feat(physics): wire physx sdk into build

engine/third_party/physx/include/vehicle2/PxVehicleMaths.h

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+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions
+// are met:
+//  * Redistributions of source code must retain the above copyright
+//    notice, this list of conditions and the following disclaimer.
+//  * Redistributions in binary form must reproduce the above copyright
+//    notice, this list of conditions and the following disclaimer in the
+//    documentation and/or other materials provided with the distribution.
+//  * Neither the name of NVIDIA CORPORATION nor the names of its
+//    contributors may be used to endorse or promote products derived
+//    from this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ''AS IS'' AND ANY
+// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+// PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
+// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+//
+// Copyright (c) 2008-2025 NVIDIA Corporation. All rights reserved.
+// Copyright (c) 2004-2008 AGEIA Technologies, Inc. All rights reserved.
+// Copyright (c) 2001-2004 NovodeX AG. All rights reserved.  
+
+#pragma once
+
+#include "foundation/PxSimpleTypes.h"
+#include "foundation/PxMemory.h"
+
+#include "PxVehicleLimits.h"
+
+#if !PX_DOXYGEN
+namespace physx
+{
+namespace vehicle2
+{
+#endif
+
+class PxVehicleVectorN
+{
+public:
+	enum
+	{
+		eMAX_SIZE = PxVehicleLimits::eMAX_NB_WHEELS + 3
+	};
+
+	PxVehicleVectorN(const PxU32 size)
+		: mSize(size)
+	{
+		PX_ASSERT(mSize <= PxVehicleVectorN::eMAX_SIZE);
+		PxMemZero(mValues, sizeof(PxReal)*PxVehicleVectorN::eMAX_SIZE);
+	}
+
+	~PxVehicleVectorN()
+	{
+	}
+
+	PxVehicleVectorN(const PxVehicleVectorN& src)
+	{
+		for (PxU32 i = 0; i < src.mSize; i++)
+		{
+			mValues[i] = src.mValues[i];
+		}
+		mSize = src.mSize;
+	}
+
+	PX_FORCE_INLINE PxVehicleVectorN& operator=(const PxVehicleVectorN& src)
+	{
+		for (PxU32 i = 0; i < src.mSize; i++)
+		{
+			mValues[i] = src.mValues[i];
+		}
+		mSize = src.mSize;
+		return *this;
+	}
+
+	PX_FORCE_INLINE PxReal& operator[] (const PxU32 i)
+	{
+		PX_ASSERT(i < mSize);
+		return (mValues[i]);
+	}
+
+	PX_FORCE_INLINE const PxReal& operator[] (const PxU32 i) const
+	{
+		//PX_ASSERT(i < mSize);
+		return (mValues[i]);
+	}
+
+	PX_FORCE_INLINE PxU32 getSize() const { return mSize; }
+
+private:
+
+	PxReal mValues[PxVehicleVectorN::eMAX_SIZE];
+	PxU32 mSize;
+};
+
+class PxVehicleMatrixNN
+{
+public:
+
+	PxVehicleMatrixNN()
+		: mSize(0)
+	{
+	}
+
+	PxVehicleMatrixNN(const PxU32 size)
+		: mSize(size)
+	{
+		PX_ASSERT(mSize <= PxVehicleVectorN::eMAX_SIZE);
+		PxMemZero(mValues, sizeof(PxReal)*PxVehicleVectorN::eMAX_SIZE*PxVehicleVectorN::eMAX_SIZE);
+	}
+
+	PxVehicleMatrixNN(const PxVehicleMatrixNN& src)
+	{
+		for (PxU32 i = 0; i < src.mSize; i++)
+		{
+			for (PxU32 j = 0; j < src.mSize; j++)
+			{
+				mValues[i][j] = src.mValues[i][j];
+			}
+		}
+		mSize = src.mSize;
+	}
+
+	~PxVehicleMatrixNN()
+	{
+	}
+
+	PX_FORCE_INLINE PxVehicleMatrixNN& operator=(const PxVehicleMatrixNN& src)
+	{
+		for (PxU32 i = 0; i < src.mSize; i++)
+		{
+			for (PxU32 j = 0; j < src.mSize; j++)
+			{
+				mValues[i][j] = src.mValues[i][j];
+			}
+		}
+		mSize = src.mSize;
+		return *this;
+	}
+
+	PX_FORCE_INLINE PxReal get(const PxU32 i, const PxU32 j) const
+	{
+		PX_ASSERT(i < mSize);
+		PX_ASSERT(j < mSize);
+		return mValues[i][j];
+	}
+
+	PX_FORCE_INLINE void set(const PxU32 i, const PxU32 j, const PxReal val)
+	{
+		PX_ASSERT(i < mSize);
+		PX_ASSERT(j < mSize);
+		mValues[i][j] = val;
+	}
+
+	PX_FORCE_INLINE PxU32 getSize() const { return mSize; }
+
+	PX_FORCE_INLINE void setSize(const PxU32 size)
+	{
+		PX_ASSERT(size <= PxVehicleVectorN::eMAX_SIZE);
+		mSize = size;
+	}
+
+public:
+
+	PxReal mValues[PxVehicleVectorN::eMAX_SIZE][PxVehicleVectorN::eMAX_SIZE];
+	PxU32 mSize;
+};
+
+
+/*
+	LUPQ decomposition
+
+	Based upon "Outer Product LU with Complete Pivoting," from Matrix Computations (4th Edition), Golub and Van Loan
+
+	Solve A*x = b using:
+
+		MatrixNNLUSolver solver;
+		solver.decomposeLU(A);
+		solver.solve(b, x);
+*/
+class PxVehicleMatrixNNLUSolver
+{
+private:
+
+	PxVehicleMatrixNN mLU;
+	PxU32	mP[PxVehicleVectorN::eMAX_SIZE - 1];	// Row permutation
+	PxU32	mQ[PxVehicleVectorN::eMAX_SIZE - 1];	// Column permutation
+	PxReal	mDetM;
+
+public:
+
+	PxVehicleMatrixNNLUSolver() {}
+	~PxVehicleMatrixNNLUSolver() {}
+
+	PxReal getDet() const { return mDetM; }
+
+	void decomposeLU(const PxVehicleMatrixNN& A);
+
+	//Given a matrix A and a vector b find x that satisfies Ax = b, where the matrix A is the matrix that was passed to #decomposeLU.
+	//Returns true if the lu decomposition indicates that the matrix has an inverse and x was successfully computed.
+	//Returns false if the lu decomposition resulted in zero determinant ie the matrix has no inverse and no solution exists for x.
+	//Returns false if the size of either b or x doesn't match the size of the matrix passed to #decomposeLU.
+	//If false is returned then each relevant element of x is set to zero. 
+	bool solve(const PxVehicleVectorN& b, PxVehicleVectorN& x) const;
+};
+
+
+class PxVehicleMatrixNGaussSeidelSolver
+{
+public:
+
+	void solve(const PxU32 maxIterations, const PxReal tolerance, const PxVehicleMatrixNN& A, const PxVehicleVectorN& b, PxVehicleVectorN& result) const;
+};
+
+class PxVehicleMatrix33Solver
+{
+public:
+
+	bool solve(const PxVehicleMatrixNN& A_, const PxVehicleVectorN& b_, PxVehicleVectorN& result) const;
+};
+
+#if !PX_DOXYGEN
+} //namespace vehicle2
+} //namespace physx
+#endif
+
+
+