Initial Commit
This commit is contained in:
654
include/J3ML/LinearAlgebra.h
Normal file
654
include/J3ML/LinearAlgebra.h
Normal file
@@ -0,0 +1,654 @@
|
||||
#pragma once
|
||||
#include <cstdint>
|
||||
#include <cmath>
|
||||
#include <cstdlib>
|
||||
#include <algorithm>
|
||||
#include <functional>
|
||||
// TODO: Make GLM redundant, and remove it thereafter.
|
||||
#include <glm/glm.hpp>
|
||||
#include <glm/ext/scalar_constants.hpp>
|
||||
|
||||
// TODO: SIMD operations for fast math (parallelization!!)
|
||||
|
||||
// Dawsh Linear Algebra Library - Everything you need for 3D math
|
||||
namespace LinearAlgebra {
|
||||
class Vector2; // A type representing a position in a 2-dimensional coordinate space.
|
||||
class Vector3; // A type representing a position in a 3-dimensional coordinate space.
|
||||
class Vector4; // A type representing a position in a 4-dimensional coordinate space.
|
||||
class Angle2D; // Uses x,y components to represent a 2D rotation.
|
||||
class EulerAngle; // Uses pitch,yaw,roll components to represent a 3D orientation.
|
||||
class AxisAngle; //
|
||||
class CoordinateFrame; //
|
||||
class Matrix2x2;
|
||||
class Matrix3x3;
|
||||
class Matrix4x4;
|
||||
class Transform2D;
|
||||
class Transform3D;
|
||||
class Quaternion;
|
||||
inline float lerp(float a, float b, float t);
|
||||
}
|
||||
|
||||
// TODO: Enforce Style Consistency (Function Names use MicroSoft Case)
|
||||
|
||||
// Note: Josh Linear Algebra Types are designed as Immutable Data Types
|
||||
// x, y, z, w, etc. values should not and can not be set directly.
|
||||
// rather, you just construct a new type and assign it.
|
||||
// This might sound ass-backwards for many object types.
|
||||
// But mathematically, a vector or matrix is defined by it's size, and values.
|
||||
// Changing the value of one axis fundamentally changes the definition of the vector/matrix.
|
||||
// So we enforce this conceptually at code level...
|
||||
// If you're wondering how it remains performant, it only heap-allocates a tiny space (4*n bytes for vectors) (4*n*m bytes for matrices)
|
||||
// Just Trust Me Bro - Josjh
|
||||
#define MUTABLE true // Toggle This For: Ugly math, ugly code, and an ugly genital infection!
|
||||
|
||||
#if MUTABLE
|
||||
#define IMMUTABLE !MUTABLE
|
||||
#endif
|
||||
|
||||
namespace LinearAlgebra
|
||||
{
|
||||
|
||||
class Vector2 {
|
||||
public:
|
||||
Vector2();
|
||||
// Constructs a new Vector2 with the value (X, Y)
|
||||
Vector2(float X, float Y);
|
||||
Vector2(const Vector2& rhs); // Copy Constructor
|
||||
Vector2(Vector2&&) = default; // Move Constructor
|
||||
float GetX() const { return x; }
|
||||
float GetY() const { return y; }
|
||||
#if MUTABLE
|
||||
void SetX(float newX) { x = newX;}
|
||||
void SetY(float newY) { y = newY; }
|
||||
#endif
|
||||
static const Vector2 Zero;
|
||||
static const Vector2 Up;
|
||||
static const Vector2 Left;
|
||||
static const Vector2 Down;
|
||||
static const Vector2 Right;
|
||||
|
||||
float operator[](std::size_t index);
|
||||
|
||||
bool IsWithinMarginOfError(const Vector2& rhs, float margin=0.001f) const;
|
||||
|
||||
bool operator == (const Vector2& rhs) const;
|
||||
bool operator != (const Vector2& rhs) const;
|
||||
|
||||
Vector2 Min(const Vector2& min) const;
|
||||
static Vector2 Min(const Vector2& value, const Vector2& minimum) { return value.Min(minimum); }
|
||||
|
||||
Vector2 Max(const Vector2& max) const;
|
||||
static Vector2 Max(const Vector2& value, const Vector2& maximum) { return value.Max(maximum);}
|
||||
|
||||
Vector2 Clamp(const Vector2& min, const Vector2& max) const;
|
||||
static Vector2 Clamp(const Vector2& min, const Vector2& middle, const Vector2& max);
|
||||
|
||||
// Returns the magnitude between the two vectors.
|
||||
float Distance(const Vector2& to) const;
|
||||
static float Distance(const Vector2& from, const Vector2& to);
|
||||
|
||||
float Length() const;
|
||||
static float Length(const Vector2& of) { return of.Length(); }
|
||||
|
||||
float LengthSquared() const;
|
||||
static float LengthSquared(const Vector2& of) { return of.LengthSquared(); }
|
||||
// Returns the length of the vector, which is sqrt(x^2 + y^2)
|
||||
float Magnitude() const;
|
||||
static float Magnitude(const Vector2& of) { return of.Magnitude();}
|
||||
|
||||
// Returns a float value equal to the magnitudes of the two vectors multiplied together and then multiplied by the cosine of the angle between them.
|
||||
// For normalized vectors, dot returns 1 if they point in exactly the same direction,
|
||||
// -1 if they point in completely opposite directions, and 0 if the vectors are perpendicular.
|
||||
float Dot(const Vector2& rhs) const;
|
||||
static float Dot(const Vector2& lhs, const Vector2& rhs) { return lhs.Dot(rhs); }
|
||||
|
||||
// Projects one vector onto another and returns the result. (IDK)
|
||||
Vector2 Project(const Vector2& rhs) const;
|
||||
// @see Project
|
||||
static Vector2 Project(const Vector2& lhs, const Vector2& rhs) { return lhs.Project(rhs); }
|
||||
|
||||
// Returns a copy of this vector, resized to have a magnitude of 1, while preserving "direction"
|
||||
Vector2 Normalize() const;
|
||||
static Vector2 Normalize(const Vector2& of) { return of.Normalize(); }
|
||||
|
||||
// Linearly interpolates between two points.
|
||||
// Interpolates between the points and b by the interpolant t.
|
||||
// The parameter is (TODO: SHOULD BE!) clamped to the range[0, 1].
|
||||
// This is most commonly used to find a point some fraction of the wy along a line between two endpoints (eg. to move an object gradually between those points).
|
||||
Vector2 Lerp(const Vector2& rhs, float alpha) const;
|
||||
// @see Lerp
|
||||
static Vector2 Lerp(const Vector2& lhs, const Vector2& rhs, float alpha) { return lhs.Lerp(rhs, alpha); }
|
||||
|
||||
float AngleBetween(const Vector2& rhs) const;
|
||||
static float AngleBetween(const Vector2& lhs, const Vector2& rhs);
|
||||
|
||||
// Adds two vectors.
|
||||
Vector2 operator +(const Vector2& rhs) const;
|
||||
Vector2 Add(const Vector2& rhs) const;
|
||||
static Vector2 Add(const Vector2& lhs, const Vector2& rhs);
|
||||
|
||||
// Subtracts two vectors.
|
||||
Vector2 operator -(const Vector2& rhs) const;
|
||||
Vector2 Sub(const Vector2& rhs) const;
|
||||
static Vector2 Sub(const Vector2& lhs, const Vector2& rhs);
|
||||
|
||||
// Multiplies this vector by a scalar value.
|
||||
Vector2 operator *(float rhs) const;
|
||||
Vector2 Mul(float scalar) const;
|
||||
static Vector2 Mul(const Vector2& lhs, float rhs);
|
||||
|
||||
// Divides this vector by a scalar.
|
||||
Vector2 operator /(float rhs) const;
|
||||
Vector2 Div(float scalar) const;
|
||||
static Vector2 Div(const Vector2& lhs, float rhs);
|
||||
|
||||
|
||||
// Unary operator +
|
||||
Vector2 operator +() const; // TODO: Implement
|
||||
Vector2 operator -() const;
|
||||
// Assigns a vector to another
|
||||
Vector2& operator=(const Vector2&v);
|
||||
|
||||
|
||||
Vector2& operator+=(const Vector2& rhs); // Adds a vector to this vector, in-place.
|
||||
Vector2& operator-=(const Vector2& rhs); // Subtracts a vector from this vector, in-place
|
||||
Vector2& operator*=(float scalar);
|
||||
Vector2& operator/=(float scalar);
|
||||
|
||||
public:
|
||||
#if MUTABLE
|
||||
float x = 0;
|
||||
float y = 0;
|
||||
#else
|
||||
const float x = 0;
|
||||
const float y = 0;
|
||||
#endif
|
||||
};
|
||||
|
||||
class Vector3 {
|
||||
public:
|
||||
Vector3();
|
||||
Vector3(float X, float Y, float Z);
|
||||
Vector3(const Vector3& rhs);
|
||||
Vector3(Vector3&&) = default;
|
||||
Vector3& operator=(const Vector3& rhs);
|
||||
|
||||
float getX() const;
|
||||
float getY() const;
|
||||
float getZ() const;
|
||||
#if MUTABLE
|
||||
void setX(float newX);
|
||||
void setY(float newY);
|
||||
void setZ(float newZ);
|
||||
#endif
|
||||
static const Vector3 Zero;
|
||||
static const Vector3 Up;
|
||||
static const Vector3 Down;
|
||||
static const Vector3 Left;
|
||||
static const Vector3 Right;
|
||||
static const Vector3 Forward;
|
||||
static const Vector3 Backward;
|
||||
|
||||
float operator[](std::size_t index) const;
|
||||
|
||||
bool IsWithinMarginOfError(const Vector3& rhs, float margin=0.001f) const;
|
||||
|
||||
bool IsNormalized(float epsilonSq = 1e-5f) const;
|
||||
bool IsZero(float epsilonSq = 1e-6f) const;
|
||||
bool IsFinite() const;
|
||||
bool IsPerpendicular(const Vector2& other, float epsilonSq=1e-5f) const;
|
||||
|
||||
bool operator == (const Vector3& rhs) const;
|
||||
bool operator != (const Vector3& rhs) const;
|
||||
|
||||
Vector3 Min(const Vector3& min) const;
|
||||
static Vector3 Min(const Vector3& lhs, const Vector3& rhs);
|
||||
|
||||
Vector3 Max(const Vector3& max) const;
|
||||
static Vector3 Max(const Vector3& lhs, const Vector3& rhs);
|
||||
|
||||
Vector3 Clamp(const Vector3& min, const Vector3& max) const;
|
||||
static Vector3 Clamp(const Vector3& min, const Vector3& input, const Vector3& max);
|
||||
|
||||
float Distance(const Vector3& to) const;
|
||||
static float Distance(const Vector3& from, const Vector3& to);
|
||||
|
||||
float Length() const;
|
||||
static float Length(const Vector3& of);
|
||||
|
||||
float LengthSquared() const;
|
||||
static float LengthSquared(const Vector3& of);
|
||||
|
||||
// Returns the length of the vector, which is sqrt(x^2 + y^2 + z^2)
|
||||
float Magnitude() const;
|
||||
static float Magnitude(const Vector3& of);
|
||||
|
||||
// Returns a float value equal to the magnitudes of the two vectors multiplied together and then multiplied by the cosine of the angle between them.
|
||||
// For normalized vectors, dot returns 1 if they point in exactly the same direction,
|
||||
// -1 if they point in completely opposite directions, and 0 if the vectors are perpendicular.
|
||||
float Dot(const Vector3& rhs) const;
|
||||
static float Dot(const Vector3& lhs, const Vector3& rhs);
|
||||
|
||||
Vector3 Project(const Vector3& rhs) const;
|
||||
static Vector3 Project(const Vector3& lhs, const Vector3& rhs);
|
||||
|
||||
// The cross product of two vectors results in a third vector which is perpendicular to the two input vectors.
|
||||
// The result's magnitude is equal to the magnitudes of the two inputs multiplied together and then multiplied by the sine of the angle between the inputs.
|
||||
Vector3 Cross(const Vector3& rhs) const;
|
||||
static Vector3 Cross(const Vector3& lhs, const Vector3& rhs);
|
||||
|
||||
// Returns a copy of this vector, resized to have a magnitude of 1, while preserving "direction"
|
||||
Vector3 Normalize() const;
|
||||
static Vector3 Normalize(const Vector3& targ);
|
||||
// Linearly interpolates between two points.
|
||||
// Interpolates between the points and b by the interpolant t.
|
||||
// The parameter is (TODO: SHOULD BE!) clamped to the range[0, 1].
|
||||
// This is most commonly used to find a point some fraction of the wy along a line between two endpoints (eg. to move an object gradually between those points).
|
||||
Vector3 Lerp(const Vector3& goal, float alpha) const;
|
||||
Vector3 operator+(const Vector3& rhs) const;
|
||||
Vector3 operator-(const Vector3& rhs) const;
|
||||
Vector3 operator*(float rhs) const;
|
||||
Vector3 operator/(float rhs) const;
|
||||
Vector3 operator+() const; // TODO: Implement
|
||||
Vector3 operator-() const;
|
||||
public:
|
||||
#if MUTABLE
|
||||
float x = 0;
|
||||
float y = 0;
|
||||
float z = 0;
|
||||
#else
|
||||
const float x = 0;
|
||||
const float y = 0;
|
||||
const float z = 0;
|
||||
#endif
|
||||
};
|
||||
|
||||
class Vector4 {
|
||||
public:
|
||||
Vector4();
|
||||
Vector4(const Vector3& xyz, float w = 0);
|
||||
Vector4(float X, float Y, float Z, float W);
|
||||
Vector4(const Vector4& copy) = default;
|
||||
Vector4(Vector4&& move) = default;
|
||||
float getX() const;
|
||||
float getY() const;
|
||||
float getZ() const;
|
||||
float getW() const;
|
||||
#if MUTABLE
|
||||
void setX(float newX);
|
||||
void setY(float newY);
|
||||
void setZ(float newZ);
|
||||
void setW(float newW);
|
||||
#endif
|
||||
float operator[](int index) const;
|
||||
bool IsWithinMarginOfError(const Vector4& rhs, float margin=0.0001f) const;
|
||||
bool operator==(const Vector4& rhs) const;
|
||||
bool operator!=(const Vector4& rhs) const;
|
||||
Vector4 min(const Vector4& min) const;
|
||||
Vector4 max(const Vector4& max) const;
|
||||
Vector4 clamp(const Vector4& min, const Vector4& max) const;
|
||||
float distance(const Vector4& to) const;
|
||||
float length() const;
|
||||
float lengthSquared() const;
|
||||
float magnitude() const;
|
||||
float dot(const Vector4& rhs) const;
|
||||
Vector4 project(const Vector4& rhs) const;
|
||||
// While it is feasable to compute a cross-product in four dimensions
|
||||
// the cross product only has the orthogonality property in 3 and 7 dimensions
|
||||
// You should consider instead looking at Gram-Schmidt Orthogonalization
|
||||
// to find orthonormal vectors.
|
||||
Vector4 cross(const Vector4& rhs) const;
|
||||
Vector4 normalize() const;
|
||||
Vector4 lerp(const Vector4& goal, float alpha) const;
|
||||
Vector4 operator+(const Vector4& rhs) const;
|
||||
Vector4 operator-(const Vector4& rhs) const;
|
||||
Vector4 operator*(float rhs) const;
|
||||
Vector4 operator/(float rhs) const;
|
||||
Vector4 operator+() const;
|
||||
Vector4 operator-() const;
|
||||
public:
|
||||
#if MUTABLE
|
||||
float x = 0;
|
||||
float y = 0;
|
||||
float z = 0;
|
||||
float w = 0;
|
||||
#else
|
||||
const float x = 0;
|
||||
const float y = 0;
|
||||
const float z = 0;
|
||||
const float w = 0;
|
||||
#endif
|
||||
};
|
||||
// Essential Reading:
|
||||
// http://www.essentialmath.com/GDC2012/GDC2012_JMV_Rotations.pdf
|
||||
class EulerAngle {
|
||||
public:
|
||||
EulerAngle();
|
||||
EulerAngle(float pitch, float yaw, float roll);
|
||||
EulerAngle(const Vector3& vec) : pitch(vec.x), yaw(vec.y), roll(vec.z) {}
|
||||
static EulerAngle FromRadians(float radians);
|
||||
static EulerAngle FromDegrees(float degrees);
|
||||
/// 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;
|
||||
};
|
||||
|
||||
/// Transitional datatype, not useful for internal representation of rotation
|
||||
/// But has uses for conversion and manipulation.
|
||||
class AxisAngle {
|
||||
Vector3 axis;
|
||||
float angle;
|
||||
};
|
||||
|
||||
using Position = Vector3;
|
||||
|
||||
/// The CFrame is fundamentally 4 vectors (position, forward, right, up vector)
|
||||
class CoordinateFrame
|
||||
{
|
||||
Vector3 getPosition();
|
||||
Vector3 getLookVector();
|
||||
Vector3 getRightVector();
|
||||
Vector3 getUpVector();
|
||||
AxisAngle GetAxisAngle();
|
||||
EulerAngle GetEulerAngleXYZ();
|
||||
EulerAngle GetWorldAngleYZX();
|
||||
};
|
||||
|
||||
class Matrix2x2 {
|
||||
public:
|
||||
static const Matrix2x2 Zero;
|
||||
static const Matrix2x2 Identity;
|
||||
static const Matrix2x2 NaN;
|
||||
|
||||
Vector2 GetRow() const;
|
||||
Vector2 GetColumn() const;
|
||||
|
||||
protected:
|
||||
float elems[2][2];
|
||||
};
|
||||
|
||||
/// A 3-by-3 matrix for linear transformations of 3D geometry.
|
||||
/* This can represent any kind of linear transformations of 3D geometry, which include
|
||||
* rotation, scale, shear, mirroring, and orthographic projection.
|
||||
* A 3x3 matrix cannot represent translation, which requires a 3x4, or perspective projection (4x4).
|
||||
* The elements of this matrix are
|
||||
* m_00, m_01, m_02
|
||||
* m_10, m_11, m_12
|
||||
* m_20, m_21, m_22
|
||||
*
|
||||
* The element m_yx is the value on the row y and column x.
|
||||
* You can access m_yx using the double-bracket notation m[y][x], or using the member function At.
|
||||
*
|
||||
* @note The member functions in this class use the convention that transforms are applied to
|
||||
* vectors in the form M * v. This means that "Matrix3x3 M, M1, M2; M = M1 * M2;" gives a transformation M
|
||||
* that applies M2 first, followed by M1 second
|
||||
*/
|
||||
class Matrix3x3 {
|
||||
public:
|
||||
enum { Rows = 3 };
|
||||
enum { Cols = 3 };
|
||||
|
||||
static const Matrix3x3 Zero;
|
||||
static const Matrix3x3 Identity;
|
||||
static const Matrix3x3 NaN;
|
||||
|
||||
Matrix3x3();
|
||||
Matrix3x3(float fillValue);
|
||||
Matrix3x3(float m00, float m01, float m02, float m10, float m11, float m12, float m20, float m21, float m22);
|
||||
Matrix3x3(const Vector3& r1, const Vector3& r2, const Vector3& r3);
|
||||
explicit Matrix3x3(const Quaternion& orientation);
|
||||
|
||||
static Matrix3x3 RotateX(float radians);
|
||||
static Matrix3x3 RotateY(float radians);
|
||||
static Matrix3x3 RotateZ(float radians);
|
||||
|
||||
Vector3 GetRow(int index) const;
|
||||
Vector3 GetColumn(int index) const;
|
||||
float At(int x, int y) const;
|
||||
|
||||
/// Creates a new M3x3 that rotates about the given axis by the given angle
|
||||
static Matrix3x3 RotateAxisAngle(const Vector3& rhs);
|
||||
|
||||
static Matrix3x3 RotateFromTo(const Vector3& source, const Vector3& direction);
|
||||
|
||||
static Matrix3x3 LookAt(const Vector3& forward, const Vector3& target, const Vector3& localUp, const Vector3& worldUp);
|
||||
|
||||
static Matrix3x3 FromQuat(const Quaternion& orientation);
|
||||
|
||||
Quaternion ToQuat() const;
|
||||
|
||||
/// Creates a new Matrix3x3 as a combination of rotation and scale.
|
||||
// This function creates a new matrix M in the form M = R * S
|
||||
// where R is a rotation matrix and S is a scale matrix.
|
||||
// Transforming a vector v using this matrix computes the vector
|
||||
// v' == M * v == R*S*v == (R * (S * v)) which means the scale operation
|
||||
// is applied to the vector first, followed by rotation, and finally translation
|
||||
static Matrix3x3 FromRS(const Quaternion& rotate, const Matrix3x3& scale);
|
||||
static Matrix3x3 FromRS(const Matrix3x3 &rotate, const Matrix3x3& scale);
|
||||
|
||||
|
||||
/// Creates a new transformation matrix that scales by the given factors.
|
||||
// This matrix scales with respect to origin.
|
||||
static Matrix3x3 Scale(float sx, float sy, float sz);
|
||||
static Matrix3x3 Scale(const Matrix3x3& scale);
|
||||
|
||||
/// Returns the main diagonal.
|
||||
Vector3 Diagonal() const;
|
||||
/// Returns the local +X/+Y/+Z axis in world space.
|
||||
/// This is the same as transforming the vector{1,0,0} by this matrix.
|
||||
Vector3 WorldX() const;
|
||||
/// Returns the local +Y axis in world space.
|
||||
/// This is the same as transforming the vector{0,1,0} by this matrix.
|
||||
Vector3 WorldY() const;
|
||||
/// Returns the local +Z axis in world space.
|
||||
/// This is the same as transforming the vector{0,0,1} by this matrix.
|
||||
Vector3 WorldZ() const;
|
||||
|
||||
/// Computes the determinant of this matrix.
|
||||
// If the determinant is nonzero, this matrix is invertible.
|
||||
// If the determinant is negative, this matrix performs reflection about some axis.
|
||||
// From http://msdn.microsoft.com/en-us/library/bb204853(VS.85).aspx :
|
||||
// "If the determinant is positive, the basis is said to be "positively" oriented (or right-handed).
|
||||
// If the determinant is negative, the basis is said to be "negatively" oriented (or left-handed)."
|
||||
// @note This function computes 9 LOADs, 9 MULs and 5 ADDs. */
|
||||
float Determinant() const;
|
||||
|
||||
// Returns an inverted copy of this matrix. This
|
||||
Matrix3x3 Inverse() const;
|
||||
|
||||
// Returns a transposed copy of this matrix.
|
||||
Matrix3x3 Transpose() const;
|
||||
|
||||
// Transforms the given vectors by this matrix M, i.e. returns M * (x,y,z)
|
||||
|
||||
Vector2 Transform(const Vector2& vector) const;
|
||||
Vector3 Transform(const Vector3& rhs) const;
|
||||
Vector2 Transform(float x, float y) const;
|
||||
Vector3 Transform(float x, float y, float z) const;
|
||||
|
||||
|
||||
|
||||
Vector3 operator[] (float index) const;
|
||||
Vector3 operator * (const Vector3& rhs) const;
|
||||
Matrix3x3 operator * (const Matrix3x3& rhs) const;
|
||||
|
||||
protected:
|
||||
float elems[3][3];
|
||||
};
|
||||
|
||||
/// A 4-by-4 matrix for affine transformations and perspective projections of 3D geometry.
|
||||
/* This matrix can represent the most generic form of transformations for 3D objects,
|
||||
* including perspective projections, which a 4-by-3 cannot store,
|
||||
* and translations, which a 3-by-3 cannot represent.
|
||||
* The elements of this matrix are
|
||||
* m_00, m_01, m_02, m_03
|
||||
* m_10, m_11, m_12, m_13
|
||||
* m_20, m_21, m_22, m_23,
|
||||
* m_30, m_31, m_32, m_33
|
||||
*
|
||||
* The element m_yx is the value on the row y and column x.
|
||||
* You can access m_yx using the double-bracket notation m[y][x]
|
||||
*/
|
||||
class Matrix4x4 {
|
||||
public:
|
||||
static const Matrix4x4 Zero;
|
||||
static const Matrix4x4 Identity;
|
||||
|
||||
Vector3 GetTranslationComponent() const;
|
||||
Matrix3x3 GetRotationComponent() const;
|
||||
|
||||
Vector4 GetRow() const;
|
||||
Vector4 GetColumn() const;
|
||||
protected:
|
||||
float elems[4][4];
|
||||
};
|
||||
|
||||
class Transform2D {
|
||||
protected:
|
||||
Matrix3x3 transformation;
|
||||
public:
|
||||
Transform2D Translate(const Vector2& offset) const;
|
||||
Transform2D Translate(float x, float y) const;
|
||||
Transform2D Scale(float scale); // Perform Uniform Scale
|
||||
Transform2D Scale(float x, float y); // Perform Nonunform Scale
|
||||
Transform2D Scale(const Vector2& scales); // Perform Nonuniform Scale
|
||||
Transform2D Rotate();
|
||||
};
|
||||
|
||||
class Transform3D {
|
||||
protected:
|
||||
Matrix4x4 transformation;
|
||||
public:
|
||||
Transform3D Scale();
|
||||
Transform3D Translate();
|
||||
Transform3D Rotate();
|
||||
};
|
||||
|
||||
struct Movement {
|
||||
EulerAngle angle;
|
||||
Position position;
|
||||
};
|
||||
class Quaternion : public Vector4
|
||||
{
|
||||
public:
|
||||
Quaternion() {}
|
||||
Quaternion(const Quaternion& rhs) = default;
|
||||
explicit Quaternion(Matrix3x3& rotationMtrx) {}
|
||||
explicit Quaternion(Matrix4x4& rotationMtrx) {}
|
||||
// @note The input data is not normalized after construction, this has to be done manually.
|
||||
Quaternion(float x, float y, float z, float w);
|
||||
// Constructs this quaternion by specifying a rotation axis and the amount of rotation to be performed about that axis
|
||||
// @param rotationAxis The normalized rotation axis to rotate about. If using Vector4 version of the constructor, the w component of this vector must be 0.
|
||||
Quaternion(const Vector3& rotationAxis, float rotationAngleBetween) { SetFromAxisAngle(rotationAxis, rotationAngleBetween); }
|
||||
Quaternion(const Vector4& rotationAxis, float rotationAngleBetween) { SetFromAxisAngle(rotationAxis, rotationAngleBetween); }
|
||||
//void Inverse();
|
||||
Quaternion Inverse() const;
|
||||
//void Normalize();
|
||||
Quaternion Normalize() const;
|
||||
Vector3 GetWorldX() const { return Transform(1.f, 0.f, 0.f); }
|
||||
Vector3 GetWorldY() const { return Transform(0.f, 1.f, 0.f); }
|
||||
Vector3 GetWorldZ() const { return Transform(0.f, 0.f, 1.f); }
|
||||
|
||||
Matrix3x3 ToMatrix3x3() const;
|
||||
|
||||
Vector3 Transform(const Vector3& vec) const
|
||||
{
|
||||
Matrix3x3 mat = this->ToMatrix3x3();
|
||||
return mat * vec;
|
||||
}
|
||||
Vector3 Transform(float X, float Y, float Z) const
|
||||
{
|
||||
return Transform(Vector3{X, Y, Z});
|
||||
}
|
||||
// Note: We only transform the x,y,z components of 4D vectors, w is left untouched
|
||||
Vector4 Transform(const Vector4& vec) const
|
||||
{
|
||||
return Vector4(Transform(vec.x, vec.y, vec.z), vec.w);
|
||||
}
|
||||
Vector4 Transform(float X, float Y, float Z, float W) const
|
||||
{
|
||||
return Transform(Vector4(X, Y, Z, W));
|
||||
}
|
||||
|
||||
Quaternion GetInverse() const;
|
||||
Quaternion Lerp(const Quaternion& b, float t) const
|
||||
{
|
||||
float angle = this->dot(b);
|
||||
if (angle >= 0.f) // Make sure we rotate the shorter arc
|
||||
return (*this * (1.f - t) + b * t).Normalize();
|
||||
else
|
||||
return (*this * (t - 1.f) + b * t).Normalize();
|
||||
}
|
||||
Quaternion Slerp(const Quaternion& target) const;
|
||||
|
||||
void SetFromAxisAngle(const Vector3& axis, float angle)
|
||||
{
|
||||
float sinz, cosz;
|
||||
|
||||
}
|
||||
|
||||
void SetFromAxisAngle(const Vector4& axis, float angle)
|
||||
{
|
||||
|
||||
}
|
||||
|
||||
|
||||
static Quaternion LookAt(const Vector3& position, const Vector3& direction, const Vector3& axisUp);
|
||||
|
||||
// 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;
|
||||
|
||||
Quaternion operator * (float scalar) const
|
||||
{
|
||||
return Quaternion(x * scalar, y * scalar, z * scalar, w * scalar);
|
||||
}
|
||||
|
||||
// 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;
|
||||
Quaternion operator +() const { return *this; }
|
||||
Quaternion operator -() const;
|
||||
};
|
||||
|
||||
inline namespace VectorMath {
|
||||
inline float distance(Position sP, Position eP) {
|
||||
return sqrt(pow(eP.x - sP.x, 2) + pow(eP.y - sP.y, 2) + pow(eP.z - sP.z, 2));
|
||||
}
|
||||
|
||||
//Basically an aimbot.
|
||||
inline Vector3 calcAngle(Position sP, Position eP) {
|
||||
const auto pi = glm::pi<float>();
|
||||
//returned.x = -(asinf((eP.y - sP.y) / distance(sP, eP)) * 180.0f / M_PI);
|
||||
//returned.y = (atan2f(eP.x - sP.x,eP.z - sP.z) / M_PI * 180.0f);
|
||||
return {static_cast<float>((-(asinf((eP.y - sP.y) / distance(sP, eP)) * 180.0f / pi ))),static_cast<float>((atan2f(eP.x - sP.x,eP.z - sP.z) / pi * 180.0f)),0};
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
}
|
||||
Reference in New Issue
Block a user