genesis-3d_engine/Engine/ExtIncludes/physX3/windows/foundation/PxMat33.h

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#ifndef PX_FOUNDATION_PX_MAT33_H
#define PX_FOUNDATION_PX_MAT33_H
/** \addtogroup foundation
@{
*/
#include "foundation/PxVec3.h"
#include "foundation/PxQuat.h"
#ifndef 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_INLINE PxMat33()
{}
//! Construct from three base vectors
PX_CUDA_CALLABLE PxMat33(const PxVec3& col0, const PxVec3& col1, const PxVec3& col2)
: column0(col0), column1(col1), column2(col2)
{}
//! Construct from float[9]
PX_CUDA_CALLABLE explicit PX_INLINE PxMat33(PxReal 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
PX_CUDA_CALLABLE explicit PX_FORCE_INLINE PxMat33(const PxQuat& q)
{
const PxReal x = q.x;
const PxReal y = q.y;
const PxReal z = q.z;
const PxReal w = q.w;
const PxReal x2 = x + x;
const PxReal y2 = y + y;
const PxReal z2 = z + z;
const PxReal xx = x2*x;
const PxReal yy = y2*y;
const PxReal zz = z2*z;
const PxReal xy = x2*y;
const PxReal xz = x2*z;
const PxReal xw = x2*w;
const PxReal yz = y2*z;
const PxReal yw = y2*w;
const PxReal 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;
}
//! Set to identity matrix
PX_CUDA_CALLABLE PX_INLINE static PxMat33 createIdentity()
{
return PxMat33(PxVec3(1,0,0), PxVec3(0,1,0), PxVec3(0,0,1));
}
//! Set to zero matrix
PX_CUDA_CALLABLE PX_INLINE static PxMat33 createZero()
{
return PxMat33(PxVec3(0.0f), PxVec3(0.0f), PxVec3(0.0f));
}
//! Construct from diagonal, off-diagonals are zero.
PX_CUDA_CALLABLE PX_INLINE static 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));
}
//! Get transposed matrix
PX_CUDA_CALLABLE PX_FORCE_INLINE 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 PxMat33 getInverse() const
{
const PxReal det = getDeterminant();
PxMat33 inverse;
if(det != 0)
{
const PxReal invDet = 1.0f/det;
inverse.column0[0] = invDet * (column1[1]*column2[2] - column2[1]*column1[2]);
inverse.column0[1] = invDet *-(column0[1]*column2[2] - column2[1]*column0[2]);
inverse.column0[2] = invDet * (column0[1]*column1[2] - column0[2]*column1[1]);
inverse.column1[0] = invDet *-(column1[0]*column2[2] - column1[2]*column2[0]);
inverse.column1[1] = invDet * (column0[0]*column2[2] - column0[2]*column2[0]);
inverse.column1[2] = invDet *-(column0[0]*column1[2] - column0[2]*column1[0]);
inverse.column2[0] = invDet * (column1[0]*column2[1] - column1[1]*column2[0]);
inverse.column2[1] = invDet *-(column0[0]*column2[1] - column0[1]*column2[0]);
inverse.column2[2] = invDet * (column0[0]*column1[1] - column1[0]*column0[1]);
return inverse;
}
else
{
return createIdentity();
}
}
//! Get determinant
PX_CUDA_CALLABLE PX_INLINE PxReal getDeterminant() const
{
return column0.dot(column1.cross(column2));
}
//! Unary minus
PX_CUDA_CALLABLE PX_INLINE PxMat33 operator-() const
{
return PxMat33(-column0, -column1, -column2);
}
//! Add
PX_CUDA_CALLABLE PX_INLINE PxMat33 operator+(const PxMat33& other) const
{
return PxMat33( column0+other.column0,
column1+other.column1,
column2+other.column2);
}
//! Subtract
PX_CUDA_CALLABLE PX_INLINE PxMat33 operator-(const PxMat33& other) const
{
return PxMat33( column0-other.column0,
column1-other.column1,
column2-other.column2);
}
//! Scalar multiplication
PX_CUDA_CALLABLE PX_INLINE PxMat33 operator*(PxReal scalar) const
{
return PxMat33(column0*scalar, column1*scalar, column2*scalar);
}
friend PxMat33 operator*(PxReal, const PxMat33&);
//! Matrix vector multiplication (returns 'this->transform(vec)')
PX_CUDA_CALLABLE PX_INLINE PxVec3 operator*(const PxVec3& vec) const
{
return transform(vec);
}
//! Matrix multiplication
PX_CUDA_CALLABLE PX_FORCE_INLINE 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));
}
// a <op>= b operators
//! 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*=(PxReal scalar)
{
column0 *= scalar;
column1 *= scalar;
column2 *= scalar;
return *this;
}
//! Element access, mathematical way!
PX_CUDA_CALLABLE PX_FORCE_INLINE PxReal operator()(unsigned int row, unsigned int col) const
{
return (*this)[col][row];
}
//! Element access, mathematical way!
PX_CUDA_CALLABLE PX_FORCE_INLINE PxReal& 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 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 PxVec3 transformTranspose(const PxVec3& other) const
{
return PxVec3( column0.dot(other),
column1.dot(other),
column2.dot(other));
}
PX_CUDA_CALLABLE PX_FORCE_INLINE const PxReal* front() const
{
return &column0.x;
}
PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3& operator[](int num) {return (&column0)[num];}
PX_CUDA_CALLABLE PX_FORCE_INLINE const PxVec3& operator[](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)
{
PxReal tr = m(0,0) + m(1,1) + m(2,2), h;
if(tr >= 0)
{
h = PxSqrt(tr +1);
w = PxReal(0.5) * h;
h = PxReal(0.5) / h;
x = (m(2,1) - m(1,2)) * h;
y = (m(0,2) - m(2,0)) * h;
z = (m(1,0) - m(0,1)) * h;
}
else
{
int i = 0;
if (m(1,1) > m(0,0))
i = 1;
if (m(2,2) > m(i,i))
i = 2;
switch (i)
{
case 0:
h = PxSqrt((m(0,0) - (m(1,1) + m(2,2))) + 1);
x = PxReal(0.5) * h;
h = PxReal(0.5) / h;
y = (m(0,1) + m(1,0)) * h;
z = (m(2,0) + m(0,2)) * h;
w = (m(2,1) - m(1,2)) * h;
break;
case 1:
h = PxSqrt((m(1,1) - (m(2,2) + m(0,0))) + 1);
y = PxReal(0.5) * h;
h = PxReal(0.5) / h;
z = (m(1,2) + m(2,1)) * h;
x = (m(0,1) + m(1,0)) * h;
w = (m(0,2) - m(2,0)) * h;
break;
case 2:
h = PxSqrt((m(2,2) - (m(0,0) + m(1,1))) + 1);
z = PxReal(0.5) * h;
h = PxReal(0.5) / h;
x = (m(2,0) + m(0,2)) * h;
y = (m(1,2) + m(2,1)) * h;
w = (m(1,0) - m(0,1)) * h;
break;
default: // Make compiler happy
x = y = z = w = 0;
break;
}
}
}
#ifndef PX_DOXYGEN
} // namespace physx
#endif
/** @} */
#endif // PX_FOUNDATION_PX_MAT33_H