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Copy pathMath.h
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Copy pathMath.h
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1033 lines (882 loc) · 21.2 KB
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// ----------------------------------------------------------------
// From Game Programming in C++ by Sanjay Madhav
// Copyright (C) 2017 Sanjay Madhav. All rights reserved.
//
// Released under the BSD License
// See LICENSE in root directory for full details.
// ----------------------------------------------------------------
#pragma once
#include <cmath>
#include <memory.h>
#include <limits>
namespace Math
{
const float Pi = 3.1415926535f;
const float TwoPi = Pi * 2.0f;
const float PiOver2 = Pi / 2.0f;
const float Infinity = std::numeric_limits<float>::infinity();
const float NegInfinity = -std::numeric_limits<float>::infinity();
inline float ToRadians(float degrees)
{
return degrees * Pi / 180.0f;
}
inline float ToDegrees(float radians)
{
return radians * 180.0f / Pi;
}
inline bool NearZero(float val, float epsilon = 0.001f)
{
if (fabs(val) <= epsilon)
{
return true;
}
else
{
return false;
}
}
template <typename T>
T Max(const T& a, const T& b)
{
return (a < b ? b : a);
}
template <typename T>
T Min(const T& a, const T& b)
{
return (a < b ? a : b);
}
template <typename T>
T Clamp(const T& value, const T& lower, const T& upper)
{
return Min(upper, Max(lower, value));
}
inline float Abs(float value)
{
return fabs(value);
}
inline float Cos(float angle)
{
return cosf(angle);
}
inline float Sin(float angle)
{
return sinf(angle);
}
inline float Tan(float angle)
{
return tanf(angle);
}
inline float Acos(float value)
{
return acosf(value);
}
inline float Atan2(float y, float x)
{
return atan2f(y, x);
}
inline float Cot(float angle)
{
return 1.0f / Tan(angle);
}
inline float Lerp(float a, float b, float f)
{
return a + f * (b - a);
}
inline float Sqrt(float value)
{
return sqrtf(value);
}
inline float Fmod(float numer, float denom)
{
return fmod(numer, denom);
}
}
// 2D Vector
class Vector2
{
public:
float x;
float y;
Vector2()
:x(0.0f)
,y(0.0f)
{}
explicit Vector2(float inX, float inY)
:x(inX)
,y(inY)
{}
// Set both components in one line
void Set(float inX, float inY)
{
x = inX;
y = inY;
}
// Vector addition (a + b)
friend Vector2 operator+(const Vector2& a, const Vector2& b)
{
return Vector2(a.x + b.x, a.y + b.y);
}
// Vector subtraction (a - b)
friend Vector2 operator-(const Vector2& a, const Vector2& b)
{
return Vector2(a.x - b.x, a.y - b.y);
}
// Component-wise multiplication
// (a.x * b.x, ...)
friend Vector2 operator*(const Vector2& a, const Vector2& b)
{
return Vector2(a.x * b.x, a.y * b.y);
}
// Scalar multiplication
friend Vector2 operator*(const Vector2& vec, float scalar)
{
return Vector2(vec.x * scalar, vec.y * scalar);
}
// Scalar multiplication
friend Vector2 operator*(float scalar, const Vector2& vec)
{
return Vector2(vec.x * scalar, vec.y * scalar);
}
// Scalar *=
Vector2& operator*=(float scalar)
{
x *= scalar;
y *= scalar;
return *this;
}
// Vector +=
Vector2& operator+=(const Vector2& right)
{
x += right.x;
y += right.y;
return *this;
}
// Vector -=
Vector2& operator-=(const Vector2& right)
{
x -= right.x;
y -= right.y;
return *this;
}
// Length squared of vector
float LengthSq() const
{
return (x*x + y*y);
}
// Length of vector
float Length() const
{
return (Math::Sqrt(LengthSq()));
}
// Normalize this vector
void Normalize()
{
float length = Length();
x /= length;
y /= length;
}
// Normalize the provided vector
static Vector2 Normalize(const Vector2& vec)
{
Vector2 temp = vec;
temp.Normalize();
return temp;
}
// Dot product between two vectors (a dot b)
static float Dot(const Vector2& a, const Vector2& b)
{
return (a.x * b.x + a.y * b.y);
}
// Lerp from A to B by f
static Vector2 Lerp(const Vector2& a, const Vector2& b, float f)
{
return Vector2(a + f * (b - a));
}
// Reflect V about (normalized) N
static Vector2 Reflect(const Vector2& v, const Vector2& n)
{
return v - 2.0f * Vector2::Dot(v, n) * n;
}
// Transform vector by matrix
static Vector2 Transform(const Vector2& vec, const class Matrix3& mat, float w = 1.0f);
static const Vector2 Zero;
static const Vector2 UnitX;
static const Vector2 UnitY;
static const Vector2 NegUnitX;
static const Vector2 NegUnitY;
};
// 3D Vector
class Vector3
{
public:
float x;
float y;
float z;
Vector3()
:x(0.0f)
,y(0.0f)
,z(0.0f)
{}
explicit Vector3(float inX, float inY, float inZ)
:x(inX)
,y(inY)
,z(inZ)
{}
// Cast to a const float pointer
const float* GetAsFloatPtr() const
{
return reinterpret_cast<const float*>(&x);
}
// Set all three components in one line
void Set(float inX, float inY, float inZ)
{
x = inX;
y = inY;
z = inZ;
}
// Vector addition (a + b)
friend Vector3 operator+(const Vector3& a, const Vector3& b)
{
return Vector3(a.x + b.x, a.y + b.y, a.z + b.z);
}
// Vector subtraction (a - b)
friend Vector3 operator-(const Vector3& a, const Vector3& b)
{
return Vector3(a.x - b.x, a.y - b.y, a.z - b.z);
}
// Component-wise multiplication
friend Vector3 operator*(const Vector3& left, const Vector3& right)
{
return Vector3(left.x * right.x, left.y * right.y, left.z * right.z);
}
// Scalar multiplication
friend Vector3 operator*(const Vector3& vec, float scalar)
{
return Vector3(vec.x * scalar, vec.y * scalar, vec.z * scalar);
}
// Scalar multiplication
friend Vector3 operator*(float scalar, const Vector3& vec)
{
return Vector3(vec.x * scalar, vec.y * scalar, vec.z * scalar);
}
// Scalar *=
Vector3& operator*=(float scalar)
{
x *= scalar;
y *= scalar;
z *= scalar;
return *this;
}
// Vector +=
Vector3& operator+=(const Vector3& right)
{
x += right.x;
y += right.y;
z += right.z;
return *this;
}
// Vector -=
Vector3& operator-=(const Vector3& right)
{
x -= right.x;
y -= right.y;
z -= right.z;
return *this;
}
// Length squared of vector
float LengthSq() const
{
return (x*x + y*y + z*z);
}
// Length of vector
float Length() const
{
return (Math::Sqrt(LengthSq()));
}
// Normalize this vector
void Normalize()
{
float length = Length();
x /= length;
y /= length;
z /= length;
}
// Normalize the provided vector
static Vector3 Normalize(const Vector3& vec)
{
Vector3 temp = vec;
temp.Normalize();
return temp;
}
// Dot product between two vectors (a dot b)
static float Dot(const Vector3& a, const Vector3& b)
{
return (a.x * b.x + a.y * b.y + a.z * b.z);
}
// Cross product between two vectors (a cross b)
static Vector3 Cross(const Vector3& a, const Vector3& b)
{
Vector3 temp;
temp.x = a.y * b.z - a.z * b.y;
temp.y = a.z * b.x - a.x * b.z;
temp.z = a.x * b.y - a.y * b.x;
return temp;
}
// Lerp from A to B by f
static Vector3 Lerp(const Vector3& a, const Vector3& b, float f)
{
return Vector3(a + f * (b - a));
}
// Reflect V about (normalized) N
static Vector3 Reflect(const Vector3& v, const Vector3& n)
{
return v - 2.0f * Vector3::Dot(v, n) * n;
}
static Vector3 Transform(const Vector3& vec, const class Matrix4& mat, float w = 1.0f);
// This will transform the vector and renormalize the w component
static Vector3 TransformWithPerspDiv(const Vector3& vec, const class Matrix4& mat, float w = 1.0f);
// Transform a Vector3 by a quaternion
static Vector3 Transform(const Vector3& v, const class Quaternion& q);
static const Vector3 Zero;
static const Vector3 UnitX;
static const Vector3 UnitY;
static const Vector3 UnitZ;
static const Vector3 NegUnitX;
static const Vector3 NegUnitY;
static const Vector3 NegUnitZ;
static const Vector3 Infinity;
static const Vector3 NegInfinity;
};
// 3x3 Matrix
class Matrix3
{
public:
float mat[3][3];
Matrix3()
{
*this = Matrix3::Identity;
}
explicit Matrix3(float inMat[3][3])
{
memcpy(mat, inMat, 9 * sizeof(float));
}
// Cast to a const float pointer
const float* GetAsFloatPtr() const
{
return reinterpret_cast<const float*>(&mat[0][0]);
}
// Matrix multiplication
friend Matrix3 operator*(const Matrix3& left, const Matrix3& right)
{
Matrix3 retVal;
// row 0
retVal.mat[0][0] =
left.mat[0][0] * right.mat[0][0] +
left.mat[0][1] * right.mat[1][0] +
left.mat[0][2] * right.mat[2][0];
retVal.mat[0][1] =
left.mat[0][0] * right.mat[0][1] +
left.mat[0][1] * right.mat[1][1] +
left.mat[0][2] * right.mat[2][1];
retVal.mat[0][2] =
left.mat[0][0] * right.mat[0][2] +
left.mat[0][1] * right.mat[1][2] +
left.mat[0][2] * right.mat[2][2];
// row 1
retVal.mat[1][0] =
left.mat[1][0] * right.mat[0][0] +
left.mat[1][1] * right.mat[1][0] +
left.mat[1][2] * right.mat[2][0];
retVal.mat[1][1] =
left.mat[1][0] * right.mat[0][1] +
left.mat[1][1] * right.mat[1][1] +
left.mat[1][2] * right.mat[2][1];
retVal.mat[1][2] =
left.mat[1][0] * right.mat[0][2] +
left.mat[1][1] * right.mat[1][2] +
left.mat[1][2] * right.mat[2][2];
// row 2
retVal.mat[2][0] =
left.mat[2][0] * right.mat[0][0] +
left.mat[2][1] * right.mat[1][0] +
left.mat[2][2] * right.mat[2][0];
retVal.mat[2][1] =
left.mat[2][0] * right.mat[0][1] +
left.mat[2][1] * right.mat[1][1] +
left.mat[2][2] * right.mat[2][1];
retVal.mat[2][2] =
left.mat[2][0] * right.mat[0][2] +
left.mat[2][1] * right.mat[1][2] +
left.mat[2][2] * right.mat[2][2];
return retVal;
}
Matrix3& operator*=(const Matrix3& right)
{
*this = *this * right;
return *this;
}
// Create a scale matrix with x and y scales
static Matrix3 CreateScale(float xScale, float yScale)
{
float temp[3][3] =
{
{ xScale, 0.0f, 0.0f },
{ 0.0f, yScale, 0.0f },
{ 0.0f, 0.0f, 1.0f },
};
return Matrix3(temp);
}
static Matrix3 CreateScale(const Vector2& scaleVector)
{
return CreateScale(scaleVector.x, scaleVector.y);
}
// Create a scale matrix with a uniform factor
static Matrix3 CreateScale(float scale)
{
return CreateScale(scale, scale);
}
// Create a rotation matrix about the Z axis
// theta is in radians
static Matrix3 CreateRotation(float theta)
{
float temp[3][3] =
{
{ Math::Cos(theta), Math::Sin(theta), 0.0f },
{ -Math::Sin(theta), Math::Cos(theta), 0.0f },
{ 0.0f, 0.0f, 1.0f },
};
return Matrix3(temp);
}
// Create a translation matrix (on the xy-plane)
static Matrix3 CreateTranslation(const Vector2& trans)
{
float temp[3][3] =
{
{ 1.0f, 0.0f, 0.0f },
{ 0.0f, 1.0f, 0.0f },
{ trans.x, trans.y, 1.0f },
};
return Matrix3(temp);
}
static const Matrix3 Identity;
};
// 4x4 Matrix
class Matrix4
{
public:
float mat[4][4];
Matrix4()
{
*this = Matrix4::Identity;
}
explicit Matrix4(float inMat[4][4])
{
memcpy(mat, inMat, 16 * sizeof(float));
}
// Cast to a const float pointer
const float* GetAsFloatPtr() const
{
return reinterpret_cast<const float*>(&mat[0][0]);
}
// Matrix multiplication (a * b)
friend Matrix4 operator*(const Matrix4& a, const Matrix4& b)
{
Matrix4 retVal;
// row 0
retVal.mat[0][0] =
a.mat[0][0] * b.mat[0][0] +
a.mat[0][1] * b.mat[1][0] +
a.mat[0][2] * b.mat[2][0] +
a.mat[0][3] * b.mat[3][0];
retVal.mat[0][1] =
a.mat[0][0] * b.mat[0][1] +
a.mat[0][1] * b.mat[1][1] +
a.mat[0][2] * b.mat[2][1] +
a.mat[0][3] * b.mat[3][1];
retVal.mat[0][2] =
a.mat[0][0] * b.mat[0][2] +
a.mat[0][1] * b.mat[1][2] +
a.mat[0][2] * b.mat[2][2] +
a.mat[0][3] * b.mat[3][2];
retVal.mat[0][3] =
a.mat[0][0] * b.mat[0][3] +
a.mat[0][1] * b.mat[1][3] +
a.mat[0][2] * b.mat[2][3] +
a.mat[0][3] * b.mat[3][3];
// row 1
retVal.mat[1][0] =
a.mat[1][0] * b.mat[0][0] +
a.mat[1][1] * b.mat[1][0] +
a.mat[1][2] * b.mat[2][0] +
a.mat[1][3] * b.mat[3][0];
retVal.mat[1][1] =
a.mat[1][0] * b.mat[0][1] +
a.mat[1][1] * b.mat[1][1] +
a.mat[1][2] * b.mat[2][1] +
a.mat[1][3] * b.mat[3][1];
retVal.mat[1][2] =
a.mat[1][0] * b.mat[0][2] +
a.mat[1][1] * b.mat[1][2] +
a.mat[1][2] * b.mat[2][2] +
a.mat[1][3] * b.mat[3][2];
retVal.mat[1][3] =
a.mat[1][0] * b.mat[0][3] +
a.mat[1][1] * b.mat[1][3] +
a.mat[1][2] * b.mat[2][3] +
a.mat[1][3] * b.mat[3][3];
// row 2
retVal.mat[2][0] =
a.mat[2][0] * b.mat[0][0] +
a.mat[2][1] * b.mat[1][0] +
a.mat[2][2] * b.mat[2][0] +
a.mat[2][3] * b.mat[3][0];
retVal.mat[2][1] =
a.mat[2][0] * b.mat[0][1] +
a.mat[2][1] * b.mat[1][1] +
a.mat[2][2] * b.mat[2][1] +
a.mat[2][3] * b.mat[3][1];
retVal.mat[2][2] =
a.mat[2][0] * b.mat[0][2] +
a.mat[2][1] * b.mat[1][2] +
a.mat[2][2] * b.mat[2][2] +
a.mat[2][3] * b.mat[3][2];
retVal.mat[2][3] =
a.mat[2][0] * b.mat[0][3] +
a.mat[2][1] * b.mat[1][3] +
a.mat[2][2] * b.mat[2][3] +
a.mat[2][3] * b.mat[3][3];
// row 3
retVal.mat[3][0] =
a.mat[3][0] * b.mat[0][0] +
a.mat[3][1] * b.mat[1][0] +
a.mat[3][2] * b.mat[2][0] +
a.mat[3][3] * b.mat[3][0];
retVal.mat[3][1] =
a.mat[3][0] * b.mat[0][1] +
a.mat[3][1] * b.mat[1][1] +
a.mat[3][2] * b.mat[2][1] +
a.mat[3][3] * b.mat[3][1];
retVal.mat[3][2] =
a.mat[3][0] * b.mat[0][2] +
a.mat[3][1] * b.mat[1][2] +
a.mat[3][2] * b.mat[2][2] +
a.mat[3][3] * b.mat[3][2];
retVal.mat[3][3] =
a.mat[3][0] * b.mat[0][3] +
a.mat[3][1] * b.mat[1][3] +
a.mat[3][2] * b.mat[2][3] +
a.mat[3][3] * b.mat[3][3];
return retVal;
}
Matrix4& operator*=(const Matrix4& right)
{
*this = *this * right;
return *this;
}
// Invert the matrix - super slow
void Invert();
// Get the translation component of the matrix
Vector3 GetTranslation() const
{
return Vector3(mat[3][0], mat[3][1], mat[3][2]);
}
// Get the X axis of the matrix (forward)
Vector3 GetXAxis() const
{
return Vector3::Normalize(Vector3(mat[0][0], mat[0][1], mat[0][2]));
}
// Get the Y axis of the matrix (left)
Vector3 GetYAxis() const
{
return Vector3::Normalize(Vector3(mat[1][0], mat[1][1], mat[1][2]));
}
// Get the Z axis of the matrix (up)
Vector3 GetZAxis() const
{
return Vector3::Normalize(Vector3(mat[2][0], mat[2][1], mat[2][2]));
}
// Extract the scale component from the matrix
Vector3 GetScale() const
{
Vector3 retVal;
retVal.x = Vector3(mat[0][0], mat[0][1], mat[0][2]).Length();
retVal.y = Vector3(mat[1][0], mat[1][1], mat[1][2]).Length();
retVal.z = Vector3(mat[2][0], mat[2][1], mat[2][2]).Length();
return retVal;
}
// Create a scale matrix with x, y, and z scales
static Matrix4 CreateScale(float xScale, float yScale, float zScale)
{
float temp[4][4] =
{
{ xScale, 0.0f, 0.0f, 0.0f },
{ 0.0f, yScale, 0.0f, 0.0f },
{ 0.0f, 0.0f, zScale, 0.0f },
{ 0.0f, 0.0f, 0.0f, 1.0f }
};
return Matrix4(temp);
}
static Matrix4 CreateScale(const Vector3& scaleVector)
{
return CreateScale(scaleVector.x, scaleVector.y, scaleVector.z);
}
// Create a scale matrix with a uniform factor
static Matrix4 CreateScale(float scale)
{
return CreateScale(scale, scale, scale);
}
// Rotation about x-axis
static Matrix4 CreateRotationX(float theta)
{
float temp[4][4] =
{
{ 1.0f, 0.0f, 0.0f , 0.0f },
{ 0.0f, Math::Cos(theta), Math::Sin(theta), 0.0f },
{ 0.0f, -Math::Sin(theta), Math::Cos(theta), 0.0f },
{ 0.0f, 0.0f, 0.0f, 1.0f },
};
return Matrix4(temp);
}
// Rotation about y-axis
static Matrix4 CreateRotationY(float theta)
{
float temp[4][4] =
{
{ Math::Cos(theta), 0.0f, -Math::Sin(theta), 0.0f },
{ 0.0f, 1.0f, 0.0f, 0.0f },
{ Math::Sin(theta), 0.0f, Math::Cos(theta), 0.0f },
{ 0.0f, 0.0f, 0.0f, 1.0f },
};
return Matrix4(temp);
}
// Rotation about z-axis
static Matrix4 CreateRotationZ(float theta)
{
float temp[4][4] =
{
{ Math::Cos(theta), Math::Sin(theta), 0.0f, 0.0f },
{ -Math::Sin(theta), Math::Cos(theta), 0.0f, 0.0f },
{ 0.0f, 0.0f, 1.0f, 0.0f },
{ 0.0f, 0.0f, 0.0f, 1.0f },
};
return Matrix4(temp);
}
// Create a rotation matrix from a quaternion
static Matrix4 CreateFromQuaternion(const class Quaternion& q);
static Matrix4 CreateTranslation(const Vector3& trans)
{
float temp[4][4] =
{
{ 1.0f, 0.0f, 0.0f, 0.0f },
{ 0.0f, 1.0f, 0.0f, 0.0f },
{ 0.0f, 0.0f, 1.0f, 0.0f },
{ trans.x, trans.y, trans.z, 1.0f }
};
return Matrix4(temp);
}
static Matrix4 CreateLookAt(const Vector3& eye, const Vector3& target, const Vector3& up)
{
Vector3 zaxis = Vector3::Normalize(target - eye);
Vector3 xaxis = Vector3::Normalize(Vector3::Cross(up, zaxis));
Vector3 yaxis = Vector3::Normalize(Vector3::Cross(zaxis, xaxis));
Vector3 trans;
trans.x = -Vector3::Dot(xaxis, eye);
trans.y = -Vector3::Dot(yaxis, eye);
trans.z = -Vector3::Dot(zaxis, eye);
float temp[4][4] =
{
{ xaxis.x, yaxis.x, zaxis.x, 0.0f },
{ xaxis.y, yaxis.y, zaxis.y, 0.0f },
{ xaxis.z, yaxis.z, zaxis.z, 0.0f },
{ trans.x, trans.y, trans.z, 1.0f }
};
return Matrix4(temp);
}
static Matrix4 CreateOrtho(float width, float height, float near, float far)
{
float temp[4][4] =
{
{ 2.0f / width, 0.0f, 0.0f, 0.0f },
{ 0.0f, 2.0f / height, 0.0f, 0.0f },
{ 0.0f, 0.0f, 1.0f / (far - near), 0.0f },
{ 0.0f, 0.0f, near / (near - far), 1.0f }
};
return Matrix4(temp);
}
static Matrix4 CreatePerspectiveFOV(float fovY, float width, float height, float near, float far)
{
float yScale = Math::Cot(fovY / 2.0f);
float xScale = yScale * height / width;
float temp[4][4] =
{
{ xScale, 0.0f, 0.0f, 0.0f },
{ 0.0f, yScale, 0.0f, 0.0f },
{ 0.0f, 0.0f, far / (far - near), 1.0f },
{ 0.0f, 0.0f, -near * far / (far - near), 0.0f }
};
return Matrix4(temp);
}
// Create "Simple" View-Projection Matrix from Chapter 6
static Matrix4 CreateSimpleViewProj(float width, float height)
{
float temp[4][4] =
{
{ 2.0f/width, 0.0f, 0.0f, 0.0f },
{ 0.0f, 2.0f/height, 0.0f, 0.0f },
{ 0.0f, 0.0f, 1.0f, 0.0f },
{ 0.0f, 0.0f, 1.0f, 1.0f }
};
return Matrix4(temp);
}
static const Matrix4 Identity;
};
// (Unit) Quaternion
class Quaternion
{
public:
float x;
float y;
float z;
float w;
Quaternion()
{
*this = Quaternion::Identity;
}
// This directly sets the quaternion components --
// don't use for axis/angle
explicit Quaternion(float inX, float inY, float inZ, float inW)
{
Set(inX, inY, inZ, inW);
}
// Construct the quaternion from an axis and angle
// It is assumed that axis is already normalized,
// and the angle is in radians
explicit Quaternion(const Vector3& axis, float angle)
{
float scalar = Math::Sin(angle / 2.0f);
x = axis.x * scalar;
y = axis.y * scalar;
z = axis.z * scalar;
w = Math::Cos(angle / 2.0f);
}
// Directly set the internal components
void Set(float inX, float inY, float inZ, float inW)
{
x = inX;
y = inY;
z = inZ;
w = inW;
}
void Conjugate()
{
x *= -1.0f;
y *= -1.0f;
z *= -1.0f;
}
float LengthSq() const
{
return (x*x + y*y + z*z + w*w);
}
float Length() const
{
return Math::Sqrt(LengthSq());
}
void Normalize()
{
float length = Length();
x /= length;
y /= length;
z /= length;
w /= length;
}
// Normalize the provided quaternion
static Quaternion Normalize(const Quaternion& q)
{
Quaternion retVal = q;
retVal.Normalize();
return retVal;
}
// Linear interpolation
static Quaternion Lerp(const Quaternion& a, const Quaternion& b, float f)
{
Quaternion retVal;
retVal.x = Math::Lerp(a.x, b.x, f);
retVal.y = Math::Lerp(a.y, b.y, f);
retVal.z = Math::Lerp(a.z, b.z, f);
retVal.w = Math::Lerp(a.w, b.w, f);
retVal.Normalize();
return retVal;
}
static float Dot(const Quaternion& a, const Quaternion& b)
{
return a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w;
}
// Spherical Linear Interpolation
static Quaternion Slerp(const Quaternion& a, const Quaternion& b, float f)
{
float rawCosm = Quaternion::Dot(a, b);
float cosom = -rawCosm;
if (rawCosm >= 0.0f)
{
cosom = rawCosm;
}
float scale0, scale1;
if (cosom < 0.9999f)
{
const float omega = Math::Acos(cosom);
const float invSin = 1.f / Math::Sin(omega);
scale0 = Math::Sin((1.f - f) * omega) * invSin;
scale1 = Math::Sin(f * omega) * invSin;
}
else
{
// Use linear interpolation if the quaternions
// are collinear
scale0 = 1.0f - f;
scale1 = f;
}
if (rawCosm < 0.0f)
{
scale1 = -scale1;
}
Quaternion retVal;
retVal.x = scale0 * a.x + scale1 * b.x;
retVal.y = scale0 * a.y + scale1 * b.y;
retVal.z = scale0 * a.z + scale1 * b.z;
retVal.w = scale0 * a.w + scale1 * b.w;
retVal.Normalize();
return retVal;
}
// Concatenate
// Rotate by q FOLLOWED BY p
static Quaternion Concatenate(const Quaternion& q, const Quaternion& p)
{
Quaternion retVal;
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