Update Vector2.cpp

change == and != to not check epsilon. ~= should check epsilon.

CMakeLists.txt

@@ -34,7 +34,7 @@ set_target_properties(J3ML PROPERTIES LINKER_LANGUAGE CXX)
 
 CPMAddPackage(
         NAME jtest
-        URL https://git.redacted.cc/josh/jtest/archive/Release-1.4.zip
+        URL https://git.redacted.cc/josh/jtest/archive/Release-1.5.zip
 )
 
 target_include_directories(J3ML PUBLIC ${jtest_SOURCE_DIR}/include)

Doxyfile

@@ -48,13 +48,13 @@ PROJECT_NAME           = J3ML
 # could be handy for archiving the generated documentation or if some version
 # control system is used.
 
-PROJECT_NUMBER         =
+PROJECT_NUMBER         = 3.1
 
 # Using the PROJECT_BRIEF tag one can provide an optional one line description
 # for a project that appears at the top of each page and should give viewer a
 # quick idea about the purpose of the project. Keep the description short.
 
-PROJECT_BRIEF          = "Linear Algebra, Geometry, and Algorithms in C++"
+PROJECT_BRIEF          = "Linear Algebra, Geometry, and Algorithms in C++ (v3.1)"
 
 # With the PROJECT_LOGO tag one can specify a logo or an icon that is included
 # in the documentation. The maximum height of the logo should not exceed 55

include/J3ML/Algorithm/Bezier.hpp

@@ -17,7 +17,7 @@
 // Transcribed from here: explicit form and derivative
 // https://en.wikipedia.org/wiki/B%C3%A9zier_curve#Cubic_B%C3%A9zier_curves
 
-#include "J3ML/LinearAlgebra/Vector2.hpp"
+#include <J3ML/LinearAlgebra/Vector2.hpp>
 
 namespace J3ML::Algorithm
 {
@@ -29,17 +29,61 @@ namespace J3ML::Algorithm
     template <typename T>
     inline T Cube(T f) { return f * f * f; }
 
+    /// Four points P0, P1, P2, P3 in the plane space define a cubic Bezier curve.
+    /// The curve can be modeled as a polynomial of third order.
+    /// The curve starts at P0, going toward P1, and arrives at P3 coming from the direction of P2.
+    /// Usually, it will not pass through P1, or P2, these points are only there to provide directional information.
     template <typename T>
     inline T Bezier(float t, const T& p0, const T& p1, const T& p2, const T& p3)
     {
         return Cube(1 - t) * p0 + 3 * Square(1 - t) * t * p1 + 3 * (1 - t) * Square(t) * p2 + Cube(t) * p3;
     }
 
+    /// Computes a point along a 2-dimensional Cubic Bezier curve.
+    /// @param t The normalized distance along the curve to compute, with range of [0, 1].
+    /// @param p0 The start-point of the curve.
+    /// @param p1
+    /// @param p2
+    /// @param p3 The end-point of the curve.
     Vector2 Bezier(float t, const Vector2& p0, const Vector2& p1, const Vector2& p2, const Vector2& p3);
 
-    // Tangent
+    /// Computes a point along the tangent of a 2-dimensional Cubic Bezier Curve.
+    /// @param t The normalized distance along the curve to compute, with range of [0, 1].
+    /// @param p0 The start-point of the curve.
+    /// @param p1
+    /// @param p2
+    /// @param p3 The end-point of the curve.
     Vector2 BezierDerivative(float t, const Vector2& p0, const Vector2& p1, const Vector2& p2, const Vector2& p3);
 
-    // Normal
+    /// Computes a point along the normal of a 2-dimensional Cubic Bezier Curve.
+    /// @param t The normalized distance along the curve to compute, with range of [0, 1].
+    /// @param p0 The start-point of the curve.
+    /// @param p1 The first control point,  which determines the direction at which the curve meets point 0.
+    /// @param p2 The second control point, which determines the direction at which the curve meets point 3.
+    /// @param p3 The end-point of the curve.
     Vector2 BezierNormal(float t, const Vector2& p0, const Vector2& p1, const Vector2& p2, const Vector2& p3);
+
+    /// Computes a point along a 3-dimensional Cubic Bezier curve.
+    /// @param t The normalized distance along the curve to compute, with range of [0, 1].
+    /// @param p0 The start-point of the curve.
+    /// @param p1 The first control point,  which determines the direction at which the curve meets point 0.
+    /// @param p2 The second control point, which determines the direction at which the curve meets point 3.
+    /// @param p3 The end-point of the curve.
+    Vector3 Bezier(float t, const Vector3& p0, const Vector3& p1, const Vector3& p2, const Vector3& p3);
+
+    /// Computes a point along the tangent of a 3-dimensional Cubic Bezier Curve.
+    /// @param t The normalized distance along the curve to compute, with range of [0, 1].
+    /// @param p0 The start-point of the curve.
+    /// @param p1 The first control point,  which determines the direction at which the curve meets point 0.
+    /// @param p2 The second control point, which determines the direction at which the curve meets point 3.
+    /// @param p3 The end-point of the curve.
+    Vector3 BezierDerivative(float t, const Vector3& p0, const Vector3& p1, const Vector3& p2, const Vector3& p3);
+
+    /// Computes a point along the normal of a 3-dimensional Cubic Bezier Curve.
+    /// @param t The normalized distance along the curve to compute, with range of [0, 1].
+    /// @param p0 The start-point of the curve.
+    /// @param p1 The first control point,  which determines the direction at which the curve meets point 0.
+    /// @param p2 The second control point, which determines the direction at which the curve meets point 3.
+    /// @param p3 The end-point of the curve.
+    Vector3 BezierNormal(float t, const Vector3& p0, const Vector3& p1, const Vector3& p2, const Vector3& p3);
 }

include/J3ML/Algorithm/GJK.hpp

@@ -1,4 +1,4 @@
-// @file GJK.hpp
+/// @file GJK.hpp
 /// Implementation of the Gilbert-Johnson-Keerthi (GJK) convex polyhedron intersection test
 
 #pragma once

include/J3ML/Algorithm/Parabola.hpp

@@ -0,0 +1,17 @@
+/// Josh's 3D Math Library
+/// A C++20 Library for 3D Math, Computer Graphics, and Scientific Computing.
+/// Developed and Maintained by Josh O'Leary @ Redacted Software.
+/// Special Thanks to William Tomasine II and Maxine Hayes.
+/// (c) 2024 Redacted Software
+/// This work is dedicated to the public domain.
+
+/// @file Parabola.hpp
+/// @desc Algorithm for calculating a parabolic curve to be used in instantaneous bullet raycasting.
+/// @edit 2024-10-22
+
+#pragma once
+
+namespace J3ML
+{
+
+}

include/J3ML/Algorithm/Triangulate.hpp

@@ -0,0 +1,18 @@
+/// Josh's 3D Math Library
+/// A C++20 Library for 3D Math, Computer Graphics, and Scientific Computing.
+/// Developed and Maintained by Josh O'Leary @ Redacted Software.
+/// Special Thanks to William Tomasine II and Maxine Hayes.
+/// (c) 2024 Redacted Software
+/// This work is dedicated to the public domain.
+
+/// @file Parabola.hpp
+/// @desc Algorithm for calculating a parabolic curve to be used in instantaneous bullet raycasting.
+/// @edit 2024-10-22
+
+#pragma once
+
+
+namespace J3ML
+{
+    /// @see class Polygon::Triangulate for current implementation.
+}

include/J3ML/Geometry/AABB2D.hpp

@@ -28,6 +28,9 @@ void AABB2DTransformAsAABB2D(AABB2D& aabb, Matrix& m);
 namespace J3ML::Geometry
 {
     using LinearAlgebra::Vector2;
+
+    // TODO: Integer AABB2D for even leaner box computation.
+
     // CaveGame AABB
     class AABB2D : public Shape2D
     {

include/J3ML/Geometry/Icosahedron.hpp

@@ -0,0 +1,109 @@
+/// Josh's 3D Math Library
+/// A C++20 Library for 3D Math, Computer Graphics, and Scientific Computing.
+/// Developed and Maintained by Josh O'Leary @ Redacted Software.
+/// Special Thanks to William Tomasine II and Maxine Hayes.
+/// (c) 2024 Redacted Software
+/// This work is dedicated to the public domain.
+
+/// @file Icosahedron.hpp
+/// @desc Icosahedron class implementation, borrowed from http://www.songho.ca/opengl/gl_sphere.html#icosphere
+/// @edit 2024-10-22
+
+/** Polyhedron with 12 vertices, 30 edges, and 20 faces (triangles) for OpenGL
+    If the radius is r, then the length of the edge is (r / sin(2pi/5))
+
+    Vertices of icosahedron are constructed with spherical coords by aligning
+    the north pole to (0,0,r) and the south pole to (0,0,-r). Other 10 vertices
+    are computed by rotating 72 degrees along y-axis at the elevation angle
+    +/- 26.565 (=arctan(1/2)).
+
+    The unwrapped (paper model) of icosahedron and texture map look like this:
+    // (S,0)  3S  5S  7S  9S
+    //    /\  /\  /\  /\  /\      : 1st row (5 triangles)       //
+    //   /__\/__\/__\/__\/__\                                   //
+    // T \  /\  /\  /\  /\  /\    : 2nd row (10 triangles)      //
+    //    \/__\/__\/__\/__\/__\                                 //
+    // 2T  \  /\  /\  /\  /\  /   : 3rd row (5 triangles)       //
+    //      \/  \/  \/  \/  \/                                  //
+    //      2S  4S  6S  8S  (10S,3T)
+    // where S = 186/2048 = 0.0908203
+    //       T = 322/1024 = 0.3144531
+    // If a texture size is 2048x1024, S=186, T=322
+
+    AUTHOR: Song Ho Ahn (song.ahn@gmail.com)
+ */
+
+#include <vector>
+#include "Color4.hpp"
+
+#pragma once
+
+namespace J3ML
+{
+
+    class Icosahedron
+    {
+    public:
+        float radius;
+        float edgeLength;
+        Icosahedron(float radius = 1.0f);
+        float Radius() const { return radius; }
+        void Radius(float new_radius) {radius = new_radius;}
+        float EdgeLength() const { return edgeLength;}
+        void EdgeLength(float new_edge_length) { edgeLength = new_edge_length;}
+        // for vertex data
+        unsigned int VertexCount() const;
+        unsigned int NormalCount() const;
+        unsigned int TexCoordCount() const;
+        unsigned int IndexCount() const;
+        unsigned int LineIndexCount() const;
+        unsigned int TriangleCount() const;
+        unsigned int VertexSize() const;
+        unsigned int NormalSize() const;
+        unsigned int TexCoordSize() const;
+        unsigned int IndexSize() const;
+        unsigned int LineIndexSize() const;
+        const float* Vertices() const;
+        const float* Normals() const;
+        const float* TexCoords() const;
+        const unsigned int* Indices() const;
+        const unsigned int* LineIndices() const;
+        // for interleaved vertices: V/N/T
+        unsigned int InterleavedVertexCount() const;
+        unsigned int InterleavedVertexSize() const;
+        int InterleavedStride() const;
+        const float* InterleavedVertices() const;
+
+        // draw in VertexArray mode
+        void draw() const;
+        void drawLines(const Color4& lineColor) const;
+        void drawWithLines(const Color4& lineColor) const;
+
+    protected:
+    private:
+        // static functions
+        static void computeFaceNormal(float v1[3], float v2[3], float v3[3], float n[3]);
+
+        // member functions
+        void updateRadius();
+        std::vector<float> computeVertices();
+        void buildVertices();
+        void buildInterleavedVertices();
+        void addVertices(float v1[3], float v2[3], float v3[3]);
+        void addNormals(float n1[3], float n2[3], float n3[3]);
+        void addTexCoords(float t1[2], float t2[2], float t3[2]);
+        void addIndices(unsigned int i1, unsigned int i2, unsigned int i3);
+        void addLineIndices(unsigned int indexFrom);
+
+        // member vars
+        //float radius;
+        //float edgeLength;
+        std::vector<float> vertices;
+        std::vector<float> normals;
+        std::vector<float> texCoords;
+        std::vector<unsigned int> indices;
+        std::vector<unsigned int> lineIndices;
+
+
+    };
+}

include/J3ML/Geometry/LineSegment2D.hpp

@@ -1,3 +1,14 @@
+/// Josh's 3D Math Library
+/// A C++20 Library for 3D Math, Computer Graphics, and Scientific Computing.
+/// Developed and Maintained by Josh O'Leary @ Redacted Software.
+/// Special Thanks to William Tomasine II and Maxine Hayes.
+/// (c) 2024 Redacted Software
+/// This work is dedicated to the public domain.
+
+/// @file LineSegment2D.hpp
+/// @desc A 2D representation of a finite line between two points.
+/// @edit 2024-10-22
+
 #pragma once
 
 #include <J3ML/LinearAlgebra/Vector2.hpp>

include/J3ML/Geometry/QuadTree.hpp

@@ -52,7 +52,7 @@ namespace J3ML::Geometry {
                 }
             }
 
-            AABB2D ComputeAABB() {}
+            AABB2D ComputeAABB() { return AABB2D(); }
 
             float DistanceSq(const Vector2 &point) const {
                 Vector2 centered = point - center;

include/J3ML/Geometry/Sphere.hpp

@@ -114,8 +114,10 @@ namespace J3ML::Geometry
         [[nodiscard]] bool Contains(const Vector3& point, float epsilon) const;
 
         [[nodiscard]] bool Contains(const LineSegment& lineseg)  const;
-        TriangleMesh GenerateUVSphere() const;
+        TriangleMesh GenerateUVSphere(int subdivisions = 10.f) const;
         TriangleMesh GenerateIcososphere() const;
+        TriangleMesh GenerateCubesphere() const;
+
 
         void ProjectToAxis(const Vector3 &direction, float &outMin, float &outMax) const;
     };

include/J3ML/Geometry/TriangleMesh.hpp

@@ -15,15 +15,17 @@ namespace J3ML::Geometry
         TriangleMesh(int expectedPolygonCount = 1000);
 
     public:
-        //std::vector<Vector3> Vertices;
-        //std::vector<Vector3> Normals;
-        //std::vector<Vector3> UVs;
-        //std::vector<u64> Indices;
+        std::vector<Vector3> Vertices;
+        std::vector<Vector3> Normals;
+        std::vector<Vector3> UVs;
+        std::vector<u64> Indices;
 
         std::vector<float> GenerateVertexList();
         //std::vector<Triangle> GenerateTriangleList();
+    public:
+
     private:
-        std::vector<float> cachedVertexList;
+
         //std::vector<Triangle> cachedTriangleList;
     };
 

include/J3ML/J3ML.hpp

@@ -17,18 +17,114 @@
 #include <cassert>
 #include <vector>
 
+/// This set of functions may be set to use lookup tables or SIMD operations.
+/// If no options are set, they will default to using standard library implementation.
+#undef USE_LOOKUP_TABLES /// Pre-computed lookup tables.
+#undef USE_SSE           /// Streaming SIMD Extensions (x86)
+#undef USE_NEON          /// ARM Vector Processing
+#undef USE_AVX           /// Advanced Vector Extensions (x86)
+
 /// TODO: Implement lookup tables.
+/// TODO: Implement constexpr Trigonometric LUT generators that are parameterized (samples, samples-per-period, etc.)
 
 #ifdef USE_LOOKUP_TABLES
 
-static float fast_cossin_table[MAX_CIRCLE_ANGLE];
+#define LUT_SAMPLES 1024
 
+#pragma region Trigonometric Lookup Tables
+
+// Formula: sin(2*pi*t/T)
+/** Generated using Dr LUT - Free Lookup Table Generator
+  * https://github.com/ppelikan/drlut
+  **/
+// Formula: sin(2*pi*t/T)
+const uint8_t u8_sin_lut[1024] = {
+127,128,129,129,130,131,132,132,133,134,135,136,136,
+137,138,139,139,140,141,142,143,143,144,145,146,146,
+147,148,149,149,150,151,152,153,153,154,155,156,156,
+157,158,159,159,160,161,162,162,163,164,165,165,166,
+167,168,168,169,170,171,171,172,173,173,174,175,176,
+176,177,178,178,179,180,181,181,182,183,183,184,185,
+185,186,187,188,188,189,190,190,191,192,192,193,194,
+194,195,196,196,197,198,198,199,199,200,201,201,202,
+203,203,204,205,205,206,206,207,208,208,209,209,210,
+211,211,212,212,213,213,214,215,215,216,216,217,217,
+218,218,219,220,220,221,221,222,222,223,223,224,224,
+225,225,226,226,227,227,228,228,229,229,229,230,230,
+231,231,232,232,233,233,233,234,234,235,235,236,236,
+236,237,237,238,238,238,239,239,239,240,240,240,241,
+241,241,242,242,242,243,243,243,244,244,244,245,245,
+245,245,246,246,246,247,247,247,247,248,248,248,248,
+249,249,249,249,249,250,250,250,250,250,251,251,251,
+251,251,251,252,252,252,252,252,252,252,253,253,253,
+253,253,253,253,253,253,253,253,254,254,254,254,254,
+254,254,254,254,254,254,254,254,254,254,254,254,254,
+254,254,254,254,254,254,254,254,254,254,254,253,253,
+253,253,253,253,253,253,253,253,253,252,252,252,252,
+252,252,252,251,251,251,251,251,251,250,250,250,250,
+250,249,249,249,249,249,248,248,248,248,247,247,247,
+247,246,246,246,245,245,245,245,244,244,244,243,243,
+243,242,242,242,241,241,241,240,240,240,239,239,239,
+238,238,238,237,237,236,236,236,235,235,234,234,233,
+233,233,232,232,231,231,230,230,229,229,229,228,228,
+227,227,226,226,225,225,224,224,223,223,222,222,221,
+221,220,220,219,218,218,217,217,216,216,215,215,214,
+213,213,212,212,211,211,210,209,209,208,208,207,206,
+206,205,205,204,203,203,202,201,201,200,199,199,198,
+198,197,196,196,195,194,194,193,192,192,191,190,190,
+189,188,188,187,186,185,185,184,183,183,182,181,181,
+180,179,178,178,177,176,176,175,174,173,173,172,171,
+171,170,169,168,168,167,166,165,165,164,163,162,162,
+161,160,159,159,158,157,156,156,155,154,153,153,152,
+151,150,149,149,148,147,146,146,145,144,143,143,142,
+141,140,139,139,138,137,136,136,135,134,133,132,132,
+131,130,129,129,128,127,126,125,125,124,123,122,122,
+121,120,119,118,118,117,116,115,115,114,113,112,111,
+111,110,109,108,108,107,106,105,105,104,103,102,101,
+101,100, 99, 98, 98, 97, 96, 95, 95, 94, 93, 92, 92,
+ 91, 90, 89, 89, 88, 87, 86, 86, 85, 84, 83, 83, 82,
+ 81, 81, 80, 79, 78, 78, 77, 76, 76, 75, 74, 73, 73,
+ 72, 71, 71, 70, 69, 69, 68, 67, 66, 66, 65, 64, 64,
+ 63, 62, 62, 61, 60, 60, 59, 58, 58, 57, 56, 56, 55,
+ 55, 54, 53, 53, 52, 51, 51, 50, 49, 49, 48, 48, 47,
+ 46, 46, 45, 45, 44, 43, 43, 42, 42, 41, 41, 40, 39,
+ 39, 38, 38, 37, 37, 36, 36, 35, 34, 34, 33, 33, 32,
+ 32, 31, 31, 30, 30, 29, 29, 28, 28, 27, 27, 26, 26,
+ 25, 25, 25, 24, 24, 23, 23, 22, 22, 21, 21, 21, 20,
+ 20, 19, 19, 18, 18, 18, 17, 17, 16, 16, 16, 15, 15,
+ 15, 14, 14, 14, 13, 13, 13, 12, 12, 12, 11, 11, 11,
+ 10, 10, 10,  9,  9,  9,  9,  8,  8,  8,  7,  7,  7,
+  7,  6,  6,  6,  6,  5,  5,  5,  5,  5,  4,  4,  4,
+  4,  4,  3,  3,  3,  3,  3,  3,  2,  2,  2,  2,  2,
+  2,  2,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,
+  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
+  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
+  0,  0,  0,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,
+  1,  2,  2,  2,  2,  2,  2,  2,  3,  3,  3,  3,  3,
+  3,  4,  4,  4,  4,  4,  5,  5,  5,  5,  5,  6,  6,
+  6,  6,  7,  7,  7,  7,  8,  8,  8,  9,  9,  9,  9,
+ 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14,
+ 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18,
+ 19, 19, 20, 20, 21, 21, 21, 22, 22, 23, 23, 24, 24,
+ 25, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30,
+ 31, 31, 32, 32, 33, 33, 34, 34, 35, 36, 36, 37, 37,
+ 38, 38, 39, 39, 40, 41, 41, 42, 42, 43, 43, 44, 45,
+ 45, 46, 46, 47, 48, 48, 49, 49, 50, 51, 51, 52, 53,
+ 53, 54, 55, 55, 56, 56, 57, 58, 58, 59, 60, 60, 61,
+ 62, 62, 63, 64, 64, 65, 66, 66, 67, 68, 69, 69, 70,
+ 71, 71, 72, 73, 73, 74, 75, 76, 76, 77, 78, 78, 79,
+ 80, 81, 81, 82, 83, 83, 84, 85, 86, 86, 87, 88, 89,
+ 89, 90, 91, 92, 92, 93, 94, 95, 95, 96, 97, 98, 98,
+ 99,100,101,101,102,103,104,105,105,106,107,108,108,
+109,110,111,111,112,113,114,115,115,116,117,118,118,
+119,120,121,122,122,123,124,125,125,126 };
+
+
+#pragma endregion
 #endif
 
-
 #include <J3ML/Algorithm/Reinterpret.hpp>
 
-
 /// Swaps two elements in-place without copying their data.
 template <typename T>
 void Swap(T &a, T &b)
@@ -38,35 +134,33 @@ void Swap(T &a, T &b)
     b = std::move(temp);
 }
 
-/// Clean symbolic names for integers of specific size.
-namespace J3ML::SizedIntegralTypes
-{
-    using u8 = uint8_t;
-    using u16 = uint16_t;
-    using u32 = uint32_t;
-    using u64 = uint64_t;
-
-    using s8 = int8_t;
-    using s16 = int16_t;
-    using s32 = int32_t;
-    using s64 = int64_t;
-}
-
-namespace J3ML::SizedFloatTypes
-{
-    // TODO: Use C++23 <stdfloat>
-    using f16  = float;
-    using f32 = float;
-    using f64 = double;
-    using f128 = long double;
+namespace J3ML {
+    /// Clean symbolic names for integers of specific size.
+    namespace SizedIntegralTypes {
+        using u8 = uint8_t;
+        using u16 = uint16_t;
+        using u32 = uint32_t;
+        using u64 = uint64_t;
+        using s8 = int8_t;
+        using s16 = int16_t;
+        using s32 = int32_t;
+        using s64 = int64_t;
+    }
+    //using namespace SizedIntegralTypes; // Bring into J3ML namespace.
 
+    namespace SizedFloatTypes { // TODO: Use C++23 <stdfloat>
+        using f16  = float;
+        using f32 = float;
+        using f64 = double;
+        using f128 = long double;
+    }
+    //using namespace SizedFloatTypes;    // Bring into J3ML namespace.
 }
 
 using namespace J3ML::SizedIntegralTypes;
 using namespace J3ML::SizedFloatTypes;
 
-namespace J3ML::Math::BitTwiddling
-{
+namespace J3ML::BitTwiddling {
     /// Parses a string of form "011101010" to a u32
     u32 BinaryStringToValue(const char* s);
 
@@ -74,43 +168,48 @@ namespace J3ML::Math::BitTwiddling
     inline int CountBitsSet(u32 value);
 }
 
+namespace J3ML::Math {
+    enum class Quadrant { I, II, III, IV };
 
+    // Zero technically isn't a sign, but zero also isn't positive, or negative, so bite me.
+    enum class Sign { ZERO, POSITIVE, NEGATIVE};
 
-// TODO: Implement "Wrappers" for most standard math functions.
-// We want to later-on implement lookup tables and SSE as conditional macros.
-
-namespace J3ML::Math::Constants {
-    /// sqrt(2pi) ^ -1
-    constexpr float RecipSqrt2Pi = 0.3989422804014326779399460599343818684758586311649346576659258296706579258993018385012523339073069364;
-    /// pi - https://www.mathsisfun.com/numbers/pi.html
-    constexpr float Pi = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679;
-    /// e - https://www.mathsisfun.com/numbers/e-eulers-number.html
-    constexpr float EulersNumber = 2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274;
-    /// 2pi - The ratio of a circle's circumferecne to its radius, and the number of radians in one turn.
-    constexpr float Tau = 6.28318530717958647692;
-    /// sqrt(2)
-    constexpr float PythagorasConstant = 1.41421356237309504880;
-    /// sqrt(3)
-    constexpr float TheodorusConstant = 1.73205080756887729352;
-    /// Golden Ratio
-    constexpr float Phi = 1.61803398874989484820;
-    /// ln 2
-    constexpr float NaturalLog2 = 0.6931471805599453094172321214581765680755001343602552541206800094933936219696947156058633269964186875;
-    /// ln 10
-    constexpr float NaturalLog10 = 2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983;
-    constexpr float Infinity = INFINITY;
-    constexpr float NegativeInfinity = -INFINITY;
-    constexpr float NotANumber = NAN;
 }
 
-/// This set of functions may be set to use lookup tables or SIMD operations.
-/// If no options are set, they will default to using standard library implementation.
-#undef USE_LOOKUP_TABLES /// Pre-computed lookup tables.
-#undef USE_SSE           /// Streaming SIMD Extensions (x86)
-#undef USE_NEON          /// ARM Vector Processing
-#undef USE_AVX           /// Advanced Vector Extensions (x86)
+namespace J3ML::Math::Constants { // TODO: Consider double precision for these.
+        /// sqrt(2pi) ^ -1
+        constexpr float RecipSqrt2Pi = 0.3989422804014326779399460599343818684758586311649346576659258296706579258993018385012523339073069364;
+        /// pi - https://www.mathsisfun.com/numbers/pi.html
+        constexpr float Pi = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679;
+        constexpr float TwoPi = Pi*2.0;
+        constexpr float PiOverTwo = Pi/2.0;
+        constexpr float ThreePiOverTwo = 3.0*Pi/2.0;
+        /// e - https://www.mathsisfun.com/numbers/e-eulers-number.html
+        constexpr float EulersNumber = 2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274;
+        /// 2pi - The ratio of a circle's circumferecne to its radius, and the number of radians in one turn.
+        constexpr float Tau = 6.28318530717958647692;
+        /// sqrt(2)
+        constexpr float PythagorasConstant = 1.41421356237309504880;
+        /// sqrt(3)
+        constexpr float TheodorusConstant = 1.73205080756887729352;
+        /// Golden Ratio
+        constexpr float Phi = 1.61803398874989484820;
+        /// ln 2
+        constexpr float NaturalLog2 = 0.6931471805599453094172321214581765680755001343602552541206800094933936219696947156058633269964186875;
+        /// ln 10
+        constexpr float NaturalLog10 = 2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983;
+        constexpr float Infinity = INFINITY;
+        constexpr float NegativeInfinity = -INFINITY;
+        constexpr float NotANumber = NAN;
+}
+
+namespace J3ML::Math {
+    using namespace Constants; // Bring into J3ML::Math namespace.
+}
 
 namespace J3ML::Math::Functions {
+         // TODO: Implement "Wrappers" for most standard math functions.
+         // We want to later-on implement lookup tables and SSE as conditional macros.
 
     /// Clamps the given input value to the range [min, max].
     /** @see Clamp01(), Min(), Max(). */
@@ -221,26 +320,37 @@ namespace J3ML::Math::Functions {
     inline bool IsInfinite(double d) { return (ReinterpretAs<u64>(d) << 1) == 0xFFE0000000000000ULL; }
 
 
+    namespace Trigonometric {
+        Sign SignOfSin(float radians);
+        Sign SignOfCos(float radians);
+        Sign SignOfTan(float radians);
 
-    float Radians(float deg); /// Converts the given amount of degrees into radians.
-    float Degrees(float rad); /// Converts the given amount of radians into degrees.
+        Quadrant QuadrantOf(float radians);
 
-    float Sin(float x); /// Computes the sine of x, in radians.
-    float Cos(float x); /// Computes the cosine of x, in radians.
-    float Tan(float x); /// Computes the tangent of x, in radians.
 
-    /// Simultaneously computes both sine and cosine of x, in radians.
-    /// This yields a small performance increase over computing them separately.
-    /// @see Sin(), Cos().
-    void SinCos(float x, float& outSin, float& outCos);
+        float Radians(float deg); /// Converts the given amount of degrees into radians.
+        float Degrees(float rad); /// Converts the given amount of radians into degrees.
 
-    float Asin(float x); /// Computes the inverse sine of x, in radians.
-    float Acos(float x); /// Computes the inverse cosine of x, in radians.
-    float Atan(float x); /// Computes the inverse tangent of x, in radians.
-    float Atan2(float y, float x); /// Computes the signed (principal value) inverse tangent of y/x, in radians.
-    float Sinh(float x); /// Computes the hyperbolic sine of x, in radians.
-    float Cosh(float x); /// Computes the hyperbolic cosine of x, in radians.
-    float Tanh(float x); /// Computes the hyperbolic tangent of x, in radians.
+        float Sin(float x); /// Computes the sine of x, in radians.
+        float Cos(float x); /// Computes the cosine of x, in radians.
+        float Tan(float x); /// Computes the tangent of x, in radians.
+
+        /// Simultaneously computes both sine and cosine of x, in radians.
+        /// This yields a small performance increase over computing them separately.
+        /// @see Sin(), Cos().
+        void SinCos(float x, float& outSin, float& outCos);
+
+        float Asin(float x); /// Computes the inverse sine of x, in radians.
+        float Acos(float x); /// Computes the inverse cosine of x, in radians.
+        float Atan(float x); /// Computes the inverse tangent of x, in radians.
+        float Atan2(float y, float x); /// Computes the signed (principal value) inverse tangent of y/x, in radians.
+        float Sinh(float x); /// Computes the hyperbolic sine of x, in radians.
+        float Cosh(float x); /// Computes the hyperbolic cosine of x, in radians.
+        float Tanh(float x); /// Computes the hyperbolic tangent of x, in radians.
+    }
+
+
+    using namespace Trigonometric;
 
     bool IsPow2(u32 number); /// Returns true if the given number is a power of 2.
     bool IsPow2(u64 number); /// Returns true if the given number is a power of 2.
@@ -338,33 +448,50 @@ namespace J3ML::Math::Functions {
     float Recip(float x); /// Returns 1/x, the reciprocal of x.
     float RecipFast(float x); /// Returns 1/x, the reciprocal of x, using a fast approximation (SSE rcp instruction).
 
+}
 
-    namespace Interp
-    {
-        inline float SmoothStart(float t);
-    }
+namespace J3ML::Math::Functions::Interpolation
+{
+    inline float SmoothStart(float t);
+}
 
 
+namespace J3ML::Math {
+    using namespace Functions;
+}
+
+namespace J3ML::Math::Types {
+
+
+    struct Radians { // TODO: Fill in with relevant members.
+        float value;
+        float operator()() const { return value; }
+    };
+
+    struct Degrees { // TODO: Fill in with relevant members.
+        float value;
+        float operator()() const { return value; }
+    };
+
 
 }
 
 namespace J3ML::Math {
-    using namespace Math::Constants;
-    using namespace Math::Functions;
-
-
-    struct Rotation
-    {
-    public:
+    struct Rotation {
         Rotation();
         Rotation(float value);
+        Rotation(const Types::Radians& radians);
+
+        Rotation(const Types::Degrees& degrees);
+
         float valueInRadians;
-        float ValueInRadians() const;
-        float ValueInDegrees() const;
+        float ValueInRadians() const { return valueInRadians; }
+        Types::Radians Radians() const { return {valueInRadians}; }
+        float Degrees() const { return Functions::Degrees(valueInRadians); }
+
         Rotation operator+(const Rotation& rhs);
     };
 
-
     Rotation operator ""_rad(long double rads);
 
     Rotation operator ""_radians(long double rads);
@@ -374,4 +501,3 @@ namespace J3ML::Math {
     Rotation operator ""_degrees(long double rads);
 }
 
-

include/J3ML/LinearAlgebra/AxisAngle.hpp

@@ -2,28 +2,23 @@
 
 #include <J3ML/LinearAlgebra/EulerAngle.hpp>
 #include <J3ML/LinearAlgebra/Quaternion.hpp>
-#include <J3ML/LinearAlgebra/AxisAngle.hpp>
 #include <J3ML/LinearAlgebra/Vector3.hpp>
 
-namespace J3ML::LinearAlgebra
-{
+namespace J3ML::LinearAlgebra {
+    class AxisAngle;
+}
 
-    /// Transitional datatype, not useful for internal representation of rotation
-    /// But has uses for conversion and manipulation.
-    class AxisAngle {
-    public:
-        Vector3 axis;
-        float angle;
-    public:
-        AxisAngle();
-        explicit AxisAngle(const Quaternion& q);
-        explicit AxisAngle(const EulerAngle& e);
+/// Transitional datatype, not useful for internal representation of rotation
+/// But has uses for conversion and manipulation.
+class J3ML::LinearAlgebra::AxisAngle {
+public:
+    Vector3 axis;
+    // Radians.
+    float angle;
+public:
+    AxisAngle();
+    explicit AxisAngle(const Quaternion& q);
+    explicit AxisAngle(const EulerAngleXYZ& e);
+    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/DirectionVector.hpp

@@ -0,0 +1,20 @@
+#pragma once
+#include <J3ML/LinearAlgebra/Vector3.hpp>
+
+namespace J3ML::LinearAlgebra {
+    class DirectionVectorRH;
+}
+
+/// Direction vector of a given Matrix3x3 RotationMatrix in a Right-handed coordinate space.
+class J3ML::LinearAlgebra::DirectionVectorRH : public Vector3 {
+private:
+    // This is purposefully not exposed because these types aren't usually convertable.
+    explicit DirectionVectorRH(const Vector3& rhs);
+public:
+    static DirectionVectorRH Forward(const Matrix3x3& rhs);
+    static DirectionVectorRH Backward(const Matrix3x3& rhs);
+    static DirectionVectorRH Left(const Matrix3x3& rhs);
+    static DirectionVectorRH Right(const Matrix3x3& rhs);
+    static DirectionVectorRH Up(const Matrix3x3& rhs);
+    static DirectionVectorRH Down(const Matrix3x3& rhs);
+};

include/J3ML/LinearAlgebra/EulerAngle.hpp

@@ -5,48 +5,19 @@
 #include <J3ML/LinearAlgebra/AxisAngle.hpp>
 
 namespace J3ML::LinearAlgebra {
+    class EulerAngleXYZ;
+}
 
-    class AxisAngle;
-
-// Essential Reading:
-// http://www.essentialmath.com/GDC2012/GDC2012_JMV_Rotations.pdf
-class EulerAngle {
+class J3ML::LinearAlgebra::EulerAngleXYZ {
 public:
-    EulerAngle();
-    EulerAngle(float pitch, float yaw, float roll);
-    EulerAngle(const Vector3& vec) : pitch(vec.x), yaw(vec.y), roll(vec.z) {}
-
-    AxisAngle ToAxisAngle() const;
-
-    [[nodiscard]] Quaternion ToQuaternion() const;
-
-
-    explicit EulerAngle(const Quaternion& rhs);
-    explicit EulerAngle(const AxisAngle& rhs);
-
-    /// TODO: Implement separate upper and lower bounds
-    /// Preserves internal value of euler angles, normalizes and clamps the output.
-    /// This does not solve gimbal lock!!!
-    float GetPitch(float pitch_limit) const;
-    float GetYaw(float yaw_limit)     const;
-    float GetRoll(float roll_limit)   const;
-
-    bool operator==(const EulerAngle& a) const;
-    void clamp();
-
-    // TODO: Euler Angles do not represent a vector, length doesn't apply, nor is this information meaningful for this data type.
-    // If you need a meaningful representation of length in 3d space, use a vector!!
-    [[nodiscard]] float length() const {
-        return 0;
-    }
-    // TODO: Implement
-    Vector3 unitVector() const;
-
-    EulerAngle movementAngle() const;
 public:
-    float pitch;
-    float yaw;
-    float roll;
+    float roll = 0; // X
+    float pitch = 0; // Y
+    float yaw = 0; // Z
+public:
+    EulerAngleXYZ(float roll, float pitch, float yaw);
+public:
+    explicit EulerAngleXYZ(const Quaternion& rhs);
+    explicit EulerAngleXYZ(const AxisAngle& rhs);
+    explicit EulerAngleXYZ(const Matrix3x3& rhs);
 };
-
-}

include/J3ML/LinearAlgebra/Forward.hpp

@@ -4,10 +4,11 @@
 namespace J3ML::LinearAlgebra
 {
     class Vector2; // A type representing a position in a 2-dimensional coordinate space.
+    class Vector2i;
     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 EulerAngleXYZ; // Uses pitch,yaw,roll components to represent a 3D orientation.
     class AxisAngle; //
     class CoordinateFrame; //
     class Matrix2x2;
@@ -15,6 +16,7 @@ namespace J3ML::LinearAlgebra
     class Matrix4x4;
     class Transform2D;
     class Transform3D;
+    class DirectionVectorRH; // A type representing a direction in 3D space.
     class Quaternion;
 
 

include/J3ML/LinearAlgebra/Matrix3x3.hpp

@@ -62,8 +62,12 @@ namespace J3ML::LinearAlgebra {
         Matrix3x3(const Vector3& col0, const Vector3& col1, const Vector3& col2);
         /// Constructs this matrix3x3 from the given quaternion.
         explicit Matrix3x3(const Quaternion& orientation);
-        /// Constructs this matrix3x3 from the given euler angle.
-        explicit Matrix3x3(const EulerAngle& orientation);
+
+        //explicit Matrix3x3(const EulerAngleXYZ& orientation);
+        explicit Matrix3x3(const EulerAngleXYZ& orientation) : Matrix3x3(Quaternion(orientation)) {};
+
+        //explicit Matrix3x3(const AxisAngle& orientation);
+        explicit Matrix3x3(const AxisAngle& orientation) : Matrix3x3(Quaternion(orientation)) {};
 
         /// Constructs this Matrix3x3 from a pointer to an array of floats.
         explicit Matrix3x3(const float *data);
@@ -153,6 +157,7 @@ namespace J3ML::LinearAlgebra {
 
         /// Sets this matrix to perform a rotation about the given axis and angle.
         void SetRotatePart(const Vector3& a, float angle);
+
         void SetRotatePart(const AxisAngle& axisAngle);
         /// Sets this matrix to perform the rotation expressed by the given quaternion.
         void SetRotatePart(const Quaternion& quat);
@@ -239,17 +244,10 @@ namespace J3ML::LinearAlgebra {
         inline float* ptr() { return &elems[0][0];}
         [[nodiscard]] inline const float* ptr() const {return &elems[0][0];}
 
-
-        /// Convers this rotation matrix to a quaternion.
-        /// This function assumes that the matrix is orthonormal (no shear or scaling) and does not perform any mirroring (determinant > 0)
-        [[nodiscard]] Quaternion ToQuat() const;
         /// Attempts to convert this matrix to a quaternion. Returns false if the conversion cannot succeed (this matrix was not a rotation
         /// matrix, and there is scaling ,shearing, or mirroring in this matrix)
         bool TryConvertToQuat(Quaternion& q) const;
 
-        /// Converts this rotation matrix to an Euler Angle.
-        [[nodiscard]] EulerAngle ToEulerAngle() const;
-
         /// Returns the main diagonal.
         /// The main diagonal consists of the elements at m[0][0], m[1][1], m[2][2]
         [[nodiscard]] Vector3 Diagonal() const;

include/J3ML/LinearAlgebra/Matrix4x4.hpp

@@ -71,8 +71,7 @@ namespace J3ML::LinearAlgebra {
 
         /// Constructs this Matrix4x4 from the given quaternion.
         explicit Matrix4x4(const Quaternion& orientation);
-        /// Constructs this Matrix4x4 from the given Euler Angle.
-        explicit Matrix4x4(const EulerAngle& orientation);
+
 
         /// Constructs this float4x4 from the given quaternion and translation.
         /// Logically, the translation occurs after the rotation has been performed.
@@ -567,8 +566,6 @@ namespace J3ML::LinearAlgebra {
 
         [[nodiscard]] Quaternion ToQuat() const;
 
-        [[nodiscard]] EulerAngle ToEulerAngle() const;
-
         /// Returns true if this Matrix4x4 is equal to the given Matrix4x4, up to given per-element epsilon.
         bool Equals(const Matrix4x4& other, float epsilon = 1e-3f) const;
 

include/J3ML/LinearAlgebra/Quaternion.hpp

@@ -4,258 +4,237 @@
 #include <J3ML/Algorithm/RNG.hpp>
 #include <cmath>
 
-namespace J3ML::LinearAlgebra
-{
-    class Quaternion {
-    public:
-        /// The identity quaternion performs no rotation when applied to a vector.
-        static const Quaternion Identity;
-        /// A compile-time constant Quaternion with the value (NAN, NAN, NAN, NAN).
-        /// For this constant, each element has the value of quiet NAN, or Not-A-Number.
-        /// @note Never compare a Quaternion to this value! Due to how IEEE floats work, "nan == nan" returns false!
-        /// That is, nothing is equal to NaN, not even NaN itself!
-        static const Quaternion NaN;
-    public:
-        /// The default constructor does not initialize any member values.
-        Quaternion();
-        /// Copy constructor
-        Quaternion(const Quaternion &rhs) = default;
-        /// Constructs a quaternion from the given data buffer.
-        /// @param data An array of four floats to use for the quaternion, in the order 'x,y,z,w.' (== 'i,j,k,w')
-        explicit Quaternion(const float *data);
+namespace J3ML::LinearAlgebra {
+    class Quaternion;
+}
 
-        explicit Quaternion(const Matrix3x3 &rotationMtrx);
-        explicit Quaternion(const Matrix4x4 &rotationMtrx);
+class J3ML::LinearAlgebra::Quaternion {
+public:
+    float x;
+    float y;
+    float z;
+    float w;
+public:
+    /// The identity quaternion performs no rotation when applied to a vector.
+    static const Quaternion Identity;
+    /// A compile-time constant Quaternion with the value (NAN, NAN, NAN, NAN).
+    /// For this constant, each element has the value of quiet NAN, or Not-A-Number.
+    /// @note Never compare a Quaternion to this value! Due to how IEEE floats work, "nan == nan" returns false!
+    /// That is, nothing is equal to NaN, not even NaN itself!
+    static const Quaternion NaN;
+public:
+    /// The default constructor does not initialize any member values.
+    Quaternion() = default;
+    /// Copy constructor
+    Quaternion(const Quaternion &rhs);
+    /// Quaternion from Matrix3x3
+    explicit Quaternion(const Matrix3x3& ro_mat);
+    /// Quaternion from Matrix4x4 RotatePart.
+    explicit Quaternion(const Matrix4x4& ro_mat);
+    /// Quaternion from EulerAngleXYZ.
+    explicit Quaternion(const EulerAngleXYZ& rhs);
+    /// Quaternion from AxisAngle.
+    explicit Quaternion(const AxisAngle& angle);
+    /// Quaternion from Vector4 (no conversion).
+    explicit Quaternion(const Vector4& vector4);
 
-        /// @param x The factor of i.
-        /// @param y The factor of j.
-        /// @param z The factor of k.
-        /// @param w The scalar factor (or 'w').
-        /// @note The input data is not normalized after construction, this has to be done manually.
-        Quaternion(float X, float Y, float Z, float W);
+    /// @param x The factor of i.
+    /// @param y The factor of j.
+    /// @param z The factor of k.
+    /// @param w The scalar factor (or 'w').
+    /// @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.
-        /// @param rotationAngleRadians The angle to rotate by, in radians. For example, Pi/4.f equals to 45 degrees, Pi/2.f is 90 degrees, etc.
-        /// @see DegToRad()
-        Quaternion(const Vector3 &rotationAxis, float rotationAngleRadians);
-        Quaternion(const Vector4 &rotationAxis, float rotationAngleRadians);
+    /// Creates a LookAt quaternion.
+    /** A LookAt quaternion is a quaternion 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
+    to 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 quaternion 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 quaternion 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. For the returned
+    quaternion Q it holds that M * localForward = targetDirection, and M * localUp lies in the plane spanned
+    by the vectors targetDirection and worldUp.
+    @see RotateFromTo() */
+    static Quaternion LookAt(const Vector3& localForward, const Vector3& targetDirection, const Vector3& localUp, const Vector3& worldUp);
 
-        explicit Quaternion(const Vector4& vector4);
-        explicit Quaternion(const EulerAngle& angle);
-        explicit Quaternion(const AxisAngle& angle);
+     /// Creates a new quaternion that rotates about the positive X axis by the given rotation.
+     static Quaternion RotateX(float rad);
+     /// Creates a new quaternion that rotates about the positive Y axis by the given rotation.
+     static Quaternion RotateY(float rad);
+     /// Creates a new quaternion that rotates about the positive Z axis by the given rotation.
+     static Quaternion RotateZ(float rad);
 
-        /// Creates a LookAt quaternion.
-        /** A LookAt quaternion is a quaternion 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
-                to 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 quaternion 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 quaternion 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. For the returned
-                quaternion Q it holds that M * localForward = targetDirection, and M * localUp lies in the plane spanned
-                by the vectors targetDirection and worldUp.
-            @see RotateFromTo() */
-        static Quaternion LookAt(const Vector3& localForward, const Vector3& targetDirection, const Vector3& localUp, const Vector3& worldUp);
+     /// Creates a new quaternion that rotates sourceDirection vector (in world space) to coincide with the
+     /// targetDirection vector (in world space).
+     /// Rotation is performed about the origin.
+     /// The vectors sourceDirection and targetDirection are assumed to be normalized.
+     /// @note There are multiple such rotations - this function returns the rotation that has the shortest angle
+     /// (when decomposed to axis-angle notation).
+     static Quaternion RotateFromTo(const Vector3& sourceDirection, const Vector3& targetDirection);
+     static Quaternion RotateFromTo(const Vector4& sourceDirection, const Vector4& targetDirection);
 
-        /// Creates a new Quaternion that rotates about the given axis by the given angle.
-        static Quaternion RotateAxisAngle(const AxisAngle& axisAngle);
-
-        /// Creates a new quaternion that rotates about the positive X axis by the given rotation.
-        static Quaternion RotateX(float angleRadians);
-        /// Creates a new quaternion that rotates about the positive Y axis by the given rotation.
-        static Quaternion RotateY(float angleRadians);
-        /// Creates a new quaternion that rotates about the positive Z axis by the given rotation.
-        static Quaternion RotateZ(float angleRadians);
-
-        /// Creates a new quaternion that rotates sourceDirection vector (in world space) to coincide with the
-        /// targetDirection vector (in world space).
-        /// Rotation is performed about the origin.
-        /// The vectors sourceDirection and targetDirection are assumed to be normalized.
-        /// @note There are multiple such rotations - this function returns the rotation that has the shortest angle
-        /// (when decomposed to axis-angle notation).
-        static Quaternion RotateFromTo(const Vector3& sourceDirection, const Vector3& targetDirection);
-        static Quaternion RotateFromTo(const Vector4& sourceDirection, const Vector4& targetDirection);
-
-        /// Creates a new quaternion that
-        /// 1. rotates sourceDirection vector to coincide with the targetDirection vector, and then
-        /// 2. rotates sourceDirection2 (which was transformed by 1.) to targetDirection2, but keeping the constraint that
-        /// sourceDirection must look at targetDirection
-        static Quaternion RotateFromTo(const Vector3& sourceDirection, const Vector3& targetDirection, const Vector3& sourceDirection2, const Vector3& targetDirection2);
+     /// Creates a new quaternion that
+     /// 1. rotates sourceDirection vector to coincide with the targetDirection vector, and then
+     /// 2. rotates sourceDirection2 (which was transformed by 1.) to targetDirection2, but keeping the constraint that
+     /// sourceDirection must look at targetDirection
+     static Quaternion RotateFromTo(const Vector3& sourceDirection, const Vector3& targetDirection, const Vector3& sourceDirection2, const Vector3& targetDirection2);
 
 
-        /// Returns a uniformly random unitary quaternion.
-        static Quaternion RandomRotation(RNG &rng);
-    public:
-        void SetFromAxisAngle(const Vector3 &vector3, float between);
+     /// Returns a uniformly random unitary quaternion.
+     static Quaternion RandomRotation(RNG &rng);
+public:
+    /// Inverses this quaternion in-place.
+    /// @note For optimization purposes, this function assumes that the quaternion is unitary, in which
+    /// case the inverse of the quaternion is simply just the same as its conjugate.
+    /// This function does not detect whether the operation succeeded or failed.
+    void Inverse();
 
-        void SetFromAxisAngle(const Vector4 &vector4, float between);
-        void SetFrom(const AxisAngle& angle);
+    /// Returns an inverted copy of this quaternion.
+    [[nodiscard]] Quaternion Inverted() const;
+    /// Computes the conjugate of this quaternion in-place.
+    void Conjugate();
+    /// Returns a conjugated copy of this quaternion.
+    [[nodiscard]] Quaternion Conjugated() const;
 
-        /// Inverses this quaternion in-place.
-        /// @note For optimization purposes, this function assumes that the quaternion is unitary, in which
-        /// case the inverse of the quaternion is simply just the same as its conjugate.
-        /// This function does not detect whether the operation succeeded or failed.
-        void Inverse();
+    /// Inverses this quaternion in-place.
+    /// Call this function when the quaternion is not known beforehand to be normalized.
+    /// This function computes the inverse proper, and normalizes the result.
+    /// @note Because of the normalization, it does not necessarily hold that q * q.InverseAndNormalize() == id.
+    /// @return Returns the old length of this quaternion (not the old length of the inverse quaternion).
+    float InverseAndNormalize();
 
-        /// Returns an inverted copy of this quaternion.
-        [[nodiscard]] Quaternion Inverted() const;
-        /// Computes the conjugate of this quaternion in-place.
-        void Conjugate();
-        /// Returns a conjugated copy of this quaternion.
-        [[nodiscard]] Quaternion Conjugated() const;
+    /// Returns the local +X axis in the post-transformed coordinate space. This is the same as transforming the vector (1,0,0) by this quaternion.
+    [[nodiscard]] Vector3 WorldX() const;
+    /// Returns the local +Y axis in the post-transformed coordinate space. This is the same as transforming the vector (0,1,0) by this quaternion.
+    [[nodiscard]] Vector3 WorldY() const;
+    /// Returns the local +Z axis in the post-transformed coordinate space. This is the same as transforming the vector (0,0,1) by this quaternion.
+    [[nodiscard]] Vector3 WorldZ() const;
+    /// Returns the axis of rotation for this quaternion.
+    [[nodiscard]] Vector3 Axis() const;
 
-        /// Inverses this quaternion in-place.
-        /// Call this function when the quaternion is not known beforehand to be normalized.
-        /// This function computes the inverse proper, and normalizes the result.
-        /// @note Because of the normalization, it does not necessarily hold that q * q.InverseAndNormalize() == id.
-        /// @return Returns the old length of this quaternion (not the old length of the inverse quaternion).
-        float InverseAndNormalize();
+    /// Returns the angle of rotation for this quaternion, in radians.
+    [[nodiscard]] float Angle() const;
 
-        /// Returns the local +X axis in the post-transformed coordinate space. This is the same as transforming the vector (1,0,0) by this quaternion.
-        [[nodiscard]] Vector3 WorldX() const;
-        /// Returns the local +Y axis in the post-transformed coordinate space. This is the same as transforming the vector (0,1,0) by this quaternion.
-        [[nodiscard]] Vector3 WorldY() const;
-        /// Returns the local +Z axis in the post-transformed coordinate space. This is the same as transforming the vector (0,0,1) by this quaternion.
-        [[nodiscard]] Vector3 WorldZ() const;
+    [[nodiscard]] float LengthSquared() const;
+    [[nodiscard]] float Length() const;
 
-        /// Returns the axis of rotation for this quaternion.
-        [[nodiscard]] Vector3 Axis() const;
+    [[nodiscard]] Matrix3x3 ToMatrix3x3() const;
+    [[nodiscard]] Matrix4x4 ToMatrix4x4() const;
 
-        /// Returns the angle of rotation for this quaternion, in radians.
-        [[nodiscard]] float Angle() const;
+    [[nodiscard]] Matrix4x4 ToMatrix4x4(const Vector3 &translation) const;
 
-        [[nodiscard]] float LengthSquared() const;
-        [[nodiscard]] float Length() const;
+    [[nodiscard]] Vector3 Transform(const Vector3& vec) const;
+    [[nodiscard]] 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
+    [[nodiscard]] Vector4 Transform(const Vector4& vec) const;
+    [[nodiscard]] Vector4 Transform(float X, float Y, float Z, float W) const;
 
-        [[nodiscard]] EulerAngle ToEulerAngle() const;
+    [[nodiscard]] Quaternion Lerp(const Quaternion& b, float t) const;
+    static Quaternion Lerp(const Quaternion &source, const Quaternion& target, float t);
+    [[nodiscard]] Quaternion Slerp(const Quaternion& q2, float t) const;
+    static Quaternion Slerp(const Quaternion &source, const Quaternion& target, float t);
+
+    /// Returns the 'from' vector rotated towards the 'to' vector by the given normalized time parameter.
+    /** This function slerps the given 'form' vector toward the 'to' vector.
+    @param from A normalized direction vector specifying the direction of rotation at t=0
+    @param to A normalized direction vector specifying the direction of rotation at t=1
+    @param t The interpolation time parameter, in the range [0, 1]. Input values outside this range are
+    silently clamped to the [0, 1] interval.
+    @return A spherical linear interpolation of the vector 'from' towards the vector 'to'. */
+    static Vector3 SlerpVector(const Vector3& from, const Vector3& to, float t);
+
+    /// Returns the 'from' vector rotated towards the 'to' vector by the given absolute angle, in radians.
+    /** This function slerps the given 'from' vector towards the 'to' vector.
+    @param from A normalized direction vector specifying the direction of rotation at angleRadians=0.
+    @param to A normalized direction vector specifying the target direction to rotate towards.
+    @param angleRadians The maximum angle to rotate the 'from' vector by, in the range [0, pi]. If the
+    angle between 'from' and 'to' is smaller than this angle, then the vector 'to' is returned.
+    Input values outside this range are silently clamped to the [0, pi] interval.
+    @return A spherical linear interpolation of the vector 'from' towards the vector 'to'. */
+    static Vector3 SlerpVectorAbs(const Vector3 &from, const Vector3& to, float angleRadians);
+
+    /// Normalizes this quaternion in-place.
+    /// @returns false if failure, true if success.
+    [[nodiscard]] bool Normalize();
+    /// Returns a normalized copy of this quaternion.
+    [[nodiscard]] Quaternion Normalized() const;
+
+    /// Returns true if the length of this quaternion is one.
+    [[nodiscard]] bool IsNormalized(float epsilon = 1e-5f) const;
+    [[nodiscard]] bool IsInvertible(float epsilon = 1e-3f) const;
+
+    /// Returns true if the entries of this quaternion are all finite.
+    [[nodiscard]] bool IsFinite() const;
+
+    /// Returns true if this quaternion equals rhs, up to the given epsilon.
+    [[nodiscard]] bool Equals(const Quaternion& rhs, float epsilon = 1e-3f) const;
+
+    /// Compares whether this Quaternion and the given Quaternion are identical bit-by-bit in the underlying representation.
+    /// @note Prefer using this over e.g. memcmp, since there can be SSE-related padding in the structures.
+    bool BitEquals(const Quaternion& rhs) const;
+
+    /// @return A pointer to the first element (x). The data is contiguous in memory.
+    /// ptr[0] gives x, ptr[1] gives y, ptr[2] gives z, ptr[3] gives w.
+    inline float *ptr() { return &x; }
+    [[nodiscard]] inline const float *ptr() const { return &x; }
 
 
-        [[nodiscard]] Matrix3x3 ToMatrix3x3() const;
-        [[nodiscard]] Matrix4x4 ToMatrix4x4() const;
+    // 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.
+    Quaternion operator * (const Quaternion& rhs) const;
 
-        [[nodiscard]] Matrix4x4 ToMatrix4x4(const Vector3 &translation) const;
+    // Unsafe
+    Quaternion operator * (float scalar) const;
 
-        [[nodiscard]] Vector3 Transform(const Vector3& vec) const;
-        [[nodiscard]] 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
-        [[nodiscard]] Vector4 Transform(const Vector4& vec) const;
-        [[nodiscard]] Vector4 Transform(float X, float Y, float Z, float W) const;
+    // Unsafe
+    Quaternion operator / (float scalar) const;
 
-        [[nodiscard]] Quaternion Lerp(const Quaternion& b, float t) const;
-        static Quaternion Lerp(const Quaternion &source, const Quaternion& target, float t);
-        [[nodiscard]] Quaternion Slerp(const Quaternion& q2, float t) const;
-        static Quaternion Slerp(const Quaternion &source, const Quaternion& target, float t);
+    // Transforms the given vector by this Quaternion.
+    Vector3 operator * (const Vector3& rhs) const;
 
-        /// Returns the 'from' vector rotated towards the 'to' vector by the given normalized time parameter.
-        /** This function slerps the given 'form' vector toward the 'to' vector.
-            @param from A normalized direction vector specifying the direction of rotation at t=0
-            @param to A normalized direction vector specifying the direction of rotation at t=1
-            @param t The interpolation time parameter, in the range [0, 1]. Input values outside this range are
-            silently clamped to the [0, 1] interval.
-            @return A spherical linear interpolation of the vector 'from' towards the vector 'to'. */
-        static Vector3 SlerpVector(const Vector3& from, const Vector3& to, float t);
+    Vector4 operator * (const Vector4& rhs) const;
 
-        /// Returns the 'from' vector rotated towards the 'to' vector by the given absolute angle, in radians.
-        /** This function slerps the given 'from' vector towards the 'to' vector.
-            @param from A normalized direction vector specifying the direction of rotation at angleRadians=0.
-            @param to A normalized direction vector specifying the target direction to rotate towards.
-            @param angleRadians The maximum angle to rotate the 'from' vector by, in the range [0, pi]. If the
-                angle between 'from' and 'to' is smaller than this angle, then the vector 'to' is returned.
-                Input values outside this range are silently clamped to the [0, pi] interval.
-            @return A spherical linear interpolation of the vector 'from' towards the vector 'to'. */
-        static Vector3 SlerpVectorAbs(const Vector3 &from, const Vector3& to, float angleRadians);
-
-        /// Normalizes this quaternion in-place.
-        /// Returns the old length of this quaternion, or 0 if normalization failed.
-        float Normalize();
-        /// Returns a normalized copy of this quaternion.
-        [[nodiscard]] Quaternion Normalized() const;
-
-        /// Returns true if the length of this quaternion is one.
-        [[nodiscard]] bool IsNormalized(float epsilon = 1e-5f) const;
-        [[nodiscard]] bool IsInvertible(float epsilon = 1e-3f) const;
-
-        /// Returns true if the entries of this quaternion are all finite.
-        [[nodiscard]] bool IsFinite() const;
-
-        /// Returns true if this quaternion equals rhs, up to the given epsilon.
-        [[nodiscard]] bool Equals(const Quaternion& rhs, float epsilon = 1e-3f) const;
-
-        /// Compares whether this Quaternion and the given Quaternion are identical bit-by-bit in the underlying representation.
-        /// @note Prefer using this over e.g. memcmp, since there can be SSE-related padding in the structures.
-        bool BitEquals(const Quaternion& rhs) const;
-
-        /// @return A pointer to the first element (x). The data is contiguous in memory.
-        /// ptr[0] gives x, ptr[1] gives y, ptr[2] gives z, ptr[3] gives w.
-        inline float *ptr() { return &x; }
-        [[nodiscard]] inline const float *ptr() const { return &x; }
-
-
-        // 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.
-        Quaternion operator * (const Quaternion& rhs) const;
-
-        // Unsafe
-        Quaternion operator * (float scalar) const;
-
-        // Unsafe
-        Quaternion operator / (float scalar) const;
-
-        // Transforms the given vector by this Quaternion.
-        Vector3 operator * (const Vector3& rhs) const;
-
-        Vector4 operator * (const Vector4& rhs) const;
-
-        // 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;
+    // 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 operator - () const;
 
-        /// Computes the dot product of this and the given quaternion.
-        /// Dot product is commutative.
-        [[nodiscard]] float Dot(const Quaternion &quaternion) const;
+    /// Computes the dot product of this and the given quaternion.
+    /// Dot product is commutative.
+    [[nodiscard]] float Dot(const Quaternion &quaternion) const;
 
-        /// Returns the angle between this and the target orientation (the shortest route) in radians.
-        [[nodiscard]] float AngleBetween(const Quaternion& target) const;
-        /// Returns the axis of rotation to get from this orientation to target orientation (the shortest route).
-        [[nodiscard]] Vector3 AxisFromTo(const Quaternion& target) const;
+    /// Returns the angle between this and the target orientation (the shortest route) in radians.
+    [[nodiscard]] float AngleBetween(const Quaternion& target) const;
+    /// Returns the axis of rotation to get from this orientation to target orientation (the shortest route).
+    [[nodiscard]] Vector3 AxisFromTo(const Quaternion& target) const;
 
 
-        [[nodiscard]] AxisAngle ToAxisAngle() const;
-        void SetFromAxisAngle(const AxisAngle& axisAngle);
+    /// Sets this quaternion to represent the same rotation as the given matrix.
+    void Set(const Matrix3x3& matrix);
+    void Set(const Matrix4x4& matrix);
+    void Set(float x, float y, float z, float w);
+    void Set(const Quaternion& q);
+    void Set(const Vector4& v);
 
-        /// Sets this quaternion to represent the same rotation as the given matrix.
-        void Set(const Matrix3x3& matrix);
-        void Set(const Matrix4x4& matrix);
-        void Set(float x, float y, float z, float w);
-        void Set(const Quaternion& q);
-        void Set(const Vector4& v);
-
-    public:
-        float x;
-        float y;
-        float z;
-        float w;
-    };
-}
+};

include/J3ML/LinearAlgebra/Vector2.hpp

@@ -58,6 +58,7 @@ namespace J3ML::LinearAlgebra {
         // Constructs a new Vector2 with the value {scalar, scalar}
         explicit Vector2(float scalar);
         Vector2(const Vector2& rhs);   // Copy Constructor
+        explicit Vector2(const Vector2i& rhs);
         //Vector2(Vector2&&) = default;   // Move Constructor
 
 
@@ -121,6 +122,8 @@ namespace J3ML::LinearAlgebra {
 
         bool operator == (const Vector2& rhs) const;
         bool operator != (const Vector2& rhs) const;
+        bool operator > (const Vector2& rhs) const;
+        bool operator < (const Vector2& rhs) const;
 
         /// Returns an element-wise minimum between two vectors.
         [[nodiscard]] Vector2 Min(const Vector2& min) const;

include/J3ML/LinearAlgebra/Vector2i.hpp

@@ -1,11 +1,31 @@
 #pragma once
+#include <string>
 
-namespace J3ML::LinearAlgebra
-{
-    class Vector2i
-    {
-    public:
-        int x;
-        int y;
-    };
-}
+namespace J3ML::LinearAlgebra {
+    class Vector2i;
+}
+
+class J3ML::LinearAlgebra::Vector2i {
+public:
+    int x, y;
+public:
+    Vector2i();
+    Vector2i(int x, int y) : x(x), y(y) {}
+    explicit Vector2i(int rhs) : x(rhs), y(rhs) {}
+public:
+    bool operator == (const Vector2i& rhs) const;
+    bool operator != (const Vector2i& rhs) const;
+    Vector2i& operator =(const Vector2i& rhs);
+    Vector2i& operator +=(const Vector2i& rhs);
+    Vector2i& operator -=(const Vector2i& rhs);
+    Vector2i& operator *=(const Vector2i& rhs);
+    Vector2i& operator /=(const Vector2i& rhs);
+    Vector2i operator +(const Vector2i& rhs) const;
+    Vector2i operator -(const Vector2i& rhs) const;
+    Vector2i operator *(const Vector2i& rhs) const;
+    Vector2i operator *(int rhs) const;
+    Vector2i operator /(const Vector2i& rhs) const;
+    Vector2i operator /(int rhs) const;
+public:
+    [[nodiscard]] std::string ToString() const;
+};

include/J3ML/LinearAlgebra/Vector3.hpp

@@ -68,15 +68,15 @@ public:
     /** @note Due to static data initialization order being undefined in C++, do NOT use this
         member to initialize other static data in other compilation units! */
     static const Vector3 NegativeInfinity;
-    /// Specifies a compile-time constant Vector3 with value (1,1,1).
+    /// Specifies a compile-time constant Vector3 with value (1,0,0).
     /** @note Due to static data initialization order being undefined in C++, do NOT use this
         member to initialize other static data in other compilation units! */
     static const Vector3 UnitX;
-    /// Specifies a compile-time constant Vector3 with value (1,1,1).
+    /// Specifies a compile-time constant Vector3 with value (0,1,0).
     /** @note Due to static data initialization order being undefined in C++, do NOT use this
         member to initialize other static data in other compilation units! */
     static const Vector3 UnitY;
-    /// Specifies a compile-time constant Vector3 with value (1,1,1).
+    /// Specifies a compile-time constant Vector3 with value (0,0,1).
     /** @note Due to static data initialization order being undefined in C++, do NOT use this
         member to initialize other static data in other compilation units! */
     static const Vector3 UnitZ;

include/J3ML/LinearAlgebra/Vector4.hpp

@@ -48,7 +48,7 @@ namespace J3ML::LinearAlgebra {
             @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 [] of this
                 class to access the elements of this vector by index. */
-        inline float* ptr();
+        float* ptr();
         [[nodiscard]] const float* ptr() const;
 
         /// Accesses an element of this vector using array notation.

main.cpp

@@ -12,11 +12,29 @@
 
 #include <iostream>
 #include <J3ML/Geometry.hpp>
-#include "J3ML/J3ML.hpp"
+#include <J3ML/J3ML.hpp>
+#include <jlog/Logger.hpp>
+
 
 int main(int argc, char** argv)
 {
 
+    using namespace J3ML::Math;
+
+    // Test quadrant
+    for (float r = 0; r < TwoPi; r+=0.25f)
+    {
+        Quadrant q = QuadrantOf(r);
+        if (q == Quadrant::I)
+            std::cout << "I" << std::endl;
+        if (q == Quadrant::II)
+            std::cout << "II" << std::endl;
+        if (q == Quadrant::III)
+            std::cout << "III" << std::endl;
+        if (q == Quadrant::IV)
+            std::cout << "IV" << std::endl;
+    }
+
     for (int i = 10; i < 9999999; i*=1.5f) {
         std::cout << J3ML::Math::Functions::Truncate(i) << std::endl;
     }

src/J3ML/Algorithm/Bezier.cpp

@@ -1,11 +1,13 @@
 #include <J3ML/Algorithm/Bezier.hpp>
+#include <J3ML/LinearAlgebra/Vector2.hpp>
+#include <J3ML/LinearAlgebra/Vector3.hpp>
 
 namespace J3ML::Algorithm
 {
     using namespace J3ML::LinearAlgebra;
     Vector2 BezierNormal(float t, const Vector2 &p0, const Vector2 &p1,
                                   const Vector2 &p2, const Vector2 &p3) {
-        auto derived = BezierDerivative(t, p0, p1, p2, p3);
+        Vector2 derived = BezierDerivative(t, p0, p1, p2, p3);
         return derived.Normalized();
     }
 
@@ -16,5 +18,24 @@ namespace J3ML::Algorithm
     Vector2 Bezier(float t, const Vector2 &p0, const Vector2 &p1, const Vector2 &p2, const Vector2 &p3) {
         return {Bezier(t, p0.x, p1.x, p2.x, p3.x), Bezier(t, p0.y, p1.y, p2.y, p3.y)};
     }
+
+    Vector3 BezierDerivative(float t, const Vector3& p0, const Vector3& p1, const Vector3& p2, const Vector3& p3)
+    {
+        return 3 * Square(1 - t) * (p1 - p0) + 6 * (1 - t) * t * (p2 - p1) + 3 * Square(t) * (p3 - p2);
+    }
+
+    Vector3 BezierNormal(float t, const Vector3& p0, const Vector3& p1, const Vector3& p2, const Vector3& p3)
+    {
+        Vector3 derived = BezierDerivative(t, p0, p1, p2, p3);
+        return derived.Normalized();
+    }
+
+    Vector3 Bezier(float t, const Vector3& p0, const Vector3& p1, const Vector3& p2, const Vector3& p3)
+    {
+        return {
+            Bezier(t, p0.x, p1.x, p2.x, p3.x),
+            Bezier(t, p0.y, p1.y, p2.y, p3.y),
+            Bezier(t, p0.z, p1.z, p2.z, p3.z)};
+    }
 }
 

src/J3ML/Geometry/Icosahedron.cpp

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

src/J3ML/Geometry/Sphere.cpp

@@ -9,18 +9,107 @@ namespace J3ML::Geometry
         return Contains(lineseg.A) && Contains(lineseg.B);
     }
 
-    TriangleMesh Sphere::GenerateUVSphere() const
+    TriangleMesh Sphere::GenerateUVSphere(int subdivisions) const
     {
-        // TODO: Implement this later
-        return TriangleMesh();
+        // http://www.songho.ca/opengl/gl_sphere.html
+
+        TriangleMesh mesh;
+
+        float x, y, z, xy;                           // Vertex Position
+        float nx, ny, nz, lengthInv = 1.f / Radius;  // Vertex Normal
+        float s, t;                                  // Vertex TexCoord
+
+        int sectorCount = subdivisions;
+        int stackCount = subdivisions;
+
+        float sectorStep = 2.f * Math::Pi / sectorCount;
+        float stackStep = Math::Pi / stackCount;
+        float sectorAngle, stackAngle;
+
+        for (int i = 0; i <= stackCount; ++i)
+        {
+            stackAngle = Math::Pi / 2.f - i * stackStep;   // starting from pi/2 to -pi/2
+            xy = Radius * Math::Cos(stackAngle);           // r * cos(u)
+            z = Radius * Math::Sin(stackAngle);            // r * sin(u)
+
+            // add (sectorCount + 1) vertices per stack
+            // first and last vertices have same position and normal, but different tex coords
+            for (int j = 0; j <= sectorCount; ++j)
+            {
+                sectorAngle = j * sectorStep;   // starting from 0 to 2pi
+
+                // vertex position (x, y, z)
+                x = xy * Math::Cos(sectorAngle);
+                y = xy * Math::Sin(sectorAngle);
+
+                Vector3 vertex = {x, y, z};
+
+                mesh.Vertices.push_back(vertex);
+
+                // normalized vertex normal (nx, ny, nz)
+                nx = x * lengthInv;
+                ny = y * lengthInv;
+                nz = z * lengthInv;
+
+                Vector3 normal = {nx, ny, nz};
+
+                mesh.Normals.push_back(normal);
+
+                // vertex tex coord (s, t) range between [0, 1]
+                s = (float)j / sectorCount;
+                t = (float)i / stackCount;
+
+                Vector2 TexCoords = {s, t};
+
+                mesh.UVs.push_back(normal);
+            }
+        }
+        return mesh;
     }
 
     TriangleMesh Sphere::GenerateIcososphere() const
     {
-        // TODO: Implement this later
-        return TriangleMesh();
+
+        // Generate 12 vertices of an icosahedron for a given radius.
+
+        const float h_angle = Math::Pi / 180.f * 72.f; // 72 degree = 360 / 5;
+        const float v_angle = Math::Atan(1.f / 2.f);
+
+        TriangleMesh mesh;
+
+        int i1, i2;
+        float z, xy;
+        float hAngle1 = -Math::Pi / 2.f - h_angle / 2.f;
+        float hAngle2 = -Math::Pi / 2;
+
+        // the first top vertex at (0,0,r)
+        Vector3 top_vertex = {0, 0, Radius};
+
+        // compute 10 vertices at 1st and 2nd rows
+        for (int i = 1; i <= 5; ++i)
+        {
+            i1 = i * 3;       // index for 1st row
+            i2 = (i + 5) * 3; // index for 2nd row
+
+            z  = Radius * Math::Sin(v_angle);   // elevation
+            xy = Radius * Math::Cos(v_angle);   // length on XY plane
+
+            Vector3 vert_0 = {xy * Math::Cos(hAngle1), xy * Math::Sin(hAngle1), z};
+            Vector3 vert_1 = {xy * Math::Cos(hAngle2), xy * Math::Sin(hAngle2), -z};
+
+            // next horizontal angles
+            hAngle1 += h_angle;
+            hAngle2 += h_angle;
+        }
+
+        // the last bottom vertex at (0, 0, -r)
+        i1 = 11 * 3;
+        Vector3 last_vertex = {0,0, -Radius};
+
+        return mesh;
     }
 
+
     void Sphere::ProjectToAxis(const Vector3 &direction, float &outMin, float &outMax) const
     {
         float d = Vector3::Dot(direction, Position);

src/J3ML/J3ML.cpp

@@ -38,14 +38,106 @@ float PowUInt(float base, u32 exponent)
 }
 
 
-namespace J3ML
-{
+namespace J3ML::Math::Functions::Trigonometric {
+    enum Sign SignOfSin(float radians) {
+        enum Quadrant q = QuadrantOf(radians);
+        if (q == Quadrant::I || q == Quadrant::II)
+            return Sign::POSITIVE;
 
-    float Math::Functions::Radians(float degrees) { return degrees * (Pi/180.f); }
+        // ReSharper disable once CppDFAConstantConditions
+        if (q == Quadrant::II || q == Quadrant::IV)
+            return Sign::NEGATIVE;
 
-    float Math::Functions::Degrees(float radians) { return radians * (180.f/Pi); }
+        // ReSharper disable once CppDFAUnreachableCode
+        return Sign::ZERO;
+    }
 
+    enum Sign SignOfCos(float radians) {
+        enum Quadrant q = QuadrantOf(radians);
+        if (q == Quadrant::I || q == Quadrant::IV)
+            return Sign::POSITIVE;
 
+        // ReSharper disable once CppDFAConstantConditions
+        if (q == Quadrant::II || q == Quadrant::III)
+            return Sign::NEGATIVE;
+
+        // ReSharper disable once CppDFAUnreachableCode
+        return Sign::ZERO;
+    }
+
+    enum Sign SignOfTan(float radians) {
+        enum Quadrant q = QuadrantOf(radians);
+        if (q == Quadrant::I || q == Quadrant::III)
+            return Sign::POSITIVE;
+
+        // ReSharper disable once CppDFAConstantConditions
+        if (q == Quadrant::II || q == Quadrant::IV)
+            return Sign::NEGATIVE;
+
+        // ReSharper disable once CppDFAUnreachableCode
+        return Sign::ZERO;
+    }
+
+    Quadrant QuadrantOf(float radians) {
+        if (radians > ThreePiOverTwo) {
+            return Quadrant::IV;
+        } else if (radians >= Pi) {
+            return Quadrant::III;
+        } else if (radians >= PiOverTwo) {
+            return Quadrant::II;
+        } else {
+            return Quadrant::I;;
+        }
+    }
+
+    float Radians(float degrees) { return degrees * (Pi/180.f); }
+
+    float Degrees(float radians) { return radians * (180.f/Pi); }
+
+    float Sin(float x) {
+#ifdef USE_LOOKUP_TABLES
+#elif USE_SSE
+#else
+        return std::sin(x);
+#endif
+    }
+
+    float Cos(float x) {
+#ifdef USE_LOOKUP_TABLES
+#elif USE_SSE
+#else
+        return std::cos(x);
+#endif
+    }
+
+    float Tan(float x) { return std::tan(x); }
+
+    void SinCos(float x, float &outSin, float &outCos) {
+        outSin = Sin(x);
+        outCos = Cos(x);
+    }
+
+    float Asin(float x) { return std::asin(x); }
+
+    float Acos(float x) { return std::acos(x); }
+
+    float Atan(float x) { return std::atan(x); }
+
+    float Atan2(float y, float x) { return std::atan2(y, x); }
+
+    float Sinh(float x) { return std::sinh(x); }
+
+    float Cosh(float x) { return std::cosh(x); }
+
+    float Tanh(float x) { return std::tanh(x); }
+
+}
+
+namespace J3ML::Math::Functions {
+
+}
+
+namespace J3ML {
 
     Math::Rotation Math::operator ""_degrees(long double rads) { return {Functions::Radians((float)rads)}; }
 
@@ -211,56 +303,26 @@ namespace J3ML
 
     Math::Rotation::Rotation(float value) : valueInRadians(value) {}
 
+    Math::Rotation::Rotation(const Types::Radians &radians): valueInRadians(radians.value) {}
+
+    Math::Rotation::Rotation(const Types::Degrees &degrees): valueInRadians(Functions::Radians(degrees.value)) {}
+
     Math::Rotation Math::Rotation::operator+(const Math::Rotation &rhs) {
         return {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) {
+
+    int BitTwiddling::CountBitsSet(u32 value) {
 
     }
 
+
+
+
     namespace Math::Functions {
-        float Sin(float x) {
-#ifdef USE_LOOKUP_TABLES
-#elif USE_SSE
-#else
-            return std::sin(x);
-#endif
-        }
 
-        float Cos(float x) {
-#ifdef USE_LOOKUP_TABLES
-#elif USE_SSE
-#else
-            return std::cos(x);
-#endif
-        }
 
-        float Tan(float x) { return std::tan(x); }
-
-        void SinCos(float x, float &outSin, float &outCos) {
-            outSin = Sin(x);
-            outCos = Cos(x);
-        }
-
-        float Asin(float x) { return std::asin(x); }
-
-        float Acos(float x) { return std::acos(x); }
-
-        float Atan(float x) { return std::atan(x); }
-
-        float Atan2(float y, float x) { return std::atan2(y, x); }
-
-        float Sinh(float x) { return std::sinh(x); }
-
-        float Cosh(float x) { return std::cosh(x); }
-
-        float Tanh(float x) { return std::tanh(x); }
 
         bool IsPow2(u32 number) {
             return (number & (number - 1)) == 0;
@@ -311,3 +373,10 @@ namespace J3ML
 
     }
 }
+
+namespace J3ML::Math::Functions::Interpolation {
+    float SmoothStart(float t) {
+        assert(t >= 0.f && t <= 1.f);
+        return t*t;
+    }
+}

src/J3ML/LinearAlgebra/AxisAngle.cpp

@@ -2,60 +2,22 @@
 #include <J3ML/LinearAlgebra/Quaternion.hpp>
 namespace J3ML::LinearAlgebra {
 
-    AxisAngle::AxisAngle() : axis(Vector3::Zero) {}
+    AxisAngle::AxisAngle() : axis(Vector3::Zero), angle(0) {}
 
-    AxisAngle::AxisAngle(const Vector3 &axis, float angle) : axis(axis), angle(angle) {}
+    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)
-        };
+
+    AxisAngle::AxisAngle(const Quaternion& rhs) {
+        float halfAngle = std::acos(rhs.w);
+        angle = halfAngle * 2.f;
+        float reciprocalSinAngle = 1.f / std::sqrt(1.f - rhs.w*rhs.w);
+
+        axis = { rhs.x*reciprocalSinAngle, rhs.y*reciprocalSinAngle, rhs.z*reciprocalSinAngle };
     }
 
-    AxisAngle::AxisAngle(const Quaternion &q) {
-        auto theta = std::acos(q.w) * 2.f;
-        auto ax = q.x / std::sin(std::acos(theta));
-        auto ay = q.y / std::sin(std::acos(theta));
-        auto az = q.z / std::sin(std::acos(theta));
-    }
-
-    AxisAngle::AxisAngle(const EulerAngle &e) {
-
-        // Assuming the angles are in radians
-
-        float heading = e.pitch;
-        float attitude = e.yaw;
-        float bank = e.roll;
-
-        float c1 = std::cos(heading / 2.f);
-        float s1 = std::sin(heading / 2.f);
-        float c2 = std::cos(attitude / 2.f);
-        float s2 = std::sin(attitude / 2.f);
-        float c3 = std::cos(bank / 2.f);
-        float s3 = std::sin(bank / 2.f);
-
-        float w = c1*c2*c3 - s1*s2*s3;
-        float x = c1*c2*c3 + s1*s2*s3;
-        float y = s1*c2*c3 + c1*s2*s3;
-        float z = c1*s2*c3 - s1*c2*s3;
-
-        angle = 2.f * std::acos(w);
-
-        double norm = x*x + y*y + z*z;
-        if (norm < 0.001) { // when all euler angles are zero angle=0, so
-            // we can set axis to anything to avoid divide by zero
-            x = 1;
-            y = z = 0;
-        } else {
-            norm = std::sqrt(norm);
-            x /= norm;
-            y /= norm;
-            z /= norm;
-        }
-
-        axis = {x, y, z};
+    AxisAngle::AxisAngle(const EulerAngleXYZ& e) {
+        auto a = AxisAngle(Quaternion(e));
+        axis = a.axis;
+        angle = a.angle;
     }
 }

src/J3ML/LinearAlgebra/DirectionVector.cpp

@@ -0,0 +1,38 @@
+#include <J3ML/LinearAlgebra/DirectionVector.hpp>
+#include <J3ML/LinearAlgebra/Matrix3x3.hpp>
+
+DirectionVectorRH::DirectionVectorRH(const Vector3& rhs) {
+    x = rhs.x;
+    y = rhs.y;
+    z = rhs.z;
+}
+
+DirectionVectorRH DirectionVectorRH::Forward(const Matrix3x3& rhs) {
+    return DirectionVectorRH(rhs.Col(2));
+}
+
+DirectionVectorRH DirectionVectorRH::Backward(const Matrix3x3& rhs) {
+    return DirectionVectorRH(-rhs.Col(2));
+}
+
+DirectionVectorRH DirectionVectorRH::Left(const Matrix3x3& rhs) {
+    return DirectionVectorRH(-rhs.Col(0));
+}
+
+DirectionVectorRH DirectionVectorRH::Right(const Matrix3x3& rhs) {
+    return DirectionVectorRH(rhs.Col(0));
+}
+
+DirectionVectorRH DirectionVectorRH::Up(const Matrix3x3 &rhs) {
+    return DirectionVectorRH(rhs.Col(1));
+}
+
+DirectionVectorRH DirectionVectorRH::Down(const Matrix3x3& rhs) {
+    return DirectionVectorRH(-rhs.Col(1));
+}
+
+
+
+
+
+

src/J3ML/LinearAlgebra/EulerAngle.cpp

@@ -1,147 +1,45 @@
 #include <J3ML/LinearAlgebra/EulerAngle.hpp>
+#include <J3ML/LinearAlgebra/Matrix3x3.hpp>
 #include <cmath>
 #include <algorithm>
 
 
 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::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); }
-
-    bool EulerAngle::operator==(const EulerAngle& a) const
-    {
-        return (pitch == a.pitch) && (yaw == a.yaw) && (roll == a.roll);
+    EulerAngleXYZ::EulerAngleXYZ(float roll, float pitch, float yaw) {
+        this->roll = roll;
+        this->pitch = pitch;
+        this->yaw = yaw;
     }
 
-    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;
+    EulerAngleXYZ::EulerAngleXYZ(const AxisAngle& rhs) {
+        *this = EulerAngleXYZ(Quaternion(rhs));
     }
 
-    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;
+    EulerAngleXYZ::EulerAngleXYZ(const Quaternion& q) {
+        float sy = 2 * q.x * q.z + 2 * q.y * q.w;
+        bool gimbal_lock = std::abs(sy) > 0.99999f;
+
+        if (!gimbal_lock)
+            roll = Math::Degrees(std::atan2(-(2 * q.y * q.z - 2 * q.x * q.w),2 * q.w * q.w + 2 * q.z * q.z - 1));
+        else
+            roll = Math::Degrees(std::atan2(2 * q.y * q.z + 2 * q.x * q.w,2 * q.w * q.w + 2 * q.y * q.y - 1));
+
+        pitch = Math::Degrees(std::asin(sy));
+
+        if (!gimbal_lock)
+            yaw = Math::Degrees(std::atan2(-(2 * q.x * q.y - 2 * q.z * q.w),2 * q.w * q.w + 2 * q.x * q.x - 1));
+        else
+            yaw = 0;
     }
 
-    EulerAngle::EulerAngle() : pitch(0), yaw(0), roll(0) {}
+    EulerAngleXYZ::EulerAngleXYZ(const Matrix3x3& rhs) {
+        auto m = rhs.Transposed();
+        auto sy = m.At(0, 2);
+        auto unlocked = std::abs(sy) < 0.99999f;
 
-    EulerAngle::EulerAngle(const AxisAngle &rhs) {
-
-        float x = rhs.axis.x;
-        float y = rhs.axis.y;
-        float z = rhs.axis.z;
-        float angle = rhs.angle;
-
-        double s = std::sin(rhs.angle);
-
-        double c = std::cos(rhs.angle);
-
-        double t = 1-c;
-
-        // if axis is not already normalized then uncomment this
-
-        // double magnitude = std::sqrt(x*x + y*y + z*z);
-        // if (magnitude == 0) throw error;
-        // x /= magnitude;
-        // y /= magnitude;
-        // z /= magnitude;
-
-        if ((x*y*t + z*s) > 0.998) { // North pole singularity detected
-            pitch = 2 * std::atan2(x * std::sin(angle/2.f), std::cos(angle/2.f));
-            yaw = Math::Pi / 2.f;
-            roll = 0;
-            return;
-        }
-
-        if ((x*y*t + z*s) < -0.998) { // South pole singularity detected
-            pitch = -2 * std::atan2(x * std::sin(angle/2.f), std::cos(angle/2.f));
-            yaw = -Math::Pi / 2.f;
-            roll = 0;
-            return;
-        }
-
-        pitch = std::atan2(y * s-x * z * t, 1 - (y*y + z*z) * t);
-        yaw = std::asin(x * y * t + z * s);
-        roll = std::atan2(x * s - y * z * t, 1 - (x*x + z*z) * t);
-    }
-
-    AxisAngle EulerAngle::ToAxisAngle() const {
-        auto c1 = std::cos(yaw / 2);
-        auto c2 = std::cos(pitch / 2);
-        auto c3 = std::cos(roll / 2);
-        auto s1 = std::sin(yaw / 2);
-        auto s2 = std::sin(pitch / 2);
-        auto s3 = std::sin(roll / 2);
-
-        auto angle = 2 * std::acos(c1*c2*c3 - s1*s2*s3);
-
-        auto x = s1*s2*c3 + c1*c2*s3;
-        auto y = s1*c2*c3 + c1*s2*s3;
-        auto z = c1*s2*c3 - s1*c2*s3;
-
-        // todo: normalize?
-        // sqrt(x^2 + y^2 + z^2) = sqrt((s1 s2 c3 +c1 c2 s3)^2+(s1 c2 c3 + c1 s2 s3)^2+(c1 s2 c3 - s1 c2 s3)^2)
-
-        return {{x,y,z}, angle};
-    }
-
-    Quaternion EulerAngle::ToQuaternion() const {
-        auto c1 = std::cos(yaw / 2);
-        auto c2 = std::cos(pitch / 2);
-        auto c3 = std::cos(roll / 2);
-        auto s1 = std::sin(yaw / 2);
-        auto s2 = std::sin(pitch / 2);
-        auto s3 = std::sin(roll / 2);
-
-        auto w = c1*c2*c3 - s1*s2*s3;
-        auto x = s1*s2*c3 + c1*c2*s3;
-        auto y = s1*c2*c3 + c1*s2*s3;
-        auto z = c1*s2*c3 - s1*c2*s3;
-
-        return {w,x,y,z};
-    }
-
-    EulerAngle::EulerAngle(const Quaternion &rhs) {
-        double test = rhs.x * rhs.y + rhs.z * rhs.w;
-        if (test > 0.499) { // Singularity at north pole
-            pitch = 2 * std::atan2(rhs.x, rhs.w);
-            yaw = Math::Pi / 2.f;
-            roll = 0;
-            return;
-        }
-
-        if (test < -0.499) { // Singularity at south pole
-            pitch = -2 * std::atan2(rhs.x, rhs.y);
-            yaw = - Math::Pi / 2.f;
-            roll = 0;
-            return;
-        }
-        float sqx = rhs.x * rhs.x;
-        float sqy = rhs.y * rhs.y;
-        float sqz = rhs.z * rhs.z;
+        roll = Math::Degrees(unlocked ? std::atan2(-m.At(1, 2), m.At(2, 2)) : std::atan2(m.At(2, 1), m.At(1, 1)));
+        pitch = Math::Degrees(std::asin(sy));
+        yaw = Math::Degrees(unlocked ? std::atan2(-m.At(0, 1), m.At(0, 0)) : 0);
     }
 }

src/J3ML/LinearAlgebra/Matrix3x3.cpp

@@ -109,27 +109,8 @@ namespace J3ML::LinearAlgebra {
         //this->elems[2][2] = r3.z;
     }
 
-    Matrix3x3::Matrix3x3(const Quaternion &orientation) {
-        SetRotatePart(orientation);
-    }
-
-    Matrix3x3::Matrix3x3(const EulerAngle &orientation) {
-        auto sa = std::sin(orientation.pitch);
-        auto ca = std::cos(orientation.pitch);
-        auto sb = std::sin(orientation.roll);
-        auto cb = std::cos(orientation.roll);
-        auto sh = std::sin(orientation.yaw);
-        auto ch = std::cos(orientation.yaw);
-
-        At(0, 0) = ch*ca;
-        At(0, 1) = -ch*sa*cb + sh*sh;
-        At(0, 2) = ch*sa*sb + sh*cb;
-        At(1, 0) = sa;
-        At(1, 1) = ca*cb;
-        At(1, 2) = -ca*cb;
-        At(2, 0) = -sh*ca;
-        At(2, 1) = sh*sa*cb + ch*sb;
-        At(2, 2) = -sh*sa*sb + ch*cb;
+    Matrix3x3::Matrix3x3(const Quaternion& orientation) {
+        //*this = Matrix3x3(EulerAngleXYZ(orientation));
     }
 
     float Matrix3x3::Determinant() const {
@@ -207,7 +188,7 @@ namespace J3ML::LinearAlgebra {
         };
     }
 
-    Quaternion Matrix3x3::ToQuat() const {
+    /*Quaternion Matrix3x3::ToQuat() const {
         auto m00 = At(0,0);
         auto m01 = At(0, 1);
         auto m02 = At(0, 2);
@@ -226,7 +207,7 @@ namespace J3ML::LinearAlgebra {
                 (m10 - m01) / w4,
                 w
         };
-    }
+    }*/
 
     void Matrix3x3::SetRotatePart(const Vector3 &a, float angle) {
         float s = std::sin(angle);
@@ -992,25 +973,12 @@ namespace J3ML::LinearAlgebra {
 
     bool Matrix3x3::TryConvertToQuat(Quaternion &q) const {
         if (IsColOrthogonal() && HasUnitaryScale() && !HasNegativeScale()) {
-            q = ToQuat();
+            q = Quaternion(*this);
             return true;
         }
         return false;
     }
 
-    EulerAngle Matrix3x3::ToEulerAngle() const {
-        auto heading = std::atan2(-At(2, 0), At(0, 0));
-        auto attitude = std::asin(At(1, 0));
-        auto bank = std::atan2(-At(1,2), At(1,1));
-        if (At(1, 0) == 1 || At(1, 0) == -1) // North Pole || South Pole
-        {
-            heading = std::atan2(At(0, 2), At(2,2));
-            bank = 0;
-        }
-
-        return {attitude, heading, bank};
-    }
-
     void Matrix3x3::BatchTransform(Vector3 *pointArray, int numPoints, int stride) const {
         assert(pointArray || numPoints == 0);
         assert(stride >= (int)sizeof(Vector3));

src/J3ML/LinearAlgebra/Matrix4x4.cpp

@@ -86,10 +86,6 @@ namespace J3ML::LinearAlgebra {
         Set3x3Part(Matrix3x3(orientation));
     }
 
-    Matrix4x4::Matrix4x4(const EulerAngle &orientation) {
-        Set3x3Part(Matrix3x3(orientation));
-    }
-
     void Matrix4x4::SetTranslatePart(float translateX, float translateY, float translateZ) {
         elems[0][3] = translateX;
         elems[1][3] = translateY;
@@ -777,19 +773,6 @@ namespace J3ML::LinearAlgebra {
         };
     }
 
-    EulerAngle Matrix4x4::ToEulerAngle() const {
-        auto heading = std::atan2(-At(2, 0), At(0, 0));
-        auto attitude = std::asin(At(1, 0));
-        auto bank = std::atan2(-At(1,2), At(1,1));
-        if (At(1, 0) == 1 || At(1, 0) == -1) // North Pole || South Pole
-        {
-            heading = std::atan2(At(0, 2), At(2,2));
-            bank = 0;
-        }
-
-        return {attitude, heading, bank};
-    }
-
     bool Matrix4x4::InverseOrthogonalUniformScale() {
         assert(!ContainsProjection());
         assert(IsColOrthogonal(1e-3f));

src/J3ML/LinearAlgebra/Quaternion.cpp

@@ -1,23 +1,46 @@
-#include <J3ML/LinearAlgebra/Vector3.hpp>
-#include <J3ML/LinearAlgebra/Vector4.hpp>
 #include <J3ML/LinearAlgebra/Matrix3x3.hpp>
 #include <J3ML/LinearAlgebra/Matrix4x4.hpp>
 #include <J3ML/LinearAlgebra/Quaternion.hpp>
 #include <J3ML/LinearAlgebra/AxisAngle.hpp>
+#include <J3ML/LinearAlgebra/EulerAngle.hpp>
+#include <J3ML/LinearAlgebra/Vector4.hpp>
+#include <J3ML/LinearAlgebra/Vector3.hpp>
 
 namespace J3ML::LinearAlgebra {
 
     const Quaternion Quaternion::Identity = Quaternion(0.f, 0.f, 0.f, 1.f);
     const Quaternion Quaternion::NaN      = Quaternion(NAN, NAN, NAN, NAN);
 
-    Quaternion Quaternion::operator-() const
-    {
+    Quaternion Quaternion::operator-() const {
         return {-x, -y, -z, -w};
     }
 
-    Quaternion::Quaternion(const Matrix3x3 &rotationMtrx) {}
+    Quaternion::Quaternion(const Matrix3x3& ro_mat) {
+        auto m = ro_mat.Transposed();
+        auto m00 = m.At(0,0);
+        auto m01 = m.At(0, 1);
+        auto m02 = m.At(0, 2);
+        auto m10 = m.At(1,0);
+        auto m11 = m.At(1, 1);
+        auto m12 = m.At(1, 2);
+        auto m20 = m.At(2,0);
+        auto m21 = m.At(2, 1);
+        auto m22 = m.At(2, 2);
 
-    Quaternion::Quaternion(const Matrix4x4 &rotationMtrx) {}
+        auto field_w = std::sqrt(1.f + m00 + m11 + m22) / 2.f;
+        float w4 = (4.f * field_w);
+
+        x = (m21 - m12) / w4;
+        y = (m02 - m20) / w4;
+        z = (m10 - m01) / w4;
+        w = field_w;
+        Normalize();
+    }
+
+    Quaternion::Quaternion(const Matrix4x4& ro_mat) {
+        auto q = Quaternion(ro_mat.GetRotatePart());
+        x = q.x; y = q.y; z = q.z; w = q.w;
+    }
 
     Vector3 Quaternion::WorldX() const { return Transform(1.f, 0.f, 0.f); }
 
@@ -50,22 +73,6 @@ namespace J3ML::LinearAlgebra {
             return (*this * (t - 1.f) + b * t).Normalized();
     }
 
-    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 {
         return Quaternion(x * scalar, y * scalar, z * scalar, w * scalar);
     }
@@ -82,8 +89,6 @@ namespace J3ML::LinearAlgebra {
 
     Quaternion Quaternion::operator+() const { return *this; }
 
-    Quaternion::Quaternion() {}
-
     Quaternion::Quaternion(float X, float Y, float Z, float W) : x(X), y(Y), z(Z), w(W) {}
 
     // TODO: implement
@@ -148,20 +153,6 @@ namespace J3ML::LinearAlgebra {
         return (*this * (a * sign) + q2 * b).Normalized();
     }
 
-    AxisAngle Quaternion::ToAxisAngle() const {
-        float halfAngle = std::acos(w);
-        float angle = halfAngle * 2.f;
-        // TODO: Can Implement Fast Inverted Sqrt Here
-        float reciprocalSinAngle = 1.f / std::sqrt(1.f - w*w);
-
-        Vector3 axis = {
-                x*reciprocalSinAngle,
-                y*reciprocalSinAngle,
-                z*reciprocalSinAngle
-        };
-        return AxisAngle(axis, angle);
-    }
-
     float Quaternion::AngleBetween(const Quaternion &target) const {
         Quaternion delta = target / *this;
         return delta.Normalized().Angle();
@@ -212,47 +203,13 @@ namespace J3ML::LinearAlgebra {
         return Vector3(x, y, z) * rcpSinAngle;
     }
 
-    Quaternion::Quaternion(const Vector3 &rotationAxis, float rotationAngleRadians) {
-        SetFromAxisAngle(rotationAxis, rotationAngleRadians);
-    }
-
-    Quaternion::Quaternion(const Vector4 &rotationAxis, float rotationAngleRadians) {
-        SetFromAxisAngle(rotationAxis, rotationAngleRadians);
-    }
-
-    Quaternion::Quaternion(const AxisAngle &angle) {
+    Quaternion::Quaternion(const AxisAngle& angle) {
         double s = std::sin(angle.angle / 2);
         x = angle.axis.x * s;
         y = angle.axis.y * s;
         z = angle.axis.z * s;
         w = std::cos(angle.angle / 2);
-    }
-
-    Quaternion::Quaternion(const EulerAngle &angle) {
-        // Abbreviations for the various angular functions
-        double cr = std::cos(angle.roll * 0.5);
-        double sr = std::sin(angle.roll * 0.5);
-        double cp = std::cos(angle.pitch * 0.5);
-        double sp = std::sin(angle.pitch * 0.5);
-        double cy = std::cos(angle.yaw * 0.5);
-        double sy = std::sin(angle.yaw * 0.5);
-
-        w = cr * cp * cy + sr * sp * sy;
-        x = sr * cp * cy - cr * sp * sy;
-        y = cr * sp * cy + sr * cp * sy;
-        z = cr * cp * sy - sr * sp * cy;
-    }
-
-    void Quaternion::SetFrom(const AxisAngle &angle) {
-        double s = std::sin(angle.angle / 2);
-        x = angle.axis.x * s;
-        y = angle.axis.y * s;
-        z = angle.axis.z * s;
-        w = std::cos(angle.angle / 2);
-    }
-
-    EulerAngle Quaternion::ToEulerAngle() const {
-        return EulerAngle(*this);
+        Normalize();
     }
 
     Quaternion Quaternion::RandomRotation(RNG &rng) {
@@ -271,16 +228,16 @@ namespace J3ML::LinearAlgebra {
         return Quaternion::Identity;
     }
 
-    float Quaternion::Normalize() {
+    bool Quaternion::Normalize() {
         float length = Length();
         if (length < 1e-4f)
-            return 0.f;
+            return false;
         float rcpLength = 1.f / length;
         x *= rcpLength;
         y *= rcpLength;
         z *= rcpLength;
         w *= rcpLength;
-        return length;
+        return true;
     }
 
     bool Quaternion::IsNormalized(float epsilon) const {
@@ -325,9 +282,10 @@ namespace J3ML::LinearAlgebra {
 
     Quaternion Quaternion::LookAt(const Vector3 &localForward, const Vector3 &targetDirection, const Vector3 &localUp,
                                   const Vector3 &worldUp) {
-        return Matrix3x3::LookAt(localForward, targetDirection, localUp, worldUp).ToQuat();
+        return Quaternion(Matrix3x3::LookAt(localForward, targetDirection, localUp, worldUp));
     }
 
+    /*
     Quaternion Quaternion::RotateX(float angleRadians) {
         return {{1,0,0}, angleRadians};
     }
@@ -343,6 +301,7 @@ namespace J3ML::LinearAlgebra {
     Quaternion Quaternion::RotateAxisAngle(const AxisAngle &axisAngle) {
         return {axisAngle.axis, axisAngle.angle};
     }
+    */
 
     Quaternion Quaternion::RotateFromTo(const Vector3 &sourceDirection, const Vector3 &targetDirection) {
         assert(sourceDirection.IsNormalized());
@@ -369,14 +328,6 @@ namespace J3ML::LinearAlgebra {
         return Quaternion::RotateFromTo(sourceDirection.XYZ(), targetDirection.XYZ());
     }
 
-    Quaternion::Quaternion(const float *data) {
-        assert(data);
-        x = data[0];
-        y = data[1];
-        z = data[2];
-        w = data[3];
-    }
-
     Quaternion Quaternion::Lerp(const Quaternion &source, const Quaternion &target, float t) { return source.Lerp(target, t);}
 
     Quaternion Quaternion::Slerp(const Quaternion &source, const Quaternion &target, float t) { return source.Slerp(target, t);}
@@ -401,4 +352,28 @@ namespace J3ML::LinearAlgebra {
     float Quaternion::LengthSquared() const { return x*x + y*y + z*z + w*w;}
 
     float Quaternion::Length() const { return std::sqrt(LengthSquared()); }
+
+    Quaternion::Quaternion(const EulerAngleXYZ& rhs) {
+        float cos_roll = Math::Cos(0.5f * Math::Radians(rhs.roll));
+        float sin_roll = Math::Sin(0.5f * Math::Radians(rhs.roll));
+
+        float cos_pitch = Math::Cos(0.5f * Math::Radians(rhs.pitch));
+        float sin_pitch = Math::Sin(0.5f * Math::Radians(rhs.pitch));
+
+        float cos_yaw = Math::Cos(0.5f * Math::Radians(rhs.yaw));
+        float sin_yaw = Math::Sin(0.5f * Math::Radians(rhs.yaw));
+
+        x = cos_roll * sin_pitch * sin_yaw + sin_roll * cos_pitch * cos_yaw;
+        y = -sin_roll * cos_pitch * sin_yaw + cos_roll * sin_pitch * cos_yaw;
+        z = cos_roll * cos_pitch * sin_yaw + sin_roll * sin_pitch * cos_yaw;
+        w = -sin_roll * sin_pitch * sin_yaw + cos_roll * cos_pitch * cos_yaw;
+        Normalize();
+    }
+
+    Quaternion::Quaternion(const Quaternion& rhs) {
+        x = rhs.x;
+        y = rhs.y;
+        z = rhs.z;
+        w = rhs.w;
+    }
 }

src/J3ML/LinearAlgebra/Vector2.cpp

@@ -7,6 +7,7 @@
 #include <J3ML/LinearAlgebra/Matrix3x3.hpp>
 #include <J3ML/LinearAlgebra/Matrix4x4.hpp>
 #include <J3ML/LinearAlgebra/Vector4.hpp>
+#include <J3ML/LinearAlgebra/Vector2i.hpp>
 
 namespace J3ML::LinearAlgebra {
 
@@ -36,12 +37,12 @@ namespace J3ML::LinearAlgebra {
 
     bool Vector2::operator==(const Vector2& rhs) const
     {
-        return this->IsWithinMarginOfError(rhs);
+        return x == rhs.x && y == rhs.y;
     }
 
     bool Vector2::operator!=(const Vector2& rhs) const
     {
-        return this->IsWithinMarginOfError(rhs) == false;
+        return !(*this == rhs);
     }
 
     Vector2 Vector2::Min(const Vector2& min) const
@@ -499,6 +500,19 @@ namespace J3ML::LinearAlgebra {
         return std::format("{},{}", x, y);
     }
 
+    bool Vector2::operator>(const Vector2 &rhs) const {
+        return this->Magnitude() > rhs.Magnitude();
+    }
+
+    bool Vector2::operator<(const Vector2 &rhs) const {
+        return this->Magnitude() < rhs.Magnitude();
+    }
+
+    Vector2::Vector2(const Vector2i& rhs) {
+        x = rhs.x;
+        y = rhs.y;
+    }
+
     Vector2 operator*(float lhs, const Vector2 &rhs) {
         return {lhs * rhs.x, lhs * rhs.y};
     }

src/J3ML/LinearAlgebra/Vector2i.cpp

@@ -0,0 +1,79 @@
+#include <J3ML/LinearAlgebra/Vector2i.hpp>
+
+J3ML::LinearAlgebra::Vector2i &J3ML::LinearAlgebra::Vector2i::operator =(const Vector2i& rhs) {
+    x = rhs.x;
+    y = rhs.y;
+    return *this;
+}
+
+bool J3ML::LinearAlgebra::Vector2i::operator ==(const Vector2i& rhs) const {
+    return (x == rhs.x && y == rhs.y);
+}
+
+bool J3ML::LinearAlgebra::Vector2i::operator !=(const Vector2i& rhs) const {
+    return !(*this == rhs);
+}
+
+J3ML::LinearAlgebra::Vector2i& J3ML::LinearAlgebra::Vector2i::operator +=(const Vector2i& rhs) {
+    x += rhs.x;
+    y += rhs.y;
+    return *this;
+}
+
+J3ML::LinearAlgebra::Vector2i& J3ML::LinearAlgebra::Vector2i::operator -=(const Vector2i& rhs) {
+    x -= rhs.x;
+    y -= rhs.y;
+    return *this;
+}
+
+J3ML::LinearAlgebra::Vector2i& J3ML::LinearAlgebra::Vector2i::operator *=(const Vector2i& rhs) {
+    x *= rhs.x;
+    y *=rhs.y;
+    return *this;
+}
+
+J3ML::LinearAlgebra::Vector2i& J3ML::LinearAlgebra::Vector2i::operator /=(const Vector2i& rhs) {
+    x /= rhs.x;
+    y /=rhs.y;
+    return *this;
+}
+
+J3ML::LinearAlgebra::Vector2i J3ML::LinearAlgebra::Vector2i::operator +(const Vector2i& rhs) const {
+    return {x + rhs.x, y + rhs.y};
+}
+
+J3ML::LinearAlgebra::Vector2i J3ML::LinearAlgebra::Vector2i::operator -(const Vector2i& rhs) const {
+    return {x - rhs.x, y - rhs.y};
+}
+
+J3ML::LinearAlgebra::Vector2i J3ML::LinearAlgebra::Vector2i::operator *(const Vector2i& rhs) const {
+    return {x * rhs.x, y * rhs.y};
+}
+
+J3ML::LinearAlgebra::Vector2i J3ML::LinearAlgebra::Vector2i::operator /(const Vector2i& rhs) const {
+    return {x / rhs.x, y / rhs.y};
+}
+
+std::string J3ML::LinearAlgebra::Vector2i::ToString() const {
+    return std::string(std::to_string(x) + " " + std::to_string(y));
+}
+
+J3ML::LinearAlgebra::Vector2i::Vector2i() {
+    x = 0;
+    y = 0;
+}
+
+J3ML::LinearAlgebra::Vector2i J3ML::LinearAlgebra::Vector2i::operator *(const int rhs) const {
+    return {x * rhs, y * rhs};
+}
+
+J3ML::LinearAlgebra::Vector2i J3ML::LinearAlgebra::Vector2i::operator/(int rhs) const {
+    return {x / rhs, y / rhs};
+}
+
+
+
+
+
+
+

src/J3ML/LinearAlgebra/Vector3.cpp

@@ -10,6 +10,7 @@
 namespace J3ML::LinearAlgebra {
 
     const Vector3 Vector3::Zero     = {0,0,0};
+    const Vector3 Vector3::One      = {1, 1, 1};
     const Vector3 Vector3::Up       = {0, -1, 0};
     const Vector3 Vector3::Down     = {0, 1, 0};
     const Vector3 Vector3::Left     = {-1, 0, 0};

tests/LinearAlgebra/AxisAngleTests.hpp

@@ -0,0 +1,25 @@
+#include <jtest/jtest.hpp>
+#include <jtest/Unit.hpp>
+
+jtest::Unit AxisAngleUnit {"AxisAngle"};
+
+namespace AxisAngleTests {
+    inline void Define() {
+        using namespace jtest;
+
+        AxisAngleUnit += Test("From_Quaternion", [] {
+            AxisAngle expected_result({0.3860166, 0.4380138, 0.8118714}, 0.6742209);
+            Quaternion q(0.1276794, 0.1448781, 0.2685358, 0.9437144);
+
+            AxisAngle from_quaternion(q);
+
+            jtest::check(Math::EqualAbs(expected_result.axis.x, from_quaternion.axis.x, 1e-6f));
+            jtest::check(Math::EqualAbs(expected_result.axis.y, from_quaternion.axis.y, 1e-6f));
+            jtest::check(Math::EqualAbs(expected_result.axis.z, from_quaternion.axis.z, 1e-6f));
+            jtest::check(Math::EqualAbs(expected_result.angle, from_quaternion.angle, 1e-6f));
+        });
+    }
+    inline void Run() {
+        AxisAngleUnit.RunAll();
+    }
+}

tests/LinearAlgebra/EulerAngleTests.hpp

@@ -5,14 +5,21 @@
 #include <jtest/jtest.hpp>
 #include <jtest/Unit.hpp>
 
-jtest::Unit EulerAngleUnit {"EulerAngle"};
+jtest::Unit EulerAngleUnit {"EulerAngle_XYZ"};
 
 namespace EulerAngleTests {
     inline void Define() {
         using namespace jtest;
 
-        EulerAngleUnit += Test("Not Implemented", [] {
-            throw("Not Implemented");
+        EulerAngleUnit += Test("From_Quaternion", [] {
+            EulerAngleXYZ expected_result(-170, 88, -160);
+            Quaternion q(0.1840604, 0.6952024, 0.1819093, 0.6706149);
+
+            EulerAngleXYZ from_quaternion(q);
+
+            jtest::check(Math::EqualAbs(Math::Radians(expected_result.roll), Math::Radians(from_quaternion.roll), 1e-5f));
+            jtest::check(Math::EqualAbs(Math::Radians(expected_result.pitch), Math::Radians(from_quaternion.pitch), 1e-5f));
+            jtest::check(Math::EqualAbs(Math::Radians(expected_result.yaw), Math::Radians(from_quaternion.yaw), 1e-5f));
         });
     }
     inline void Run() {

tests/LinearAlgebra/Matrix3x3Tests.hpp

@@ -10,7 +10,43 @@ namespace Matrix3x3Tests
     {
         using namespace jtest;
         using namespace J3ML::LinearAlgebra;
+        /*
+        Matrix3x3Unit += Test("AngleTypeRound-TripConversion", [] {
+            EulerAngleXYZ expected_result(8, 60, -27);
 
+            Matrix3x3 m(expected_result);
+            //AxisAngle a(expected_result);
+            Quaternion q(m);
+            Matrix3x3 m2(q);
+            Quaternion q2(m2);
+            //AxisAngle a2(q2);
+            EulerAngleXYZ round_trip(a2);
+
+            jtest::check(Math::EqualAbs(Math::Radians(expected_result.roll), Math::Radians(round_trip.roll), 1e-6f));
+            jtest::check(Math::EqualAbs(Math::Radians(expected_result.pitch), Math::Radians(round_trip.pitch), 1e-6f));
+            jtest::check(Math::EqualAbs(Math::Radians(expected_result.yaw), Math::Radians(round_trip.yaw), 1e-6f));
+        });
+
+        Matrix3x3Unit += Test("From_EulerAngleXYZ", []{
+            Matrix3x3 expected_result(Vector3(0.4455033, 0.2269952, 0.8660254),
+                                      Vector3(-0.3421816, 0.9370536,  -0.0695866),
+                                      Vector3(-0.8273081, -0.2653369, 0.4951340)
+                                      );
+
+            EulerAngleXYZ e(8, 60, -27);
+            Matrix3x3 from_euler(e);
+
+            jtest::check(Math::EqualAbs(expected_result.At(0, 0), from_euler.At(0, 0), 1e-6f));
+            jtest::check(Math::EqualAbs(expected_result.At(0, 1), from_euler.At(0, 1), 1e-6f));
+            jtest::check(Math::EqualAbs(expected_result.At(0, 2), from_euler.At(0, 2), 1e-6f));
+            jtest::check(Math::EqualAbs(expected_result.At(1, 0), from_euler.At(1, 0), 1e-6f));
+            jtest::check(Math::EqualAbs(expected_result.At(1, 1), from_euler.At(1, 1), 1e-6f));
+            jtest::check(Math::EqualAbs(expected_result.At(1, 2), from_euler.At(1, 2), 1e-6f));
+            jtest::check(Math::EqualAbs(expected_result.At(2, 0), from_euler.At(2, 0), 1e-6f));
+            jtest::check(Math::EqualAbs(expected_result.At(2, 1), from_euler.At(2, 1), 1e-6f));
+            jtest::check(Math::EqualAbs(expected_result.At(2, 2), from_euler.At(2, 2), 1e-6f));
+        });
+*/
         Matrix3x3Unit += Test("Add_Unary", []
         {
             Matrix3x3 m(1,2,3, 4,5,6, 7,8,9);

tests/LinearAlgebra/Matrix4x4Tests.hpp

@@ -111,20 +111,6 @@ namespace Matrix4x4Tests {
         Matrix4x4Unit += Test("InverseOrthonormal", [] {});
         Matrix4x4Unit += Test("DeterminantCorrectness", [] { });
         Matrix4x4Unit += Test("MulMat3x3", [] {});
-
-
-        Matrix4x4Unit += Test("AngleTypeRoundtripConversion", [] {
-            Matrix4x4 matrix;
-            EulerAngle a(Math::Radians(45), Math::Radians(45), Math::Radians(45));
-            Quaternion q(a);
-            matrix.SetRotatePart(q);
-            //matrix.SetRotatePartX(a.pitch);
-            //matrix.SetRotatePartY(a.yaw);
-            //matrix.SetRotatePartZ(a.roll);
-            EulerAngle fromMatrix = matrix.GetRotatePart().ToQuat().ToEulerAngle();
-            jtest::check(a == fromMatrix);
-        });
-
     }
 
     inline void Run() {

tests/LinearAlgebra/QuaternionTests.hpp

@@ -4,10 +4,14 @@
 #include <jtest/jtest.hpp>
 #include <jtest/Unit.hpp>
 #include <J3ML/LinearAlgebra/Quaternion.hpp>
+#include <J3ML/LinearAlgebra/EulerAngle.hpp>
 #include <J3ML/Algorithm/RNG.hpp>
 
 jtest::Unit QuaternionUnit {"Quaternion"};
 namespace QuaternionTests {
+
+    // This is here to check the accuracy of the Slerp inside the Quaternion class.
+    // Although you don't jtest::check anything :shrug: - Redacted.
     Quaternion PreciseSlerp(const Quaternion &a, const Quaternion& b, float t)
     {
         double angle = a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w;
@@ -69,6 +73,28 @@ namespace QuaternionTests {
                 Quaternion lerp = q.Lerp(q2, t);
             }
         });
+        QuaternionUnit += Test("From_EulerAngleXYZ", [] {
+            Quaternion expected_result(0.1819093, 0.6706149, 0.1840604, 0.6952024);
+            EulerAngleXYZ e(10, 88, 20);
+            Quaternion from_euler(e);
+
+            jtest::check(Math::EqualAbs(expected_result.x, from_euler.x, 1e-6f));
+            jtest::check(Math::EqualAbs(expected_result.y, from_euler.y, 1e-6f));
+            jtest::check(Math::EqualAbs(expected_result.z, from_euler.z, 1e-6f));
+            jtest::check(Math::EqualAbs(expected_result.w, from_euler.w, 1e-6f));
+        });
+
+        QuaternionUnit += Test("From_AxisAngle", [] {
+            Quaternion expected_result(0.0579133, 0.0782044, 0.1765667, 0.9794664);
+            AxisAngle a({0.2872573, 0.3879036, 0.8757934}, 0.4059981);
+            Quaternion from_axis(a);
+
+            jtest::check(Math::EqualAbs(expected_result.x, from_axis.x, 1e-6f));
+            jtest::check(Math::EqualAbs(expected_result.y, from_axis.y, 1e-6f));
+            jtest::check(Math::EqualAbs(expected_result.z, from_axis.z, 1e-6f));
+            jtest::check(Math::EqualAbs(expected_result.w, from_axis.w, 1e-6f));
+        });
+
         QuaternionUnit += Test("Mat4x4Conversion", [] { throw("Not Implemented"); });
         QuaternionUnit += Test("MulOpQuat", [] { throw("Not Implemented"); });
         QuaternionUnit += Test("DivOpQuat", [] { throw("Not Implemented"); });

tests/tests.cpp

@@ -16,6 +16,7 @@
 #include "Geometry/FrustumTests.hpp"
 
 #include "LinearAlgebra/EulerAngleTests.hpp"
+#include "LinearAlgebra/AxisAngleTests.hpp"
 #include "LinearAlgebra/Matrix2x2Tests.hpp"
 #include "LinearAlgebra/Matrix3x3Tests.hpp"
 #include "LinearAlgebra/Matrix4x4Tests.hpp"
@@ -64,10 +65,11 @@ namespace LinearAlgebraTests
 {
     void Define()
     {
-        EulerAngleTests::Define();
         Vector2Tests::Define();
         Vector3Tests::Define();
         Vector4Tests::Define();
+        AxisAngleTests::Define();
+        EulerAngleTests::Define();
         QuaternionTests::Define();
         Matrix2x2Tests::Define();
         Matrix3x3Tests::Define();
@@ -76,10 +78,11 @@ namespace LinearAlgebraTests
     }
     void Run()
     {
-        EulerAngleTests::Run();
         Vector2Tests::Run();
         Vector3Tests::Run();
         Vector4Tests::Run();
+        AxisAngleTests::Run();
+        EulerAngleTests::Run();
         QuaternionTests::Run();
         Matrix2x2Tests::Run();
         Matrix3x3Tests::Run();