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+// This code contains NVIDIA Confidential Information and is disclosed to you
+// under a form of NVIDIA software license agreement provided separately to you.
+//
+// Notice
+// NVIDIA Corporation and its licensors retain all intellectual property and
+// proprietary rights in and to this software and related documentation and
+// any modifications thereto. Any use, reproduction, disclosure, or
+// distribution of this software and related documentation without an express
+// license agreement from NVIDIA Corporation is strictly prohibited.
+//
+// ALL NVIDIA DESIGN SPECIFICATIONS, CODE ARE PROVIDED "AS IS.". NVIDIA MAKES
+// NO WARRANTIES, EXPRESSED, IMPLIED, STATUTORY, OR OTHERWISE WITH RESPECT TO
+// THE MATERIALS, AND EXPRESSLY DISCLAIMS ALL IMPLIED WARRANTIES OF NONINFRINGEMENT,
+// MERCHANTABILITY, AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// Information and code furnished is believed to be accurate and reliable.
+// However, NVIDIA Corporation assumes no responsibility for the consequences of use of such
+// information or for any infringement of patents or other rights of third parties that may
+// result from its use. No license is granted by implication or otherwise under any patent
+// or patent rights of NVIDIA Corporation. Details are subject to change without notice.
+// This code supersedes and replaces all information previously supplied.
+// NVIDIA Corporation products are not authorized for use as critical
+// components in life support devices or systems without express written approval of
+// NVIDIA Corporation.
+//
+// Copyright (c) 2008-2014 NVIDIA Corporation. All rights reserved.
+// Copyright (c) 2004-2008 AGEIA Technologies, Inc. All rights reserved.
+// Copyright (c) 2001-2004 NovodeX AG. All rights reserved.
+
+#ifndef NV_NVFOUNDATION_NVMAT33_H
+#define NV_NVFOUNDATION_NVMAT33_H
+/** \addtogroup foundation
+@{
+*/
+
+#include "NvVec3.h"
+#include "NvQuat.h"
+
+#if !NV_DOXYGEN
+namespace nvidia
+{
+#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 NvMat33
+{
+  public:
+	//! Default constructor
+	NV_CUDA_CALLABLE NV_FORCE_INLINE NvMat33()
+	{
+	}
+
+	//! identity constructor
+	NV_CUDA_CALLABLE NV_INLINE NvMat33(NvIDENTITY r)
+	: column0(1.0f, 0.0f, 0.0f), column1(0.0f, 1.0f, 0.0f), column2(0.0f, 0.0f, 1.0f)
+	{
+		NV_UNUSED(r);
+	}
+
+	//! zero constructor
+	NV_CUDA_CALLABLE NV_INLINE NvMat33(NvZERO r) : column0(0.0f), column1(0.0f), column2(0.0f)
+	{
+		NV_UNUSED(r);
+	}
+
+	//! Construct from three base vectors
+	NV_CUDA_CALLABLE NvMat33(const NvVec3& col0, const NvVec3& col1, const NvVec3& col2)
+	: column0(col0), column1(col1), column2(col2)
+	{
+	}
+
+	//! constructor from a scalar, which generates a multiple of the identity matrix
+	explicit NV_CUDA_CALLABLE NV_INLINE NvMat33(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 NV_CUDA_CALLABLE NV_INLINE NvMat33(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 NV_CUDA_CALLABLE NV_FORCE_INLINE NvMat33(const NvQuat& 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 = NvVec3(1.0f - yy - zz, xy + zw, xz - yw);
+		column1 = NvVec3(xy - zw, 1.0f - xx - zz, yz + xw);
+		column2 = NvVec3(xz + yw, yz - xw, 1.0f - xx - yy);
+	}
+
+	//! Copy constructor
+	NV_CUDA_CALLABLE NV_INLINE NvMat33(const NvMat33& other)
+	: column0(other.column0), column1(other.column1), column2(other.column2)
+	{
+	}
+
+	//! Assignment operator
+	NV_CUDA_CALLABLE NV_FORCE_INLINE NvMat33& operator=(const NvMat33& other)
+	{
+		column0 = other.column0;
+		column1 = other.column1;
+		column2 = other.column2;
+		return *this;
+	}
+
+	//! Construct from diagonal, off-diagonals are zero.
+	NV_CUDA_CALLABLE NV_INLINE static NvMat33 createDiagonal(const NvVec3& d)
+	{
+		return NvMat33(NvVec3(d.x, 0.0f, 0.0f), NvVec3(0.0f, d.y, 0.0f), NvVec3(0.0f, 0.0f, d.z));
+	}
+
+	/**
+	\brief returns true if the two matrices are exactly equal
+	*/
+	NV_CUDA_CALLABLE NV_INLINE bool operator==(const NvMat33& m) const
+	{
+		return column0 == m.column0 && column1 == m.column1 && column2 == m.column2;
+	}
+
+	//! Get transposed matrix
+	NV_CUDA_CALLABLE NV_FORCE_INLINE NvMat33 getTranspose() const
+	{
+		const NvVec3 v0(column0.x, column1.x, column2.x);
+		const NvVec3 v1(column0.y, column1.y, column2.y);
+		const NvVec3 v2(column0.z, column1.z, column2.z);
+
+		return NvMat33(v0, v1, v2);
+	}
+
+	//! Get the real inverse
+	NV_CUDA_CALLABLE NV_INLINE NvMat33 getInverse() const
+	{
+		const float det = getDeterminant();
+		NvMat33 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 NvMat33(NvIdentity);
+		}
+	}
+
+	//! Get determinant
+	NV_CUDA_CALLABLE NV_INLINE float getDeterminant() const
+	{
+		return column0.dot(column1.cross(column2));
+	}
+
+	//! Unary minus
+	NV_CUDA_CALLABLE NV_INLINE NvMat33 operator-() const
+	{
+		return NvMat33(-column0, -column1, -column2);
+	}
+
+	//! Add
+	NV_CUDA_CALLABLE NV_INLINE NvMat33 operator+(const NvMat33& other) const
+	{
+		return NvMat33(column0 + other.column0, column1 + other.column1, column2 + other.column2);
+	}
+
+	//! Subtract
+	NV_CUDA_CALLABLE NV_INLINE NvMat33 operator-(const NvMat33& other) const
+	{
+		return NvMat33(column0 - other.column0, column1 - other.column1, column2 - other.column2);
+	}
+
+	//! Scalar multiplication
+	NV_CUDA_CALLABLE NV_INLINE NvMat33 operator*(float scalar) const
+	{
+		return NvMat33(column0 * scalar, column1 * scalar, column2 * scalar);
+	}
+
+	friend NvMat33 operator*(float, const NvMat33&);
+
+	//! Matrix vector multiplication (returns 'this->transform(vec)')
+	NV_CUDA_CALLABLE NV_INLINE NvVec3 operator*(const NvVec3& vec) const
+	{
+		return transform(vec);
+	}
+
+	// a <op>= b operators
+
+	//! Matrix multiplication
+	NV_CUDA_CALLABLE NV_FORCE_INLINE NvMat33 operator*(const NvMat33& other) const
+	{
+		// Rows from this <dot> columns from other
+		// column0 = transform(other.column0) etc
+		return NvMat33(transform(other.column0), transform(other.column1), transform(other.column2));
+	}
+
+	//! Equals-add
+	NV_CUDA_CALLABLE NV_INLINE NvMat33& operator+=(const NvMat33& other)
+	{
+		column0 += other.column0;
+		column1 += other.column1;
+		column2 += other.column2;
+		return *this;
+	}
+
+	//! Equals-sub
+	NV_CUDA_CALLABLE NV_INLINE NvMat33& operator-=(const NvMat33& other)
+	{
+		column0 -= other.column0;
+		column1 -= other.column1;
+		column2 -= other.column2;
+		return *this;
+	}
+
+	//! Equals scalar multiplication
+	NV_CUDA_CALLABLE NV_INLINE NvMat33& operator*=(float scalar)
+	{
+		column0 *= scalar;
+		column1 *= scalar;
+		column2 *= scalar;
+		return *this;
+	}
+
+	//! Equals matrix multiplication
+	NV_CUDA_CALLABLE NV_INLINE NvMat33& operator*=(const NvMat33& other)
+	{
+		*this = *this * other;
+		return *this;
+	}
+
+	//! Element access, mathematical way!
+	NV_DEPRECATED NV_CUDA_CALLABLE NV_FORCE_INLINE float operator()(unsigned int row, unsigned int col) const
+	{
+		return (*this)[col][row];
+	}
+
+	//! Element access, mathematical way!
+	NV_DEPRECATED NV_CUDA_CALLABLE NV_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
+	NV_CUDA_CALLABLE NV_FORCE_INLINE NvVec3 transform(const NvVec3& other) const
+	{
+		return column0 * other.x + column1 * other.y + column2 * other.z;
+	}
+
+	//! Transform vector by matrix transpose, v' = M^t*v
+	NV_CUDA_CALLABLE NV_INLINE NvVec3 transformTranspose(const NvVec3& other) const
+	{
+		return NvVec3(column0.dot(other), column1.dot(other), column2.dot(other));
+	}
+
+	NV_CUDA_CALLABLE NV_FORCE_INLINE const float* front() const
+	{
+		return &column0.x;
+	}
+
+	NV_DEPRECATED NV_CUDA_CALLABLE NV_FORCE_INLINE NvVec3& operator[](unsigned int num)
+	{
+		return (&column0)[num];
+	}
+	NV_DEPRECATED NV_CUDA_CALLABLE NV_FORCE_INLINE const NvVec3& operator[](unsigned int num) const
+	{
+		return (&column0)[num];
+	}
+
+	// Data, see above for format!
+
+	NvVec3 column0, column1, column2; // the three base vectors
+};
+
+// implementation from NvQuat.h
+NV_CUDA_CALLABLE NV_INLINE NvQuat::NvQuat(const NvMat33& 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 = NvQuat(t, m.column0.y + m.column1.x, m.column2.x + m.column0.z, m.column1.z - m.column2.y) * (0.5f / NvSqrt(t));
+		}
+		else
+		{
+			float t = 1 - m.column0.x + m.column1.y - m.column2.z;
+			*this = NvQuat(m.column0.y + m.column1.x, t, m.column1.z + m.column2.y, m.column2.x - m.column0.z) * (0.5f / NvSqrt(t));
+		}
+	}
+	else
+	{
+		if (m.column0.x < -m.column1.y)
+		{
+			float t = 1 - m.column0.x - m.column1.y + m.column2.z;
+			*this = NvQuat(m.column2.x + m.column0.z, m.column1.z + m.column2.y, t, m.column0.y - m.column1.x) * (0.5f / NvSqrt(t));
+		}
+		else
+		{
+			float t = 1 + m.column0.x + m.column1.y + m.column2.z;
+			*this = NvQuat(m.column1.z - m.column2.y, m.column2.x - m.column0.z, m.column0.y - m.column1.x, t) * (0.5f / NvSqrt(t));
+		}
+	}
+}
+
+#if !NV_DOXYGEN
+} // namespace nvidia
+#endif
+
+/** @} */
+#endif // #ifndef NV_NVFOUNDATION_NVMAT33_H