2, 2) * rhs.At(2, 0);
+        float r21 = At(2, 0) * rhs.At(0, 1) + At(2, 1) * rhs.At(1, 1) + At(2, 2) * rhs.At(2, 1);
+        float r22 = At(2, 0) * rhs.At(0, 2) + At(2, 1) * rhs.At(1, 2) + At(2, 2) * rhs.At(2, 2);
+        float r23 = At(2, 3);
+
+        float r30 = At(3, 0) * rhs.At(0, 0) + At(3, 1) * rhs.At(1, 0) + At(3, 2) * rhs.At(2, 0);
+        float r31 = At(3, 0) * rhs.At(0, 1) + At(3, 1) * rhs.At(1, 1) + At(3, 2) * rhs.At(2, 1);
+        float r32 = At(3, 0) * rhs.At(0, 2) + At(3, 1) * rhs.At(1, 2) + At(3, 2) * rhs.At(2, 2);
+        float r33 = At(3, 3);
+
+        return {r00,r01,r02,r03, r10, r11, r12, r13, r20,r21,r22,r23, r30,r31,r32,r33};
+    }
+
+    Matrix4x4 Matrix4x4::operator+() const { return *this; }
+
+    Matrix4x4 Matrix4x4::FromTranslation(const Vector3 &rhs) {
+        return Matrix4x4(1.f, 0, 0, rhs.x,
+                         0, 1.f, 0, rhs.y,
+                         0, 0, 1.f, rhs.z,
+                         0, 0, 0,     1.f);
+    }
+
+    Matrix4x4 Matrix4x4::Translate(const Vector3 &rhs) const {
+        return *this * FromTranslation(rhs);
+    }
+
+    Vector3 Matrix4x4::Transform(const Vector3 &rhs) const {
+        return Transform(rhs.x, rhs.y, rhs.z);
+    }
+
+    Vector3 Matrix4x4::Transform(float tx, float ty, float tz) const {
+        return Vector3(At(0, 0) * tx + At(0, 1) * ty + At(0, 2) * tz + At(0, 3),
+                       At(1, 0) * tx + At(1, 1) * ty + At(1, 2) * tz + At(1, 3),
+                       At(2, 0) * tx + At(2, 1) * ty + At(2, 2) * tz + At(2, 3));
+    }
+
+    Vector2 Matrix4x4::Transform(float tx, float ty) const {
+        return Vector2(At(0, 0) * tx + At(0, 1) * ty + At(0, 2) + At(0, 3),
+                       At(1, 0) * tx + At(1, 1) * ty + At(1, 2) + At(1, 3));
+    }
+
+    Vector2 Matrix4x4::Transform(const Vector2 &rhs) const {
+        return Transform(rhs.x, rhs.y);
+    }
+
+    Matrix4x4 &Matrix4x4::operator=(const Matrix3x3 &rhs) {
+        Set3x3Part(rhs);
+        SetTranslatePart(0,0,0);
+        SetRow(3, 0, 0, 0, 1);
+        return *this;
+    }
+
+    Matrix4x4 &Matrix4x4::operator=(const Quaternion &rhs) {
+        *this = rhs.ToMatrix4x4();
+        return *this;
+    }
+
+    float &Matrix4x4::At(int row, int col) {
+        return elems[row][col];
+    }
+
+    Matrix4x4 Matrix4x4::Inverse() const {
+        // Compute the inverse directly using Cramer's rule
+        // Warning: This method is numerically very unstable!
+        float d = Determinant();
+
+        d = 1.f / d;
+
+        float a11 = At(0, 0);float a12 = At(0, 1);float a13 = At(0, 2);float a14 = At(0, 3);
+        float a21 = At(1, 0);float a22 = At(1, 1);float a23 = At(1, 2);float a24 = At(1, 3);
+        float a31 = At(2, 0);float a32 = At(2, 1);float a33 = At(2, 2);float a34 = At(2, 3);
+        float a41 = At(3, 0);float a42 = At(3, 1);float a43 = At(3, 2);float a44 = At(3, 3);
+
+        Matrix4x4 i = {
+                d * (a22*a33*a44 + a23*a34*a42 + a24*a32*a43 - a22*a34*a43 - a23*a32*a44 - a24*a33*a42),
+                d * (a12*a34*a43 + a13*a32*a44 + a14*a33*a42 - a12*a33*a44 - a13*a34*a42 - a14*a32*a43),
+                d * (a12*a23*a44 + a13*a24*a42 + a14*a22*a43 - a12*a24*a43 - a13*a22*a44 - a14*a23*a42),
+                d * (a12*a24*a33 + a13*a22*a34 + a14*a23*a32 - a12*a23*a34 - a13*a24*a32 - a14*a22*a33),
+                d * (a21*a34*a43 + a23*a31*a44 + a24*a33*a41 - a21*a33*a44 - a23*a34*a41 - a24*a31*a43),
+                d * (a11*a33*a44 + a13*a34*a41 + a14*a31*a43 - a11*a34*a43 - a13*a31*a44 - a14*a33*a41),
+                d * (a11*a24*a43 + a13*a21*a44 + a14*a23*a41 - a11*a23*a44 - a13*a24*a41 - a14*a21*a43),
+                d * (a11*a23*a34 + a13*a24*a31 + a14*a21*a33 - a11*a24*a33 - a13*a21*a34 - a14*a23*a31),
+                d * (a21*a32*a44 + a22*a34*a41 + a24*a31*a42 - a21*a34*a42 - a22*a31*a44 - a24*a32*a41),
+                d * (a11*a34*a42 + a12*a31*a44 + a14*a32*a41 - a11*a32*a44 - a12*a34*a41 - a14*a31*a42),
+                d * (a11*a22*a44 + a12*a24*a41 + a14*a21*a42 - a11*a24*a42 - a12*a21*a44 - a14*a22*a41),
+                d * (a11*a24*a32 + a12*a21*a34 + a14*a22*a31 - a11*a22*a34 - a12*a24*a31 - a14*a21*a32),
+                d * (a21*a33*a42 + a22*a31*a43 + a23*a32*a41 - a21*a32*a43 - a22*a33*a41 - a23*a31*a42),
+                d * (a11*a32*a43 + a12*a33*a41 + a13*a31*a42 - a11*a33*a42 - a12*a31*a43 - a13*a32*a41),
+                d * (a11*a23*a42 + a12*a21*a43 + a13*a22*a41 - a11*a22*a43 - a12*a23*a41 - a13*a21*a42),
+                d * (a11*a22*a33 + a12*a23*a31 + a13*a21*a32 - a11*a23*a32 - a12*a21*a33 - a13*a22*a31)
+        };
+        return i;
+    }
+
+    float Matrix4x4::Minor(int i, int j) const {
+        int r0 = SKIPNUM(0, i);
+        int r1 = SKIPNUM(1, i);
+        int r2 = SKIPNUM(2, i);
+        int c0 = SKIPNUM(0, j);
+        int c1 = SKIPNUM(1, j);
+        int c2 = SKIPNUM(2, j);
+
+        float a = At(r0, c0);
+        float b = At(r0, c1);
+        float c = At(r0, c2);
+        float d = At(r1, c0);
+        float e = At(r1, c1);
+        float f = At(r1, c2);
+        float g = At(r2, c0);
+        float h = At(r2, c1);
+        float k = At(r2, c2);
+
+        return a*e*k + b*f*g + c*d*h - a*f*h - b*d*k - c*e*g;
+    }
+
+    float Matrix4x4::Determinant() const {
+        return At(0, 0) * Minor(0,0) - At(0, 1) * Minor(0,1) + At(0, 2) * Minor(0,2) - At(0, 3) * Minor(0,3);
+    }
+
+    float Matrix4x4::Determinant3x3() const {
+
+        const float a = elems[0][0];
+        const float b = elems[0][1];
+        const float c = elems[0][2];
+        const float d = elems[1][0];
+        const float e = elems[1][1];
+        const float f = elems[1][2];
+        const float g = elems[2][0];
+        const float h = elems[2][1];
+        const float i = elems[2][2];
+
+        return a*e*i + b*f*g + c*d*h - a*f*h - b*d*i - c*e*g;
+    }
+
+    Matrix3x3 Matrix4x4::GetRotatePart() const {
+        return Matrix3x3 {
+                At(0, 0), At(0, 1), At(0, 2),
+                At(1, 0), At(1, 1), At(1, 2),
+                At(2, 0), At(2, 1), At(2, 2)
+        };
+    }
+
+    Matrix4x4 Matrix4x4::Transpose() const {
+        Matrix4x4 copy;
+        copy.elems[0][0] = elems[0][0]; copy.elems[0][1] = elems[1][0]; copy.elems[0][2] = elems[2][0]; copy.elems[0][3] = elems[3][0];
+        copy.elems[1][0] = elems[0][1]; copy.elems[1][1] = elems[1][1]; copy.elems[1][2] = elems[2][1]; copy.elems[1][3] = elems[3][1];
+        copy.elems[2][0] = elems[0][2]; copy.elems[2][1] = elems[1][2]; copy.elems[2][2] = elems[2][2]; copy.elems[2][3] = elems[3][2];
+        copy.elems[3][0] = elems[0][3]; copy.elems[3][1] = elems[1][3]; copy.elems[3][2] = elems[2][3]; copy.elems[3][3] = elems[3][3];
+        return copy;
+    }
+
+    Vector4 Matrix4x4::Diagonal() const {
+        return Vector4{At(0, 0), At(1,1), At(2,2), At(3,3)};
+    }
+
+    Vector3 Matrix4x4::Diagonal3() const {
+        return Vector3 { At(0, 0), At(1,1), At(2,2) };
+    }
+
+    Vector3 Matrix4x4::WorldX() const {
+        return GetColumn3(0);
+    }
+
+    Vector3 Matrix4x4::WorldY() const {
+        return GetColumn3(1);
+    }
+
+    Vector3 Matrix4x4::WorldZ() const {
+        return GetColumn3(2);
+    }
+
+    bool Matrix4x4::IsFinite() const {
+        for(int iy = 0; iy < Rows; ++iy)
+            for(int ix = 0; ix < Cols; ++ix)
+                if (!std::isfinite(elems[iy][ix]))
+                    return false;
+        return true;
+    }
+
+    Vector3 Matrix4x4::GetColumn3(int index) const {
+        return Vector3{At(0, index), At(1, index), At(2, index)};
+    }
+
+    Vector2 Matrix4x4::operator*(const Vector2 &rhs) const { return this->Transform(rhs);}
+
+    Vector3 Matrix4x4::operator*(const Vector3 &rhs) const { return this->Transform(rhs);}
+
+    Vector4 Matrix4x4::operator*(const Vector4 &rhs) const { return this->Transform(rhs);}
+
+    Vector4 Matrix4x4::Transform(float tx, float ty, float tz, float tw) const {
+        return Transform({tx, ty, tz, tw});
+    }
+
+    Vector4 Matrix4x4::Transform(const Vector4 &rhs) const {
+        return Vector4(At(0, 0) * rhs.x + At(0, 1) * rhs.y + At(0, 2) * rhs.z + At(0, 3) * rhs.w,
+                       At(1, 0) * rhs.x + At(1, 1) * rhs.y + At(1, 2) * rhs.z + At(1, 3) * rhs.w,
+                       At(2, 0) * rhs.x + At(2, 1) * rhs.y + At(2, 2) * rhs.z + At(2, 3) * rhs.w,
+                       At(3, 0) * rhs.x + At(3, 1) * rhs.y + At(3, 2) * rhs.z + At(3, 3) * rhs.w);
+    }
+
+    Vector3 Matrix4x4::GetTranslatePart() const {
+        return GetColumn3(3);
+    }
+
+    Matrix4x4 Matrix4x4::Scale(const Vector3& scale)
+    {
+        auto mat = *this;
+
+        mat.At(3, 0) *= scale.x;
+        mat.At(3, 1) *= scale.y;
+        mat.At(3, 2) *= scale.z;
+        return mat;
+    }
+
+    Matrix4x4
+    Matrix4x4::LookAt(const Vector3 &localFwd, const Vector3 &targetDir, const Vector3 &localUp, const Vector3 &worldUp) {
+        Matrix4x4 m;
+        m.Set3x3Part(Matrix3x3::LookAt(localFwd, targetDir, localUp, worldUp));
+        m.SetTranslatePart(0,0,0);
+        m.SetRow(3, 0,0,0,1);
+        return m;
+    }
+
+    Vector4 Matrix4x4::GetRow(int index) const {
+        return { At(index, 0), At(index, 1), At(index, 2), At(index, 3)};
+    }
+
+    Vector4 Matrix4x4::GetColumn(int index) const {
+        return { At(0, index), At(1, index), At(2, index), At(3, index)};
+    }
+
+    Vector3 Matrix4x4::GetRow3(int index) const {
+        return Vector3{ At(index, 0), At(index, 1), At(index, 2)};
+    }
+
+    void Matrix4x4::SwapColumns(int col1, int col2) {
+        Swap(At(0, col1), At(0, col2));
+        Swap(At(1, col1), At(1, col2));
+        Swap(At(2, col1), At(2, col2));
+        Swap(At(3, col1), At(3, col2));
+    }
+
+    void Matrix4x4::SwapRows(int row1, int row2) {
+        Swap(At(row1, 0), At(row2, 0));
+        Swap(At(row1, 1), At(row2, 1));
+        Swap(At(row1, 2), At(row2, 2));
+        Swap(At(row1, 3), At(row2, 3));
+    }
+
+    void Matrix4x4::SwapRows3(int row1, int row2) {
+        Swap(At(row1, 0), At(row2, 0));
+        Swap(At(row1, 1), At(row2, 1));
+        Swap(At(row1, 2), At(row2, 2));
+    }
+
+    void Matrix4x4::Pivot() {
+        int rowIndex = 0;
+
+        for(int col = 0; col < Cols; ++col)
+        {
+            int greatest = rowIndex;
+
+            // find the rowIndex k with k >= 1 for which Mkj has the largest absolute value.
+            for(int i = rowIndex; i < Rows; ++i)
+                if (std::abs(At(i, col)) > std::abs(At(greatest, col)))
+                    greatest = i;
+
+            if (std::abs(At(greatest, col)) != 0)
+            {
+                if (rowIndex != greatest)
+                    SwapRows(rowIndex, greatest); // the greatest now in rowIndex
+
+                ScaleRow(rowIndex, 1.f/At(rowIndex, col));
+
+                for(int r = 0; r < Rows; ++r)
+                    if (r != rowIndex)
+                        SetRow(r, GetRow(r) - GetRow(rowIndex) * At(r, col));
+
+                ++rowIndex;
+            }
+        }
+    }
+
+    void Matrix4x4::ScaleColumn3(int col, float scalar) {
+        At(0, col) *= scalar;
+        At(1, col) *= scalar;
+        At(2, col) *= scalar;
+    }
+
+    void Matrix4x4::ScaleColumn(int col, float scalar) {
+        At(0, col) *= scalar;
+        At(1, col) *= scalar;
+        At(2, col) *= scalar;
+        At(3, col) *= scalar;
+    }
+
+    void Matrix4x4::ScaleRow3(int row, float scalar) {
+        At(row, 0) *= scalar;
+        At(row, 1) *= scalar;
+        At(row, 2) *= scalar;
+    }
+
+    void Matrix4x4::ScaleRow(int row, float scalar) {
+        At(row, 0) *= scalar;
+        At(row, 1) *= scalar;
+        At(row, 2) *= scalar;
+        At(row, 3) *= scalar;
+    }
+
+    Matrix4x4 Matrix4x4::OpenGLOrthoProjLH(float n, float f, float h, float v) {
+        /// Same as OpenGLOrthoProjRH, except that the camera looks towards +Z in view space, instead of -Z.
+        using f32 = float;
+        f32 p00 = 2.f / h; f32 p01 = 0;           f32 p02 = 0;       float p03 = 0.f;
+        f32 p10 = 0;       f32 p11 = 2.f / v; f32 p12 = 0;           float p13 = 0.f;
+        f32 p20 = 0;       f32 p21 = 0;       f32 p22 = 2.f / (f-n); float p23 = (f+n) / (n-f);
+        f32 p30 = 0;       f32 p31 = 0;       f32 p32 = 0;           float p33 = 1.f;
+
+        return {p00, p01, p02, p03, p10, p11, p12, p13, p20, p21, p22, p23, p30, p31, p32, p33};
+
+    }
+
+    Matrix4x4 Matrix4x4::OpenGLOrthoProjRH(float n, float f, float h, float v) {
+        using f32 = float;
+        f32 p00 = 2.f / h; f32 p01 = 0;       f32 p02 = 0;           f32 p03 = 0.f;
+        f32 p10 = 0;       f32 p11 = 2.f / v; f32 p12 = 0;           f32 p13 = 0.f;
+        f32 p20 = 0;       f32 p21 = 0;       f32 p22 = 2.f / (n-f); f32 p23 = (f+n) / (n-f);
+        f32 p30 = 0;       f32 p31 = 0;       f32 p32 = 0;           f32 p33 = 1.f;
+
+        return {p00, p01, p02, p03, p10, p11, p12, p13, p20, p21, p22, p23, p30, p31, p32, p33};
+    }
+
+    Matrix4x4 Matrix4x4::OpenGLPerspProjLH(float n, float f, float h, float v) {
+        // Same as OpenGLPerspProjRH, except that the camera looks towards +Z in view space, instead of -Z.
+        using f32 = float;
+        f32 p00 = 2.f *n / h;  f32 p01 = 0;           f32 p02 = 0;              f32 p03 = 0.f;
+        f32 p10 = 0;           f32 p11 = 2.f * n / v; f32 p12 = 0;              f32 p13 = 0.f;
+        f32 p20 = 0;           f32 p21 = 0;           f32 p22 = (n+f) / (f-n);  f32 p23 = 2.f*n*f / (n-f);
+        f32 p30 = 0;           f32 p31 = 0;           f32 p32 = 1.f;            f32 p33 = 0.f;
+
+        return {p00, p01, p02, p03, p10, p11, p12, p13, p20, p21, p22, p23, p30, p31, p32, p33};
+    }
+
+    Matrix4x4 Matrix4x4::OpenGLPerspProjRH(float n, float f, float h, float v) {
+        // In OpenGL, the post-perspective unit cube ranges in [-1, 1] in all X, Y and Z directions.
+        // See http://www.songho.ca/opengl/gl_projectionmatrix.html , unlike in Direct3D, where the
+        // Z coordinate ranges in [0, 1]. This is the only difference between D3DPerspProjRH and OpenGLPerspProjRH.
+        using f32 = float;
+        float p00 = 2.f *n / h;  float p01 = 0;           float p02 = 0;              float p03 = 0.f;
+        float p10 = 0;           float p11 = 2.f * n / v; float p12 = 0;              float p13 = 0.f;
+        float p20 = 0;           float p21 = 0;           float p22 = (n+f) / (n-f);  float p23 = 2.f*n*f / (n-f);
+        float p30 = 0;           float p31 = 0;           float p32 = -1.f;           float p33 = 0.f;
+
+        return {p00, p01, p02, p03, p10, p11, p12, p13, p20, p21, p22, p23, p30, p31, p32, p33};
+    }
+
+    Matrix4x4::Matrix4x4(const float *data) {
+        assert(data);
+        At(0, 0) = data[0];
+        At(0, 1) = data[1];
+        At(0, 2) = data[2];
+        At(0, 3) = data[3];
+
+        At(1, 0) = data[4];
+        At(1, 1) = data[5];
+        At(1, 2) = data[6];
+        At(1, 3) = data[7];
+
+        At(2, 0) = data[8];
+        At(2, 1) = data[9];
+        At(2, 2) = data[10];
+        At(2, 3) = data[11];
+
+        At(3, 0) = data[12];
+        At(3, 1) = data[13];
+        At(3, 2) = data[14];
+        At(3, 3) = data[15];
+    }
 }

src/J3ML/LinearAlgebra/Quaternion.cpp

@@ -1,9 +1,10 @@
 #include <J3ML/LinearAlgebra/Vector3.h>
 #include <J3ML/LinearAlgebra/Vector4.h>
 #include <J3ML/LinearAlgebra/Matrix3x3.h>
+#include <J3ML/LinearAlgebra/Matrix4x4.h>
 #include <J3ML/LinearAlgebra/Quaternion.h>
 
-namespace LinearAlgebra {
+namespace J3ML::LinearAlgebra {
     Quaternion Quaternion::operator-() const
     {
         return {-x, -y, -z, -w};
@@ -46,7 +47,18 @@ namespace LinearAlgebra {
 
     void Quaternion::SetFromAxisAngle(const Vector3 &axis, float angle) {
         float sinz, cosz;
+        sinz = std::sin(angle*0.5f);
+        cosz = std::cos(angle*0.5f);
 
+        x = axis.x * sinz;
+        y = axis.y * sinz;
+        z = axis.z * sinz;
+        w = cosz;
+    }
+
+    void Quaternion::SetFromAxisAngle(const Vector4 &axis, float angle)
+    {
+        SetFromAxisAngle(Vector3(axis.x, axis.y, axis.z), angle);
     }
 
     Quaternion Quaternion::operator*(float scalar) const {
@@ -60,16 +72,14 @@ namespace LinearAlgebra {
     Quaternion::Quaternion(float X, float Y, float Z, float W) : Vector4(X,Y,Z,W) {}
 
     // TODO: implement
-    float Quaternion::Dot(const Quaternion &quaternion) const {}
+    float Quaternion::Dot(const Quaternion &rhs) const {
+        return x * rhs.x + y * rhs.y + z * rhs.z + w * rhs.w;
+    }
 
     Quaternion::Quaternion(Vector4 vector4) {
 
     }
 
-    float Quaternion::Angle() const {
-        return std::acos(w) * 2.f;
-    }
-
     Quaternion Quaternion::Normalize() const {
         float length = Length();
         if (length < 1e-4f)
@@ -165,4 +175,30 @@ namespace LinearAlgebra {
                 x + rhs.x, y + rhs.y, z + rhs.z,w + rhs.w
         };
     }
+
+    Matrix4x4 Quaternion::ToMatrix4x4() const {
+        return Matrix4x4(*this);
+    }
+
+    Matrix4x4 Quaternion::ToMatrix4x4(const Vector3 &translation) const {
+        return {*this, translation};
+    }
+
+    float Quaternion::GetAngle() const {
+        return std::acos(w) * 2.f;
+    }
+
+    Vector3 Quaternion::GetAxis() const {
+        float rcpSinAngle = 1 - (std::sqrt(1 - w * w));
+
+        return Vector3(x, y, z) * rcpSinAngle;
+    }
+
+    Quaternion::Quaternion(const Vector3 &rotationAxis, float rotationAngleBetween) {
+        SetFromAxisAngle(rotationAxis, rotationAngleBetween);
+    }
+
+    Quaternion::Quaternion(const Vector4 &rotationAxis, float rotationAngleBetween) {
+        SetFromAxisAngle(rotationAxis, rotationAngleBetween);
+    }
 }

src/J3ML/LinearAlgebra/Transform2D.cpp

@@ -1,5 +1,30 @@
 #include <J3ML/LinearAlgebra/Transform2D.h>
 
-namespace LinearAlgebra {
+namespace J3ML::LinearAlgebra {
 
+    const Transform2D Transform2D::Identity = Transform2D({0, 0}, {1, 1}, {0,0}, {0,0}, 0);
+    const Transform2D Transform2D::FlipX    = Transform2D({0, 0}, {-1, 1}, {0,0}, {0,0}, 0);
+    const Transform2D Transform2D::FlipY    = Transform2D({0, 0}, {1, -1}, {0,0}, {0,0}, 0);
+
+
+    Vector2 Transform2D::Transform(const Vector2 &input) const {
+        return transformation.Transform(input);
+    }
+
+    Transform2D::Transform2D(const Matrix3x3 &transform) : transformation(transform) { }
+
+    Transform2D::Transform2D(const Vector2& pos, const Vector2& scale, const Vector2& origin, const Vector2& skew, float rotation) {
+        transformation = Matrix3x3(pos.x, pos.y, rotation, scale.x, scale.y, origin.x, origin.y, skew.x, skew.y);
+    }
+
+    Transform2D Transform2D::Translate(float x, float y) const {
+        auto copy = Matrix3x3(transformation);
+        copy.SetAt(0, 0, transformation.At(0, 0) + x);
+        copy.SetAt(0, 1, transformation.At(0, 1) + y);
+        return Transform2D(copy);
+    }
+
+    Transform2D Transform2D::Translate(const LinearAlgebra::Vector2 &input) const {
+        return Translate(input.x, input.y);
+    }
 }

src/J3ML/LinearAlgebra/Vector2.cpp

@@ -4,7 +4,7 @@
 #include <valarray>
 #include <iostream>
 
-namespace LinearAlgebra {
+namespace J3ML::LinearAlgebra {
 
     Vector2::Vector2(): x(0), y(0)
     {}
@@ -15,12 +15,14 @@ namespace LinearAlgebra {
     Vector2::Vector2(const Vector2& rhs): x(rhs.x), y(rhs.y)
     {}
 
-    float Vector2::operator[](std::size_t index)
+    float Vector2::operator[](std::size_t index) const
     {
-        assert(index < 2);
-        if (index == 0) return x;
-        if (index == 1) return y;
-        return 0;
+        return At(index);
+    }
+
+    float &Vector2::operator[](std::size_t index)
+    {
+        return At(index);
     }
 
     bool Vector2::IsWithinMarginOfError(const Vector2& rhs, float margin) const
@@ -116,7 +118,6 @@ namespace LinearAlgebra {
     {
         auto numer = this->Dot(rhs);
         auto denom = this->Magnitude() * rhs.Magnitude();
-        std::cout << numer << ", " << denom << std::endl;
         return std::acos(numer / denom);
     }
 
@@ -160,6 +161,7 @@ namespace LinearAlgebra {
     const Vector2 Vector2::Left  = {-1, 0};
     const Vector2 Vector2::Right = {1, 0};
     const Vector2 Vector2::NaN = {NAN, NAN};
+    const Vector2 Vector2::Infinity = {INFINITY, INFINITY};
 
     float Vector2::GetX() const { return x; }
 
@@ -232,5 +234,103 @@ namespace LinearAlgebra {
         return *this / scalar;
     }
 
+    bool Vector2::IsFinite(const Vector2 &v) {
+        return v.IsFinite();
+    }
 
+    float Vector2::MinElement() const {
+        return std::min(x, y);
+    }
+
+    float Vector2::MaxElement() const {
+        return std::max(x, y);
+    }
+
+    Vector2 Vector2::Mul(const Vector2 &v) const {
+        return {this->x*v.x, this->y*v.y};
+    }
+
+    bool Vector2::IsFinite() const {
+        return std::isfinite(x) && std::isfinite(y);
+    }
+
+    Vector2 Vector2::Div(const Vector2 &v) const {
+        return {this->x/v.x, this->y/v.y};
+    }
+
+    Vector2 Vector2::Abs() const { return {std::abs(x), std::abs(y)};}
+
+    float *Vector2::ptr() {
+        return &x;
+    }
+
+    const float *Vector2::ptr() const { return &x;}
+
+    const float Vector2::At(std::size_t index) const {
+        assert(index >= 0);
+        assert(index < Dimensions);
+        return ptr()[index];
+    }
+
+    float &Vector2::At(std::size_t index) {
+        assert(index >= 0);
+        assert(index < Dimensions);
+        return ptr()[index];
+    }
+
+    Vector2 &Vector2::operator/=(float scalar) {
+        x /= scalar;
+        y /= scalar;
+
+        return *this;
+    }
+
+    Vector2 &Vector2::operator*=(float scalar) {
+        x *= scalar;
+        y *= scalar;
+
+        return *this;
+    }
+
+    Vector2 &Vector2::operator-=(const Vector2 &rhs) // Subtracts a vector from this vector, in-place
+    {
+        x -= rhs.x;
+        y -= rhs.y;
+
+        return *this;
+    }
+
+    Vector2 &Vector2::operator+=(const Vector2 &rhs) // Adds a vector to this vector, in-place.
+    {
+        x += rhs.x;
+        y += rhs.y;
+
+        return *this;
+    }
+
+    Vector2 &Vector2::operator=(const Vector2 &rhs) {
+        x = rhs.x;
+        y = rhs.y;
+
+        return *this;
+    }
+
+    Vector2::Vector2(const float *data) {
+        assert(data);
+        x = data[0];
+        y = data[1];
+    }
+
+    Vector2::Vector2(float scalar) {
+        x = scalar;
+        y = scalar;
+    }
+
+    float Vector2::DistanceSq(const Vector2 &to) const {
+        return (*this-to).LengthSquared();
+    }
+
+    float Vector2::DistanceSq(const Vector2 &from, const Vector2 &to) {
+        return (from-to).LengthSquared();
+    }
 }

src/J3ML/LinearAlgebra/Vector3.cpp

@@ -3,9 +3,7 @@
 #include <cassert>
 #include <cmath>
 
-namespace LinearAlgebra {
-
-#pragma region vector3
+namespace J3ML::LinearAlgebra {
 
     const Vector3 Vector3::Zero     = {0,0,0};
     const Vector3 Vector3::Up       = {0, -1, 0};
@@ -15,6 +13,8 @@ namespace LinearAlgebra {
     const Vector3 Vector3::Forward  = {0, 0, -1};
     const Vector3 Vector3::Backward = {0, 0, 1};
     const Vector3 Vector3::NaN      = {NAN, NAN, NAN};
+    const Vector3 Vector3::Infinity = {INFINITY, INFINITY, INFINITY};
+    const Vector3 Vector3::NegativeInfinity = {-INFINITY, -INFINITY, -INFINITY};
 
     Vector3 Vector3::operator+(const Vector3& rhs) const
     {
@@ -80,6 +80,14 @@ namespace LinearAlgebra {
         return 0;
     }
 
+    float &Vector3::operator[](std::size_t index)
+    {
+        assert(index < 3);
+        if (index == 0) return x;
+        if (index == 1) return y;
+        if (index == 2) return z;
+    }
+
     bool Vector3::IsWithinMarginOfError(const Vector3& rhs, float margin) const
     {
         return this->Distance(rhs) <= margin;
@@ -269,7 +277,7 @@ namespace LinearAlgebra {
     }
 
     Vector3 Vector3::Sub(const Vector3 &lhs, const Vector3 &rhs) {
-        lhs.Sub(rhs);
+        return lhs.Sub(rhs);
     }
 
     Vector3 Vector3::Mul(float scalar) const {
@@ -288,5 +296,114 @@ namespace LinearAlgebra {
         return lhs.Div(rhs);
     }
 
-#pragma endregion
+    Angle2D Vector3::AngleBetween(const Vector3 &rhs) const {
+        const auto Pi_x_180 = 180.f / M_PI;
+        auto dist = this->Distance(rhs);
+        float x = -(asinf((rhs.y - this->y) / dist));
+        float y = (atan2f(rhs.x - this->x,rhs.z - this->z));
+        return {x, y};
+    }
+
+    Angle2D Vector3::AngleBetween(const Vector3 &lhs, const Vector3 &rhs) // TODO: 3D Angle representation?
+    {
+        return lhs.AngleBetween(rhs);
+    }
+
+    Vector3 Vector3::Direction(const Vector3 &rhs) {
+        float x = (cos(Math::Radians(rhs.y)) * cos(Math::Radians(rhs.x)));
+        float y = -sin(Math::Radians(rhs.x));
+        float z = (sin(Math::Radians(rhs.y)) * cos(Math::Radians(rhs.x)));
+        return {x, y, z};
+    }
+
+    Vector3 Vector3::Abs() const {
+        return {std::abs(x), std::abs(y), std::abs(z)};
+    }
+
+    float *Vector3::ptr() {
+        return &x;
+    }
+
+    void Vector3::Orthonormalize(Vector3 &a, Vector3 &b) {
+        a = a.Normalize();
+        b = b - b.ProjectToNorm(a);
+        b = b.Normalize();
+    }
+
+    void Vector3::Orthonormalize(Vector3 &a, Vector3 &b, Vector3 &c) {
+        a = a.Normalize();
+        b = b - b.ProjectToNorm(a);
+        b = b.Normalize();
+        c = c - c.ProjectToNorm(a);
+        c = c - c.ProjectToNorm(b);
+        c = c.Normalize();
+    }
+
+    Vector3 Vector3::ProjectToNorm(const Vector3 &direction) const {
+        return direction * this->Dot(direction);
+    }
+
+    bool Vector3::IsFinite() const {
+        return std::isfinite(x) && std::isfinite(y) && std::isfinite(z);
+    }
+
+    Vector3::Vector3(const float *data) {
+        x = data[0];
+        y = data[1];
+        z = data[2];
+    }
+
+    Vector3 &Vector3::operator+=(const Vector3 &rhs) {
+        x += rhs.x;
+        y += rhs.y;
+        z += rhs.z;
+        return *this;
+    }
+
+    Vector3 &Vector3::operator-=(const Vector3 &rhs) {
+        x -= rhs.x;
+        y -= rhs.y;
+        z -= rhs.z;
+        return *this;
+    }
+
+    Vector3 &Vector3::operator*=(float scalar) {
+        x *= scalar;
+        y *= scalar;
+        z *= scalar;
+        return *this;
+    }
+
+    Vector3 &Vector3::operator/=(float scalar) {
+        x /= scalar;
+        y /= scalar;
+        z /= scalar;
+        return *this;
+    }
+
+    float Vector3::MinElement() const {
+        return std::min(x, std::min(y, z));
+    }
+
+    bool Vector3::AreOrthonormal(const Vector3 &a, const Vector3 &b, float epsilon) {
+        return a.IsPerpendicular(b, epsilon) && a.IsNormalized(epsilon*epsilon) && b.IsNormalized(epsilon*epsilon);
+    }
+
+    Vector3 Vector3::Mul(const Vector3 &rhs) const {
+        return {
+                this->x * rhs.x,
+                this->y * rhs.y,
+                this->z * rhs.z
+        };
+    }
+
+    Vector3 Vector3::Div(const Vector3 &v) const {
+        return {
+                this->x/v.x,
+                this->y/v.y,
+                this->z/v.z
+        };
+    }
+
+
 }

src/J3ML/LinearAlgebra/Vector4.cpp

@@ -7,8 +7,10 @@
 #include <cmath>
 #include <algorithm>
 
-namespace LinearAlgebra {
+namespace J3ML::LinearAlgebra {
 
+    const Vector4 Vector4::Zero = {0,0,0,0};
+    const Vector4 Vector4::NaN = {NAN, NAN, NAN, NAN};
 
     Vector4::Vector4(): x(0), y(0), z(0), w(0)
     {}
@@ -139,6 +141,15 @@ Vector4 Vector4::operator-(const Vector4& rhs) const
 
     }
 
+    Vector4 &Vector4::operator=(const Vector4 &rhs) {
+        x = rhs.x;
+        y = rhs.y;
+        z = rhs.z;
+        w = rhs.w;
+
+        return *this;
+    }
+
 
 }
 #pragma endregion

tests/LinearAlgebra/Vector2Tests.cpp

@@ -1,7 +1,7 @@
 #include <gtest/gtest.h>
 #include <J3ML/LinearAlgebra/Vector2.h>
 
-using Vector2 = LinearAlgebra::Vector2;
+using J3ML::LinearAlgebra::Vector2;
 
 TEST(Vector2Test, V2_Constructor_Default)
 {

tests/LinearAlgebra/Vector3Tests.cpp

@@ -1,113 +1,120 @@
 #include <gtest/gtest.h>
 #include <J3ML/LinearAlgebra/Vector3.h>
 
-using Vector3 = LinearAlgebra::Vector3;
+using J3ML::LinearAlgebra::Vector3;
+
+void EXPECT_V3_EQ(const Vector3& lhs, const Vector3& rhs)
+{
+    EXPECT_FLOAT_EQ(lhs.x, rhs.x);
+    EXPECT_FLOAT_EQ(lhs.y, rhs.y);
+    EXPECT_FLOAT_EQ(lhs.z, rhs.z);
+}
 
 TEST(Vector3Test, V3_Constructor_Default)
 {
-    EXPECT_EQ(Vector3(), Vector3::Zero);
+    EXPECT_V3_EQ(Vector3(), Vector3::Zero);
 }
 
 TEST(Vector3Test, V3_Constructor_XYZ)
 {
     Vector3 Input {0, 1, 0};
 
-    EXPECT_EQ(Input, Vector3::Down);
+    EXPECT_V3_EQ(Input, Vector3::Down);
 }
 
 TEST(Vector3Test, V3_Addition_Op) {
-    Vector3 A {};
-    Vector3 B {};
+    Vector3 A {1,1,1};
+    Vector3 B {2,2,2};
 
-    Vector3 ExpectedResult {};
+    Vector3 ExpectedResult {3,3,3};
 
-    EXPECT_EQ(A + B, ExpectedResult);
+    EXPECT_V3_EQ(A + B, ExpectedResult);
 }
 TEST(Vector3Test, V3_Addition_Method) {
-    Vector3 A {};
-    Vector3 B {};
+    Vector3 A {1,1,1};
+    Vector3 B {2,2,2};
 
-    Vector3 ExpectedResult {};
+    Vector3 ExpectedResult {3,3,3};
 
-    EXPECT_EQ(A.Add(B), ExpectedResult);
+    EXPECT_V3_EQ(A.Add(B), ExpectedResult);
 }
 TEST(Vector3Test, V3_Addition_Static) {
-    Vector3 A {};
-    Vector3 B {};
+    Vector3 A {1,1,1};
+    Vector3 B {3,3,3};
 
-    Vector3 ExpectedResult {};
+    Vector3 ExpectedResult {4,4,4};
 
-    EXPECT_EQ(Vector3::Add(A, B), ExpectedResult);
+    EXPECT_V3_EQ(Vector3::Add(A, B), ExpectedResult);
 }
 TEST(Vector3Test, V3_Subtract_Op) {
-    Vector3 A {};
-    Vector3 B {};
+    Vector3 A {2,2,2};
+    Vector3 B {.5f, .5f, .5f};
 
-    Vector3 ExpectedResult {};
+    Vector3 ExpectedResult {1.5f, 1.5f, 1.5f};
 
-    EXPECT_EQ(A - B, ExpectedResult);
+    EXPECT_V3_EQ(A - B, ExpectedResult);
 }
 TEST(Vector3Test, V3_Subtract_Method) {
-    Vector3 A {};
-    Vector3 B {};
+    Vector3 A {3,3,3};
+    Vector3 B {1,1,1};
 
-    Vector3 ExpectedResult {};
+    Vector3 ExpectedResult {2,2,2};
 
-    EXPECT_EQ(A.Sub(B), ExpectedResult);
+    EXPECT_V3_EQ(A.Sub(B), ExpectedResult);
 }
 TEST(Vector3Test, V3_Subtract_Static) {
-    Vector3 A {};
-    Vector3 B {};
+    Vector3 A {4,4,4};
+    Vector3 B {1,1,1};
 
-    Vector3 ExpectedResult {};
+    Vector3 ExpectedResult {3,3,3};
 
-    EXPECT_EQ(Vector3::Sub(A, B), ExpectedResult);
+    EXPECT_V3_EQ(Vector3::Sub(A, B), ExpectedResult);
 }
 TEST(Vector3Test, V3_Scalar_Mult_Op) {
-    Vector3 A { };
+    Vector3 A { 1,1,1};
     float B = 1.5f;
 
-    Vector3 ExpectedResult {};
+    Vector3 ExpectedResult {1.5f, 1.5f, 1.5f};
 
-    EXPECT_EQ(A * B, ExpectedResult);
+    EXPECT_V3_EQ(A * B, ExpectedResult);
 }
 TEST(Vector3Test, V3_Scalar_Mult_Method) {
-    Vector3 A { };
+    Vector3 A {3,3,3};
     float B = 1.5f;
 
-    Vector3 ExpectedResult {};
+    Vector3 ExpectedResult {4.5f, 4.5f, 4.5f};
 
-    EXPECT_EQ(A.Mul(B), ExpectedResult);
+    EXPECT_V3_EQ(A.Mul(B), ExpectedResult);
 }
 TEST(Vector3Test, V3_Scalar_Mult_Static) {
-    Vector3 A { };
+    Vector3 A {2,2,2};
     float B = 1.5f;
 
-    Vector3 ExpectedResult {};
+    Vector3 ExpectedResult {3.f, 3.f, 3.f};
 
-    EXPECT_EQ(Vector3::Mul(A, B), ExpectedResult);
+    EXPECT_V3_EQ(Vector3::Mul(A, B), ExpectedResult);
 }
 TEST(Vector3Test, V3_Scalar_Div_Op) {
-    Vector3 A {};
-    float B = 1.5f;
+    Vector3 A {4,4,4};
+    float B = 2.f;
 
-    Vector3 ExpectedResult { };
-    EXPECT_EQ(A / B, ExpectedResult);
+    Vector3 ExpectedResult {2,2,2};
+    EXPECT_V3_EQ(A / B, ExpectedResult);
 }
 TEST(Vector3Test, V3_Scalar_Div_Method) {
-    Vector3 A { };
-    float B = 1.5f;
-    Vector3 ExpectedResult { };
+    Vector3 A {6,6,6};
+    float B = 2.f;
+    Vector3 ExpectedResult { 3,3,3};
 
-    EXPECT_EQ(A.Div(B), ExpectedResult);
+    EXPECT_V3_EQ(A.Div(B), ExpectedResult);
 }
 TEST(Vector3Test, V3_Scalar_Div_Static) {
-    Vector3 A { };
+    Vector3 A {3,3,3};
     float B = 1.5f;
 
-    Vector3 ExpectedResult { };
+    Vector3 ExpectedResult { 2.f, 2.f, 2.f};
 
-    EXPECT_EQ(Vector3::Div(A, B), ExpectedResult);
+    EXPECT_V3_EQ(Vector3::Div(A, B), ExpectedResult);
 }
 TEST(Vector3Test, V3_Sizeof) {
     EXPECT_EQ(sizeof(Vector3), 12);
@@ -116,12 +123,76 @@ TEST(Vector3Test, V3_NaN) {
     EXPECT_NE(Vector3(0, 0, 0), Vector3::NaN);
 
 }
-TEST(Vector3Test, V3_Min) {}
-TEST(Vector3Test, V3_Max) {}
-TEST(Vector3Test, V3_Clamp) {}
-TEST(Vector3Test, V3_DotProduct) {}
-TEST(Vector3Test, V3_CrossProduct) {}
-TEST(Vector3Test, V3_Project) {}
-TEST(Vector3Test, V3_Normalize) {}
-TEST(Vector3Test, V3_Lerp) {}
-TEST(Vector3Test, V3_AngleBetween) {}
+TEST(Vector3Test, V3_Min) {
+    Vector3 Input {2,2,2};
+    Vector3 Minimum {3,3,3};
+    Vector3 ExpectedResult {2,2,2};
+
+    EXPECT_V3_EQ(Input.Min(Minimum), ExpectedResult);
+}
+TEST(Vector3Test, V3_Max) {
+    Vector3 Input {2,2,2};
+    Vector3 Maximum {3,3,3};
+    Vector3 ExpectedResult {3,3,3};
+
+    EXPECT_V3_EQ(Input.Max(Maximum), ExpectedResult);
+}
+TEST(Vector3Test, V3_Clamp) {
+    Vector3 Input {5,-1,8};
+    Vector3 Minimum {1,1,1};
+    Vector3 Maximum {5,5,5};
+
+    Vector3 ExpectedResult {5,1,5};
+
+    EXPECT_V3_EQ(Input.Clamp(Minimum, Maximum), ExpectedResult);
+
+}
+TEST(Vector3Test, V3_DotProduct) {
+    Vector3 A{6,6,6};
+    Vector3 B{1,1,1};
+
+
+    float ExpectedResult = 1;
+
+    EXPECT_FLOAT_EQ(A.Dot(B), ExpectedResult);
+}
+TEST(Vector3Test, V3_CrossProduct) {
+    Vector3 A{1,1,1};
+    Vector3 B{2,2,2};
+
+    Vector3 ExpectedResult {0,0,0};
+
+    EXPECT_V3_EQ(A.Cross(B), ExpectedResult);
+
+}
+TEST(Vector3Test, V3_Project) {
+    Vector3 Base {};
+    Vector3 Projection {};
+    Vector3 ExpectedResult {};
+}
+TEST(Vector3Test, V3_Normalize) {
+    Vector3 Input {2, 0, 0};
+    Vector3 ExpectedResult {1, 0, 0};
+
+    EXPECT_V3_EQ(Input.Normalize(), ExpectedResult);
+}
+TEST(Vector3Test, V3_Lerp)
+{
+    Vector3 Start {};
+    Vector3 Finish {};
+    float Percent = 50;
+    Vector3 ExpectedResult {};
+    EXPECT_V3_EQ(Start.Lerp(Finish, Percent), ExpectedResult);
+}
+TEST(Vector3Test, V3_AngleBetween) {
+    using J3ML::LinearAlgebra::Angle2D;
+    Vector3 A{ .5f, .5f, .5f};
+    Vector3 B {.25f, .75f, .25f};
+    A = A.Normalize();
+    B = B.Normalize();
+    Angle2D ExpectedResult {-0.69791365, -2.3561945};
+    std::cout << A.AngleBetween(B).x << ", " << A.AngleBetween(B).y << "";
+    auto angle = A.AngleBetween(B);
+    EXPECT_FLOAT_EQ(angle.x, ExpectedResult.x);
+    EXPECT_FLOAT_EQ(angle.y, ExpectedResult.y);
+}

tests/LinearAlgebra/Vector4Tests.cpp

@@ -1,3 +1,106 @@
-//
-// Created by josh on 12/26/2023.
-//
+#include <gtest/gtest.h>
+#include <J3ML/LinearAlgebra/Vector4.h>
+
+using Vector4 = J3ML::LinearAlgebra::Vector4;
+
+
+void EXPECT_V4_EQ(const Vector4& lhs, const Vector4& rhs)
+{
+
+}
+
+TEST(Vector4Test, V4_Constructor_Default)
+{
+    EXPECT_V4_EQ(Vector4(), Vector4::Zero);
+}
+
+TEST(Vector4Test, V4_Constructor_XYZW)
+{
+    Vector4 Input {0, 1, 0, 1};
+    EXPECT_FLOAT_EQ(Input.x, 0);
+    EXPECT_FLOAT_EQ(Input.y, 1);
+    EXPECT_FLOAT_EQ(Input.z, 0);
+    EXPECT_FLOAT_EQ(Input.w, 1);
+}
+
+TEST(Vector4Test, V4_Addition_Op) {
+    Vector4 A {1, 1, 1, 1};
+    Vector4 B {2, 2, 2, 2};
+
+    Vector4 ExpectedResult {3, 3, 3, 3};
+
+    EXPECT_V4_EQ(A + B, ExpectedResult);
+}
+
+TEST(Vector4Test, V4_Addition_Method)
+{
+
+}
+
+TEST(Vector4Test, V4_Addition_Static)
+{
+
+}
+
+TEST(Vector4Test, V4_Subtract_Op)
+{
+
+}
+
+TEST(Vector4Test, V4_Subtract_Method)
+{
+
+}
+
+TEST(Vector4Test, V4_Subtract_Static)
+{
+
+}
+
+TEST(Vector4Test, V4_Scalar_Mult_Op)
+{
+
+}
+
+TEST(Vector4Test, V4_Scalar_Mult_Method)
+{
+
+}
+
+TEST(Vector4Test, V4_Scalar_Mult_Static)
+{
+
+}
+
+TEST(Vector4Test, V4_Scalar_Div_Op)
+{
+
+}
+
+TEST(Vector4Test, V4_Scalar_Div_Method)
+{
+
+}
+
+TEST(Vector4Test, V4_Scalar_Div_Static)
+{
+
+}
+
+TEST(Vector4Test, V4_Sizeof)
+{
+
+}
+
+TEST(Vector4Test, V4_NaN)
+{
+
+}
+
+TEST(Vector4Tests, V4_Min) {}
+TEST(Vector4Tests, V4_Max) {}
+TEST(Vector4Tests, V4_Clamp) {}
+TEST(Vector4Tests, V4_DotProduct) {}
+TEST(Vector4Tests, V4_CrossProduct) {}
+TEST(Vector4Tests, V4_Project) {}
+TEST(Vector4Test, V4_Normalize) {}