426 lines
12 KiB
C
426 lines
12 KiB
C
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions
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// are met:
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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// * Neither the name of NVIDIA CORPORATION nor the names of its
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// contributors may be used to endorse or promote products derived
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// from this software without specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ''AS IS'' AND ANY
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// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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// Copyright (c) 2008-2023 NVIDIA Corporation. All rights reserved.
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// Copyright (c) 2004-2008 AGEIA Technologies, Inc. All rights reserved.
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// Copyright (c) 2001-2004 NovodeX AG. All rights reserved.
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#ifndef PX_MAT33_H
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#define PX_MAT33_H
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/** \addtogroup foundation
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@{
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*/
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#include "foundation/PxVec3.h"
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#include "foundation/PxQuat.h"
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#if !PX_DOXYGEN
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namespace physx
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{
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#endif
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/*!
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\brief 3x3 matrix class
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Some clarifications, as there have been much confusion about matrix formats etc in the past.
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Short:
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- Matrix have base vectors in columns (vectors are column matrices, 3x1 matrices).
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- Matrix is physically stored in column major format
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- Matrices are concaternated from left
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Long:
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Given three base vectors a, b and c the matrix is stored as
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|a.x b.x c.x|
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|a.y b.y c.y|
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|a.z b.z c.z|
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Vectors are treated as columns, so the vector v is
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|x|
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|y|
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|z|
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And matrices are applied _before_ the vector (pre-multiplication)
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v' = M*v
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|x'| |a.x b.x c.x| |x| |a.x*x + b.x*y + c.x*z|
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|y'| = |a.y b.y c.y| * |y| = |a.y*x + b.y*y + c.y*z|
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|z'| |a.z b.z c.z| |z| |a.z*x + b.z*y + c.z*z|
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Physical storage and indexing:
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To be compatible with popular 3d rendering APIs (read D3d and OpenGL)
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the physical indexing is
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|0 3 6|
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|1 4 7|
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|2 5 8|
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index = column*3 + row
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which in C++ translates to M[column][row]
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The mathematical indexing is M_row,column and this is what is used for _-notation
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so _12 is 1st row, second column and operator(row, column)!
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*/
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template<class Type>
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class PxMat33T
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{
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public:
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//! Default constructor
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PX_CUDA_CALLABLE PX_FORCE_INLINE PxMat33T()
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{
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}
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//! identity constructor
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PX_CUDA_CALLABLE PX_INLINE PxMat33T(PxIDENTITY) :
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column0(Type(1.0), Type(0.0), Type(0.0)),
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column1(Type(0.0), Type(1.0), Type(0.0)),
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column2(Type(0.0), Type(0.0), Type(1.0))
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{
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}
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//! zero constructor
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PX_CUDA_CALLABLE PX_INLINE PxMat33T(PxZERO) :
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column0(Type(0.0)),
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column1(Type(0.0)),
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column2(Type(0.0))
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{
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}
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//! Construct from three base vectors
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PX_CUDA_CALLABLE PxMat33T(const PxVec3T<Type>& col0, const PxVec3T<Type>& col1, const PxVec3T<Type>& col2) :
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column0(col0),
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column1(col1),
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column2(col2)
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{
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}
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//! constructor from a scalar, which generates a multiple of the identity matrix
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explicit PX_CUDA_CALLABLE PX_INLINE PxMat33T(Type r) :
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column0(r, Type(0.0), Type(0.0)),
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column1(Type(0.0), r, Type(0.0)),
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column2(Type(0.0), Type(0.0), r)
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{
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}
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//! Construct from Type[9]
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explicit PX_CUDA_CALLABLE PX_INLINE PxMat33T(Type values[]) :
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column0(values[0], values[1], values[2]),
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column1(values[3], values[4], values[5]),
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column2(values[6], values[7], values[8])
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{
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}
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//! Construct from a quaternion
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explicit PX_CUDA_CALLABLE PX_FORCE_INLINE PxMat33T(const PxQuatT<Type>& q)
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{
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// PT: TODO: PX-566
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const Type x = q.x;
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const Type y = q.y;
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const Type z = q.z;
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const Type w = q.w;
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const Type x2 = x + x;
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const Type y2 = y + y;
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const Type z2 = z + z;
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const Type xx = x2 * x;
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const Type yy = y2 * y;
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const Type zz = z2 * z;
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const Type xy = x2 * y;
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const Type xz = x2 * z;
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const Type xw = x2 * w;
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const Type yz = y2 * z;
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const Type yw = y2 * w;
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const Type zw = z2 * w;
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column0 = PxVec3T<Type>(Type(1.0) - yy - zz, xy + zw, xz - yw);
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column1 = PxVec3T<Type>(xy - zw, Type(1.0) - xx - zz, yz + xw);
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column2 = PxVec3T<Type>(xz + yw, yz - xw, Type(1.0) - xx - yy);
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}
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//! Copy constructor
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PX_CUDA_CALLABLE PX_INLINE PxMat33T(const PxMat33T& other) :
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column0(other.column0),
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column1(other.column1),
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column2(other.column2)
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{
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}
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//! Assignment operator
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PX_CUDA_CALLABLE PX_FORCE_INLINE PxMat33T& operator=(const PxMat33T& other)
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{
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column0 = other.column0;
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column1 = other.column1;
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column2 = other.column2;
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return *this;
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}
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//! Construct from diagonal, off-diagonals are zero.
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PX_CUDA_CALLABLE PX_INLINE static const PxMat33T createDiagonal(const PxVec3T<Type>& d)
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{
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return PxMat33T(PxVec3T<Type>(d.x, Type(0.0), Type(0.0)),
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PxVec3T<Type>(Type(0.0), d.y, Type(0.0)),
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PxVec3T<Type>(Type(0.0), Type(0.0), d.z));
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}
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//! Computes the outer product of two vectors
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PX_CUDA_CALLABLE PX_INLINE static const PxMat33T outer(const PxVec3T<Type>& a, const PxVec3T<Type>& b)
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{
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return PxMat33T(a * b.x, a * b.y, a * b.z);
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}
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/**
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\brief returns true if the two matrices are exactly equal
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*/
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PX_CUDA_CALLABLE PX_INLINE bool operator==(const PxMat33T& m) const
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{
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return column0 == m.column0 && column1 == m.column1 && column2 == m.column2;
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}
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//! Get transposed matrix
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PX_CUDA_CALLABLE PX_FORCE_INLINE const PxMat33T getTranspose() const
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{
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const PxVec3T<Type> v0(column0.x, column1.x, column2.x);
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const PxVec3T<Type> v1(column0.y, column1.y, column2.y);
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const PxVec3T<Type> v2(column0.z, column1.z, column2.z);
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return PxMat33T(v0, v1, v2);
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}
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//! Get the real inverse
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PX_CUDA_CALLABLE PX_INLINE const PxMat33T getInverse() const
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{
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const Type det = getDeterminant();
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PxMat33T inverse;
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if(det != Type(0.0))
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{
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const Type invDet = Type(1.0) / det;
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inverse.column0.x = invDet * (column1.y * column2.z - column2.y * column1.z);
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inverse.column0.y = invDet * -(column0.y * column2.z - column2.y * column0.z);
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inverse.column0.z = invDet * (column0.y * column1.z - column0.z * column1.y);
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inverse.column1.x = invDet * -(column1.x * column2.z - column1.z * column2.x);
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inverse.column1.y = invDet * (column0.x * column2.z - column0.z * column2.x);
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inverse.column1.z = invDet * -(column0.x * column1.z - column0.z * column1.x);
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inverse.column2.x = invDet * (column1.x * column2.y - column1.y * column2.x);
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inverse.column2.y = invDet * -(column0.x * column2.y - column0.y * column2.x);
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inverse.column2.z = invDet * (column0.x * column1.y - column1.x * column0.y);
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return inverse;
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}
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else
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{
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return PxMat33T(PxIdentity);
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}
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}
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//! Get determinant
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PX_CUDA_CALLABLE PX_INLINE Type getDeterminant() const
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{
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return column0.dot(column1.cross(column2));
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}
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//! Unary minus
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PX_CUDA_CALLABLE PX_INLINE const PxMat33T operator-() const
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{
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return PxMat33T(-column0, -column1, -column2);
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}
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//! Add
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PX_CUDA_CALLABLE PX_INLINE const PxMat33T operator+(const PxMat33T& other) const
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{
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return PxMat33T(column0 + other.column0, column1 + other.column1, column2 + other.column2);
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}
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//! Subtract
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PX_CUDA_CALLABLE PX_INLINE const PxMat33T operator-(const PxMat33T& other) const
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{
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return PxMat33T(column0 - other.column0, column1 - other.column1, column2 - other.column2);
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}
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//! Scalar multiplication
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PX_CUDA_CALLABLE PX_INLINE const PxMat33T operator*(Type scalar) const
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{
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return PxMat33T(column0 * scalar, column1 * scalar, column2 * scalar);
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}
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template<class Type2>
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PX_CUDA_CALLABLE PX_INLINE friend PxMat33T<Type2> operator*(Type2, const PxMat33T<Type2>&);
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//! Matrix vector multiplication (returns 'this->transform(vec)')
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PX_CUDA_CALLABLE PX_INLINE const PxVec3T<Type> operator*(const PxVec3T<Type>& vec) const
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{
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return transform(vec);
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}
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// a <op>= b operators
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//! Matrix multiplication
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PX_CUDA_CALLABLE PX_FORCE_INLINE const PxMat33T operator*(const PxMat33T& other) const
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{
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// Rows from this <dot> columns from other
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// column0 = transform(other.column0) etc
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return PxMat33T(transform(other.column0),
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transform(other.column1),
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transform(other.column2));
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}
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//! Equals-add
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PX_CUDA_CALLABLE PX_INLINE PxMat33T& operator+=(const PxMat33T& other)
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{
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column0 += other.column0;
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column1 += other.column1;
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column2 += other.column2;
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return *this;
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}
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//! Equals-sub
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PX_CUDA_CALLABLE PX_INLINE PxMat33T& operator-=(const PxMat33T& other)
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{
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column0 -= other.column0;
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column1 -= other.column1;
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column2 -= other.column2;
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return *this;
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}
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//! Equals scalar multiplication
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PX_CUDA_CALLABLE PX_INLINE PxMat33T& operator*=(Type scalar)
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{
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column0 *= scalar;
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column1 *= scalar;
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column2 *= scalar;
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return *this;
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}
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//! Equals matrix multiplication
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PX_CUDA_CALLABLE PX_INLINE PxMat33T& operator*=(const PxMat33T& other)
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{
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*this = *this * other;
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return *this;
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}
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//! Element access, mathematical way!
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PX_CUDA_CALLABLE PX_FORCE_INLINE Type operator()(PxU32 row, PxU32 col) const
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{
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return (*this)[col][row];
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}
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//! Element access, mathematical way!
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PX_CUDA_CALLABLE PX_FORCE_INLINE Type& operator()(PxU32 row, PxU32 col)
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{
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return (*this)[col][row];
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}
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// Transform etc
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//! Transform vector by matrix, equal to v' = M*v
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PX_CUDA_CALLABLE PX_FORCE_INLINE const PxVec3T<Type> transform(const PxVec3T<Type>& other) const
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{
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return column0 * other.x + column1 * other.y + column2 * other.z;
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}
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//! Transform vector by matrix transpose, v' = M^t*v
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PX_CUDA_CALLABLE PX_INLINE const PxVec3T<Type> transformTranspose(const PxVec3T<Type>& other) const
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{
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|
|
return PxVec3T<Type>(column0.dot(other), column1.dot(other), column2.dot(other));
|
||
|
|
}
|
||
|
|
|
||
|
|
PX_CUDA_CALLABLE PX_FORCE_INLINE const Type* front() const
|
||
|
|
{
|
||
|
|
return &column0.x;
|
||
|
|
}
|
||
|
|
|
||
|
|
PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3T<Type>& operator[](PxU32 num)
|
||
|
|
{
|
||
|
|
return (&column0)[num];
|
||
|
|
}
|
||
|
|
|
||
|
|
PX_CUDA_CALLABLE PX_FORCE_INLINE const PxVec3T<Type>& operator[](PxU32 num) const
|
||
|
|
{
|
||
|
|
return (&column0)[num];
|
||
|
|
}
|
||
|
|
|
||
|
|
// Data, see above for format!
|
||
|
|
|
||
|
|
PxVec3T<Type> column0, column1, column2; // the three base vectors
|
||
|
|
};
|
||
|
|
|
||
|
|
template<class Type>
|
||
|
|
PX_CUDA_CALLABLE PX_INLINE PxMat33T<Type> operator*(Type scalar, const PxMat33T<Type>& m)
|
||
|
|
{
|
||
|
|
return PxMat33T<Type>(scalar * m.column0, scalar * m.column1, scalar * m.column2);
|
||
|
|
}
|
||
|
|
|
||
|
|
// implementation from PxQuat.h
|
||
|
|
template<class Type>
|
||
|
|
PX_CUDA_CALLABLE PX_INLINE PxQuatT<Type>::PxQuatT(const PxMat33T<Type>& m)
|
||
|
|
{
|
||
|
|
if(m.column2.z < Type(0))
|
||
|
|
{
|
||
|
|
if(m.column0.x > m.column1.y)
|
||
|
|
{
|
||
|
|
const Type t = Type(1.0) + m.column0.x - m.column1.y - m.column2.z;
|
||
|
|
*this = PxQuatT<Type>(t, m.column0.y + m.column1.x, m.column2.x + m.column0.z, m.column1.z - m.column2.y) * (Type(0.5) / PxSqrt(t));
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
const Type t = Type(1.0) - m.column0.x + m.column1.y - m.column2.z;
|
||
|
|
*this = PxQuatT<Type>(m.column0.y + m.column1.x, t, m.column1.z + m.column2.y, m.column2.x - m.column0.z) * (Type(0.5) / PxSqrt(t));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
if(m.column0.x < -m.column1.y)
|
||
|
|
{
|
||
|
|
const Type t = Type(1.0) - m.column0.x - m.column1.y + m.column2.z;
|
||
|
|
*this = PxQuatT<Type>(m.column2.x + m.column0.z, m.column1.z + m.column2.y, t, m.column0.y - m.column1.x) * (Type(0.5) / PxSqrt(t));
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
const Type t = Type(1.0) + m.column0.x + m.column1.y + m.column2.z;
|
||
|
|
*this = PxQuatT<Type>(m.column1.z - m.column2.y, m.column2.x - m.column0.z, m.column0.y - m.column1.x, t) * (Type(0.5) / PxSqrt(t));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
typedef PxMat33T<float> PxMat33;
|
||
|
|
typedef PxMat33T<double> PxMat33d;
|
||
|
|
|
||
|
|
#if !PX_DOXYGEN
|
||
|
|
} // namespace physx
|
||
|
|
#endif
|
||
|
|
|
||
|
|
/** @} */
|
||
|
|
#endif
|
||
|
|
|