Space-Project/dependencies/physx-4.1/include/foundation/PxMat33.h
2021-01-16 17:11:39 +01:00

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#ifndef PXFOUNDATION_PXMAT33_H
#define PXFOUNDATION_PXMAT33_H
/** \addtogroup foundation
@{
*/
#include "foundation/PxVec3.h"
#include "foundation/PxQuat.h"
#if !PX_DOXYGEN
namespace physx
{
#endif
/*!
\brief 3x3 matrix class
Some clarifications, as there have been much confusion about matrix formats etc in the past.
Short:
- Matrix have base vectors in columns (vectors are column matrices, 3x1 matrices).
- Matrix is physically stored in column major format
- Matrices are concaternated from left
Long:
Given three base vectors a, b and c the matrix is stored as
|a.x b.x c.x|
|a.y b.y c.y|
|a.z b.z c.z|
Vectors are treated as columns, so the vector v is
|x|
|y|
|z|
And matrices are applied _before_ the vector (pre-multiplication)
v' = M*v
|x'| |a.x b.x c.x| |x| |a.x*x + b.x*y + c.x*z|
|y'| = |a.y b.y c.y| * |y| = |a.y*x + b.y*y + c.y*z|
|z'| |a.z b.z c.z| |z| |a.z*x + b.z*y + c.z*z|
Physical storage and indexing:
To be compatible with popular 3d rendering APIs (read D3d and OpenGL)
the physical indexing is
|0 3 6|
|1 4 7|
|2 5 8|
index = column*3 + row
which in C++ translates to M[column][row]
The mathematical indexing is M_row,column and this is what is used for _-notation
so _12 is 1st row, second column and operator(row, column)!
*/
class PxMat33
{
public:
//! Default constructor
PX_CUDA_CALLABLE PX_FORCE_INLINE PxMat33()
{
}
//! identity constructor
PX_CUDA_CALLABLE PX_INLINE PxMat33(PxIDENTITY r)
: column0(1.0f, 0.0f, 0.0f), column1(0.0f, 1.0f, 0.0f), column2(0.0f, 0.0f, 1.0f)
{
PX_UNUSED(r);
}
//! zero constructor
PX_CUDA_CALLABLE PX_INLINE PxMat33(PxZERO r) : column0(0.0f), column1(0.0f), column2(0.0f)
{
PX_UNUSED(r);
}
//! Construct from three base vectors
PX_CUDA_CALLABLE PxMat33(const PxVec3& col0, const PxVec3& col1, const PxVec3& col2)
: column0(col0), column1(col1), column2(col2)
{
}
//! constructor from a scalar, which generates a multiple of the identity matrix
explicit PX_CUDA_CALLABLE PX_INLINE PxMat33(float r)
: column0(r, 0.0f, 0.0f), column1(0.0f, r, 0.0f), column2(0.0f, 0.0f, r)
{
}
//! Construct from float[9]
explicit PX_CUDA_CALLABLE PX_INLINE PxMat33(float values[])
: column0(values[0], values[1], values[2])
, column1(values[3], values[4], values[5])
, column2(values[6], values[7], values[8])
{
}
//! Construct from a quaternion
explicit PX_CUDA_CALLABLE PX_FORCE_INLINE PxMat33(const PxQuat& q)
{
const float x = q.x;
const float y = q.y;
const float z = q.z;
const float w = q.w;
const float x2 = x + x;
const float y2 = y + y;
const float z2 = z + z;
const float xx = x2 * x;
const float yy = y2 * y;
const float zz = z2 * z;
const float xy = x2 * y;
const float xz = x2 * z;
const float xw = x2 * w;
const float yz = y2 * z;
const float yw = y2 * w;
const float zw = z2 * w;
column0 = PxVec3(1.0f - yy - zz, xy + zw, xz - yw);
column1 = PxVec3(xy - zw, 1.0f - xx - zz, yz + xw);
column2 = PxVec3(xz + yw, yz - xw, 1.0f - xx - yy);
}
//! Copy constructor
PX_CUDA_CALLABLE PX_INLINE PxMat33(const PxMat33& other)
: column0(other.column0), column1(other.column1), column2(other.column2)
{
}
//! Assignment operator
PX_CUDA_CALLABLE PX_FORCE_INLINE PxMat33& operator=(const PxMat33& other)
{
column0 = other.column0;
column1 = other.column1;
column2 = other.column2;
return *this;
}
//! Construct from diagonal, off-diagonals are zero.
PX_CUDA_CALLABLE PX_INLINE static const PxMat33 createDiagonal(const PxVec3& d)
{
return PxMat33(PxVec3(d.x, 0.0f, 0.0f), PxVec3(0.0f, d.y, 0.0f), PxVec3(0.0f, 0.0f, d.z));
}
/**
\brief returns true if the two matrices are exactly equal
*/
PX_CUDA_CALLABLE PX_INLINE bool operator==(const PxMat33& m) const
{
return column0 == m.column0 && column1 == m.column1 && column2 == m.column2;
}
//! Get transposed matrix
PX_CUDA_CALLABLE PX_FORCE_INLINE const PxMat33 getTranspose() const
{
const PxVec3 v0(column0.x, column1.x, column2.x);
const PxVec3 v1(column0.y, column1.y, column2.y);
const PxVec3 v2(column0.z, column1.z, column2.z);
return PxMat33(v0, v1, v2);
}
//! Get the real inverse
PX_CUDA_CALLABLE PX_INLINE const PxMat33 getInverse() const
{
const float det = getDeterminant();
PxMat33 inverse;
if(det != 0)
{
const float invDet = 1.0f / det;
inverse.column0.x = invDet * (column1.y * column2.z - column2.y * column1.z);
inverse.column0.y = invDet * -(column0.y * column2.z - column2.y * column0.z);
inverse.column0.z = invDet * (column0.y * column1.z - column0.z * column1.y);
inverse.column1.x = invDet * -(column1.x * column2.z - column1.z * column2.x);
inverse.column1.y = invDet * (column0.x * column2.z - column0.z * column2.x);
inverse.column1.z = invDet * -(column0.x * column1.z - column0.z * column1.x);
inverse.column2.x = invDet * (column1.x * column2.y - column1.y * column2.x);
inverse.column2.y = invDet * -(column0.x * column2.y - column0.y * column2.x);
inverse.column2.z = invDet * (column0.x * column1.y - column1.x * column0.y);
return inverse;
}
else
{
return PxMat33(PxIdentity);
}
}
//! Get determinant
PX_CUDA_CALLABLE PX_INLINE float getDeterminant() const
{
return column0.dot(column1.cross(column2));
}
//! Unary minus
PX_CUDA_CALLABLE PX_INLINE const PxMat33 operator-() const
{
return PxMat33(-column0, -column1, -column2);
}
//! Add
PX_CUDA_CALLABLE PX_INLINE const PxMat33 operator+(const PxMat33& other) const
{
return PxMat33(column0 + other.column0, column1 + other.column1, column2 + other.column2);
}
//! Subtract
PX_CUDA_CALLABLE PX_INLINE const PxMat33 operator-(const PxMat33& other) const
{
return PxMat33(column0 - other.column0, column1 - other.column1, column2 - other.column2);
}
//! Scalar multiplication
PX_CUDA_CALLABLE PX_INLINE const PxMat33 operator*(float scalar) const
{
return PxMat33(column0 * scalar, column1 * scalar, column2 * scalar);
}
friend PxMat33 operator*(float, const PxMat33&);
//! Matrix vector multiplication (returns 'this->transform(vec)')
PX_CUDA_CALLABLE PX_INLINE const PxVec3 operator*(const PxVec3& vec) const
{
return transform(vec);
}
// a <op>= b operators
//! Matrix multiplication
PX_CUDA_CALLABLE PX_FORCE_INLINE const PxMat33 operator*(const PxMat33& other) const
{
// Rows from this <dot> columns from other
// column0 = transform(other.column0) etc
return PxMat33(transform(other.column0), transform(other.column1), transform(other.column2));
}
//! Equals-add
PX_CUDA_CALLABLE PX_INLINE PxMat33& operator+=(const PxMat33& other)
{
column0 += other.column0;
column1 += other.column1;
column2 += other.column2;
return *this;
}
//! Equals-sub
PX_CUDA_CALLABLE PX_INLINE PxMat33& operator-=(const PxMat33& other)
{
column0 -= other.column0;
column1 -= other.column1;
column2 -= other.column2;
return *this;
}
//! Equals scalar multiplication
PX_CUDA_CALLABLE PX_INLINE PxMat33& operator*=(float scalar)
{
column0 *= scalar;
column1 *= scalar;
column2 *= scalar;
return *this;
}
//! Equals matrix multiplication
PX_CUDA_CALLABLE PX_INLINE PxMat33& operator*=(const PxMat33& other)
{
*this = *this * other;
return *this;
}
//! Element access, mathematical way!
PX_CUDA_CALLABLE PX_FORCE_INLINE float operator()(unsigned int row, unsigned int col) const
{
return (*this)[col][row];
}
//! Element access, mathematical way!
PX_CUDA_CALLABLE PX_FORCE_INLINE float& operator()(unsigned int row, unsigned int col)
{
return (*this)[col][row];
}
// Transform etc
//! Transform vector by matrix, equal to v' = M*v
PX_CUDA_CALLABLE PX_FORCE_INLINE const PxVec3 transform(const PxVec3& other) const
{
return column0 * other.x + column1 * other.y + column2 * other.z;
}
//! Transform vector by matrix transpose, v' = M^t*v
PX_CUDA_CALLABLE PX_INLINE const PxVec3 transformTranspose(const PxVec3& other) const
{
return PxVec3(column0.dot(other), column1.dot(other), column2.dot(other));
}
PX_CUDA_CALLABLE PX_FORCE_INLINE const float* front() const
{
return &column0.x;
}
PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3& operator[](unsigned int num)
{
return (&column0)[num];
}
PX_CUDA_CALLABLE PX_FORCE_INLINE const PxVec3& operator[](unsigned int num) const
{
return (&column0)[num];
}
// Data, see above for format!
PxVec3 column0, column1, column2; // the three base vectors
};
// implementation from PxQuat.h
PX_CUDA_CALLABLE PX_INLINE PxQuat::PxQuat(const PxMat33& m)
{
if(m.column2.z < 0)
{
if(m.column0.x > m.column1.y)
{
float t = 1 + m.column0.x - m.column1.y - m.column2.z;
*this = PxQuat(t, m.column0.y + m.column1.x, m.column2.x + m.column0.z, m.column1.z - m.column2.y) *
(0.5f / PxSqrt(t));
}
else
{
float t = 1 - m.column0.x + m.column1.y - m.column2.z;
*this = PxQuat(m.column0.y + m.column1.x, t, m.column1.z + m.column2.y, m.column2.x - m.column0.z) *
(0.5f / PxSqrt(t));
}
}
else
{
if(m.column0.x < -m.column1.y)
{
float t = 1 - m.column0.x - m.column1.y + m.column2.z;
*this = PxQuat(m.column2.x + m.column0.z, m.column1.z + m.column2.y, t, m.column0.y - m.column1.x) *
(0.5f / PxSqrt(t));
}
else
{
float t = 1 + m.column0.x + m.column1.y + m.column2.z;
*this = PxQuat(m.column1.z - m.column2.y, m.column2.x - m.column0.z, m.column0.y - m.column1.x, t) *
(0.5f / PxSqrt(t));
}
}
}
#if !PX_DOXYGEN
} // namespace physx
#endif
/** @} */
#endif // #ifndef PXFOUNDATION_PXMAT33_H