minetest/irr/include/matrix4.h

// Copyright (C) 2002-2012 Nikolaus Gebhardt
// This file is part of the "Irrlicht Engine".
// For conditions of distribution and use, see copyright notice in irrlicht.h

#pragma once

#include <cstring> // memset, memcpy
#include "irrMath.h"
#include "vector3d.h"
#include "vector2d.h"
#include "plane3d.h"
#include "aabbox3d.h"
#include "rect.h"
#include "IrrCompileConfig.h" // for IRRLICHT_API

// enable this to keep track of changes to the matrix
// and make simpler identity check for seldom changing matrices
// otherwise identity check will always compare the elements
// #define USE_MATRIX_TEST

namespace irr
{
namespace core
{

//! 4x4 matrix. Mostly used as transformation matrix for 3d calculations.
/** Conventions: Matrices are considered to be in row-major order.
 * Multiplication of a matrix A with a row vector v is the premultiplication vA.
 * Translations are thus in the 4th row.
 * The matrix product AB yields a matrix C such that vC = (vB)A:
 * B is applied first, then A.
 */
template <class T>
class CMatrix4
{
public:
	//! Constructor Flags
	enum eConstructor
	{
		EM4CONST_NOTHING = 0,
		EM4CONST_COPY,
		EM4CONST_IDENTITY,
		EM4CONST_TRANSPOSED,
		EM4CONST_INVERSE,
		EM4CONST_INVERSE_TRANSPOSED
	};

	//! Default constructor
	/** \param constructor Choose the initialization style */
	CMatrix4(eConstructor constructor = EM4CONST_IDENTITY);

	//! Constructor with value initialization
	constexpr CMatrix4(const T &r0c0, const T &r0c1, const T &r0c2, const T &r0c3,
			const T &r1c0, const T &r1c1, const T &r1c2, const T &r1c3,
			const T &r2c0, const T &r2c1, const T &r2c2, const T &r2c3,
			const T &r3c0, const T &r3c1, const T &r3c2, const T &r3c3)
	{
		M[0] = r0c0;
		M[1] = r0c1;
		M[2] = r0c2;
		M[3] = r0c3;
		M[4] = r1c0;
		M[5] = r1c1;
		M[6] = r1c2;
		M[7] = r1c3;
		M[8] = r2c0;
		M[9] = r2c1;
		M[10] = r2c2;
		M[11] = r2c3;
		M[12] = r3c0;
		M[13] = r3c1;
		M[14] = r3c2;
		M[15] = r3c3;
	}

	//! Copy constructor
	/** \param other Other matrix to copy from
	\param constructor Choose the initialization style */
	CMatrix4(const CMatrix4<T> &other, eConstructor constructor = EM4CONST_COPY);

	//! Simple operator for directly accessing every element of the matrix.
	T &operator()(const s32 row, const s32 col)
	{
#if defined(USE_MATRIX_TEST)
		definitelyIdentityMatrix = false;
#endif
		return M[row * 4 + col];
	}

	//! Simple operator for directly accessing every element of the matrix.
	const T &operator()(const s32 row, const s32 col) const { return M[row * 4 + col]; }

	//! Simple operator for linearly accessing every element of the matrix.
	T &operator[](u32 index)
	{
#if defined(USE_MATRIX_TEST)
		definitelyIdentityMatrix = false;
#endif
		return M[index];
	}

	//! Simple operator for linearly accessing every element of the matrix.
	const T &operator[](u32 index) const { return M[index]; }

	//! Sets this matrix equal to the other matrix.
	CMatrix4<T> &operator=(const CMatrix4<T> &other) = default;

	//! Sets all elements of this matrix to the value.
	inline CMatrix4<T> &operator=(const T &scalar);

	//! Returns pointer to internal array
	const T *pointer() const { return M; }
	T *pointer()
	{
#if defined(USE_MATRIX_TEST)
		definitelyIdentityMatrix = false;
#endif
		return M;
	}

	//! Returns true if other matrix is equal to this matrix.
	constexpr bool operator==(const CMatrix4<T> &other) const
	{
#if defined(USE_MATRIX_TEST)
		if (definitelyIdentityMatrix && other.definitelyIdentityMatrix)
			return true;
#endif
		for (s32 i = 0; i < 16; ++i)
			if (M[i] != other.M[i])
				return false;

		return true;
	}

	//! Returns true if other matrix is not equal to this matrix.
	constexpr bool operator!=(const CMatrix4<T> &other) const
	{
		return !(*this == other);
	}

	//! Add another matrix.
	CMatrix4<T> operator+(const CMatrix4<T> &other) const;

	//! Add another matrix.
	CMatrix4<T> &operator+=(const CMatrix4<T> &other);

	//! Subtract another matrix.
	CMatrix4<T> operator-(const CMatrix4<T> &other) const;

	//! Subtract another matrix.
	CMatrix4<T> &operator-=(const CMatrix4<T> &other);

	//! set this matrix to the product of two matrices
	/** Calculate b*a */
	inline CMatrix4<T> &setbyproduct(const CMatrix4<T> &other_a, const CMatrix4<T> &other_b);

	//! Set this matrix to the product of two matrices
	/** Calculate b*a, no optimization used,
	use it if you know you never have an identity matrix */
	CMatrix4<T> &setbyproduct_nocheck(const CMatrix4<T> &other_a, const CMatrix4<T> &other_b);

	//! Multiply by another matrix.
	/** Calculate other*this */
	CMatrix4<T> operator*(const CMatrix4<T> &other) const;

	//! Multiply by another matrix.
	/** Like calling: (*this) = (*this) * other
	 */
	CMatrix4<T> &operator*=(const CMatrix4<T> &other);

	//! Multiply by scalar.
	CMatrix4<T> operator*(const T &scalar) const;

	//! Multiply by scalar.
	CMatrix4<T> &operator*=(const T &scalar);

	//! Set matrix to identity.
	inline CMatrix4<T> &makeIdentity();

	//! Returns true if the matrix is the identity matrix
	inline bool isIdentity() const;

	//! Returns true if the matrix is orthogonal
	inline bool isOrthogonal() const;

	//! Returns true if the matrix is the identity matrix
	bool isIdentity_integer_base() const;

	//! Set the translation of the current matrix. Will erase any previous values.
	CMatrix4<T> &setTranslation(const vector3d<T> &translation);

	//! Gets the current translation
	vector3d<T> getTranslation() const;

	//! Set the inverse translation of the current matrix. Will erase any previous values.
	CMatrix4<T> &setInverseTranslation(const vector3d<T> &translation);

	//! Make a rotation matrix from Euler angles. The 4th row and column are unmodified.
	inline CMatrix4<T> &setRotationRadians(const vector3d<T> &rotation);

	//! Make a rotation matrix from Euler angles. The 4th row and column are unmodified.
	CMatrix4<T> &setRotationDegrees(const vector3d<T> &rotation);

	//! Get the rotation, as set by setRotation() when you already know the scale used to create the matrix
	/** NOTE: The scale needs to be the correct one used to create this matrix.
		You can _not_ use the result of getScale(), but have to save your scale
		variable in another place (like ISceneNode does).
	NOTE: No scale value can be 0 or the result is undefined.
	NOTE: It does not necessarily return the *same* Euler angles as those set by setRotationDegrees(),
		but the rotation will be equivalent,  i.e. will have the same result when used to rotate a vector or node.
	NOTE: It will (usually) give wrong results when further transformations have been added in the matrix (like shear).
	WARNING: There have been troubles with this function over the years and we may still have missed some corner cases.
		It's generally safer to keep the rotation and scale you used to create the matrix around and work with those.
	*/
	core::vector3d<T> getRotationDegrees(const vector3d<T> &scale) const;

	//! Returns the rotation, as set by setRotation().
	/** NOTE: You will have the same end-rotation as used in setRotation, but it might not use the same axis values.
		NOTE: This only works correct if no other matrix operations have been done on the inner 3x3 matrix besides
			setting rotation (so no scale/shear). Thought it (probably) works as long as scale doesn't flip handedness.
		NOTE: It does not necessarily return the *same* Euler angles as those set by setRotationDegrees(),
		but the rotation will be equivalent,  i.e. will have the same result when used to rotate a vector or node.
	*/
	core::vector3d<T> getRotationDegrees() const;

	//! Make an inverted rotation matrix from Euler angles.
	/** The 4th row and column are unmodified. */
	inline CMatrix4<T> &setInverseRotationRadians(const vector3d<T> &rotation);

	//! Make an inverted rotation matrix from Euler angles.
	/** The 4th row and column are unmodified. */
	inline CMatrix4<T> &setInverseRotationDegrees(const vector3d<T> &rotation);

	//! Make a rotation matrix from angle and axis, assuming left handed rotation.
	/** The 4th row and column are unmodified. */
	inline CMatrix4<T> &setRotationAxisRadians(const T &angle, const vector3d<T> &axis);

	//! Set Scale
	CMatrix4<T> &setScale(const vector3d<T> &scale);

	//! Set Scale
	CMatrix4<T> &setScale(const T scale) { return setScale(core::vector3d<T>(scale, scale, scale)); }

	//! Get Scale
	core::vector3d<T> getScale() const;

	//! Translate a vector by the inverse of the translation part of this matrix.
	void inverseTranslateVect(vector3df &vect) const;

	//! Scale a vector, then rotate by the inverse of the rotation part of this matrix.
	[[nodiscard]] vector3d<T> scaleThenInvRotVect(const vector3d<T> &vect) const;

	//! Rotate and scale a vector. Applies both rotation & scale part of the matrix.
	[[nodiscard]] vector3d<T> rotateAndScaleVect(const vector3d<T> &vect) const;

	//! Transforms the vector by this matrix
	/** This operation is performed as if the vector was 4d with the 4th component =1 */
	void transformVect(vector3df &vect) const;

	//! Transforms input vector by this matrix and stores result in output vector
	/** This operation is performed as if the vector was 4d with the 4th component =1 */
	void transformVect(vector3df &out, const vector3df &in) const;

	//! An alternate transform vector method, writing into an array of 4 floats
	/** This operation is performed as if the vector was 4d with the 4th component =1.
		NOTE: out[3] will be written to (4th vector component)*/
	void transformVect(T *out, const core::vector3df &in) const;

	//! An alternate transform vector method, reading from and writing to an array of 3 floats
	/** This operation is performed as if the vector was 4d with the 4th component =1
		NOTE: out[3] will be written to (4th vector component)*/
	void transformVec3(T *out, const T *in) const;

	//! An alternate transform vector method, reading from and writing to an array of 4 floats
	void transformVec4(T *out, const T *in) const;

	//! Translate a vector by the translation part of this matrix.
	/** This operation is performed as if the vector was 4d with the 4th component =1 */
	void translateVect(vector3df &vect) const;

	//! Transforms a plane by this matrix
	void transformPlane(core::plane3d<f32> &plane) const;

	//! Transforms a plane by this matrix
	void transformPlane(const core::plane3d<f32> &in, core::plane3d<f32> &out) const;

	//! Transforms a axis aligned bounding box
	void transformBoxEx(core::aabbox3d<f32> &box) const;

	//! Multiplies this matrix by a 1x4 matrix
	void multiplyWith1x4Matrix(T *matrix) const;

	//! Calculates inverse of matrix. Slow.
	/** \return Returns false if there is no inverse matrix.*/
	bool makeInverse();

	//! Inverts a primitive matrix which only contains a translation and a rotation
	/** \param out: where result matrix is written to. */
	bool getInversePrimitive(CMatrix4<T> &out) const;

	//! Gets the inverse matrix of this one
	/** \param out: where result matrix is written to.
	\return Returns false if there is no inverse matrix. */
	bool getInverse(CMatrix4<T> &out) const;

	//! Builds a right-handed perspective projection matrix based on a field of view
	//\param zClipFromZero: Clipping of z can be projected from 0 to w when true (D3D style) and from -w to w when false (OGL style).
	CMatrix4<T> &buildProjectionMatrixPerspectiveFovRH(f32 fieldOfViewRadians, f32 aspectRatio, f32 zNear, f32 zFar, bool zClipFromZero = true);

	//! Builds a left-handed perspective projection matrix based on a field of view
	CMatrix4<T> &buildProjectionMatrixPerspectiveFovLH(f32 fieldOfViewRadians, f32 aspectRatio, f32 zNear, f32 zFar, bool zClipFromZero = true);

	//! Builds a left-handed perspective projection matrix based on a field of view, with far plane at infinity
	CMatrix4<T> &buildProjectionMatrixPerspectiveFovInfinityLH(f32 fieldOfViewRadians, f32 aspectRatio, f32 zNear, f32 epsilon = 0);

	//! Builds a right-handed perspective projection matrix.
	CMatrix4<T> &buildProjectionMatrixPerspectiveRH(f32 widthOfViewVolume, f32 heightOfViewVolume, f32 zNear, f32 zFar, bool zClipFromZero = true);

	//! Builds a left-handed perspective projection matrix.
	CMatrix4<T> &buildProjectionMatrixPerspectiveLH(f32 widthOfViewVolume, f32 heightOfViewVolume, f32 zNear, f32 zFar, bool zClipFromZero = true);

	//! Builds a left-handed orthogonal projection matrix.
	//\param zClipFromZero: Clipping of z can be projected from 0 to 1 when true (D3D style) and from -1 to 1 when false (OGL style).
	CMatrix4<T> &buildProjectionMatrixOrthoLH(f32 widthOfViewVolume, f32 heightOfViewVolume, f32 zNear, f32 zFar, bool zClipFromZero = true);

	//! Builds a right-handed orthogonal projection matrix.
	CMatrix4<T> &buildProjectionMatrixOrthoRH(f32 widthOfViewVolume, f32 heightOfViewVolume, f32 zNear, f32 zFar, bool zClipFromZero = true);

	//! Builds a left-handed look-at matrix.
	CMatrix4<T> &buildCameraLookAtMatrixLH(
			const vector3df &position,
			const vector3df &target,
			const vector3df &upVector);

	//! Builds a right-handed look-at matrix.
	CMatrix4<T> &buildCameraLookAtMatrixRH(
			const vector3df &position,
			const vector3df &target,
			const vector3df &upVector);

	//! Builds a matrix that flattens geometry into a plane.
	/** \param light: light source
	\param plane: plane into which the geometry if flattened into
	\param point: value between 0 and 1, describing the light source.
	If this is 1, it is a point light, if it is 0, it is a directional light. */
	CMatrix4<T> &buildShadowMatrix(const core::vector3df &light, core::plane3df plane, f32 point = 1.0f);

	//! Builds a matrix which transforms a normalized Device Coordinate to Device Coordinates.
	/** Used to scale <-1,-1><1,1> to viewport, for example from <-1,-1> <1,1> to the viewport <0,0><0,640> */
	CMatrix4<T> &buildNDCToDCMatrix(const core::rect<s32> &area, f32 zScale);

	//! Creates a new matrix as interpolated matrix from two other ones.
	/** \param b: other matrix to interpolate with
	\param time: Must be a value between 0 and 1. */
	CMatrix4<T> interpolate(const core::CMatrix4<T> &b, f32 time) const;

	//! Gets transposed matrix
	CMatrix4<T> getTransposed() const;

	//! Gets transposed matrix
	inline void getTransposed(CMatrix4<T> &dest) const;

	//! Builds a matrix that rotates from one vector to another
	/** \param from: vector to rotate from
	\param to: vector to rotate to
	 */
	CMatrix4<T> &buildRotateFromTo(const core::vector3df &from, const core::vector3df &to);

	//! Builds a combined matrix which translates to a center before rotation and translates from origin afterwards
	/** \param center Position to rotate around
	\param translate Translation applied after the rotation
	 */
	void setRotationCenter(const core::vector3df &center, const core::vector3df &translate);

	//! Builds a matrix which rotates a source vector to a look vector over an arbitrary axis
	/** \param camPos: viewer position in world coo
	\param center: object position in world-coo and rotation pivot
	\param translation: object final translation from center
	\param axis: axis to rotate about
	\param from: source vector to rotate from
	 */
	void buildAxisAlignedBillboard(const core::vector3df &camPos,
			const core::vector3df &center,
			const core::vector3df &translation,
			const core::vector3df &axis,
			const core::vector3df &from);

	/*
		construct 2D Texture transformations
		rotate about center, scale, and transform.
	*/
	//! Set to a texture transformation matrix with the given parameters.
	CMatrix4<T> &buildTextureTransform(f32 rotateRad,
			const core::vector2df &rotatecenter,
			const core::vector2df &translate,
			const core::vector2df &scale);

	//! Set texture transformation rotation
	/** Rotate about z axis, recenter at (0.5,0.5).
	Doesn't clear other elements than those affected
	\param radAngle Angle in radians
	\return Altered matrix */
	CMatrix4<T> &setTextureRotationCenter(f32 radAngle);

	//! Set texture transformation translation
	/** Doesn't clear other elements than those affected.
	\param x Offset on x axis
	\param y Offset on y axis
	\return Altered matrix */
	CMatrix4<T> &setTextureTranslate(f32 x, f32 y);

	//! Get texture transformation translation
	/** \param x returns offset on x axis
	\param y returns offset on y axis */
	void getTextureTranslate(f32 &x, f32 &y) const;

	//! Set texture transformation translation, using a transposed representation
	/** Doesn't clear other elements than those affected.
	\param x Offset on x axis
	\param y Offset on y axis
	\return Altered matrix */
	CMatrix4<T> &setTextureTranslateTransposed(f32 x, f32 y);

	//! Set texture transformation scale
	/** Doesn't clear other elements than those affected.
	\param sx Scale factor on x axis
	\param sy Scale factor on y axis
	\return Altered matrix. */
	CMatrix4<T> &setTextureScale(f32 sx, f32 sy);

	//! Get texture transformation scale
	/** \param sx Returns x axis scale factor
	\param sy Returns y axis scale factor */
	void getTextureScale(f32 &sx, f32 &sy) const;

	//! Set texture transformation scale, and recenter at (0.5,0.5)
	/** Doesn't clear other elements than those affected.
	\param sx Scale factor on x axis
	\param sy Scale factor on y axis
	\return Altered matrix. */
	CMatrix4<T> &setTextureScaleCenter(f32 sx, f32 sy);

	//! Sets all matrix data members at once
	CMatrix4<T> &setM(const T *data);

	//! Sets if the matrix is definitely identity matrix
	void setDefinitelyIdentityMatrix(bool isDefinitelyIdentityMatrix);

	//! Gets if the matrix is definitely identity matrix
	bool getDefinitelyIdentityMatrix() const;

	//! Compare two matrices using the equal method
	bool equals(const core::CMatrix4<T> &other, const T tolerance = (T)ROUNDING_ERROR_f64) const;

private:
	//! Matrix data, stored in row-major order
	T M[16];
#if defined(USE_MATRIX_TEST)
	//! Flag is this matrix is identity matrix
	mutable u32 definitelyIdentityMatrix;
#endif
};

// Default constructor
template <class T>
inline CMatrix4<T>::CMatrix4(eConstructor constructor)
#if defined(USE_MATRIX_TEST)
		:
		definitelyIdentityMatrix(BIT_UNTESTED)
#endif
{
	switch (constructor) {
	case EM4CONST_NOTHING:
	case EM4CONST_COPY:
		break;
	case EM4CONST_IDENTITY:
	case EM4CONST_INVERSE:
	default:
		makeIdentity();
		break;
	}
}

// Copy constructor
template <class T>
inline CMatrix4<T>::CMatrix4(const CMatrix4<T> &other, eConstructor constructor)
#if defined(USE_MATRIX_TEST)
		:
		definitelyIdentityMatrix(BIT_UNTESTED)
#endif
{
	switch (constructor) {
	case EM4CONST_IDENTITY:
		makeIdentity();
		break;
	case EM4CONST_NOTHING:
		break;
	case EM4CONST_COPY:
		*this = other;
		break;
	case EM4CONST_TRANSPOSED:
		other.getTransposed(*this);
		break;
	case EM4CONST_INVERSE:
		if (!other.getInverse(*this))
			memset(M, 0, 16 * sizeof(T));
		break;
	case EM4CONST_INVERSE_TRANSPOSED:
		if (!other.getInverse(*this))
			memset(M, 0, 16 * sizeof(T));
		else
			*this = getTransposed();
		break;
	}
}

//! Add another matrix.
template <class T>
inline CMatrix4<T> CMatrix4<T>::operator+(const CMatrix4<T> &other) const
{
	CMatrix4<T> temp(EM4CONST_NOTHING);

	temp[0] = M[0] + other[0];
	temp[1] = M[1] + other[1];
	temp[2] = M[2] + other[2];
	temp[3] = M[3] + other[3];
	temp[4] = M[4] + other[4];
	temp[5] = M[5] + other[5];
	temp[6] = M[6] + other[6];
	temp[7] = M[7] + other[7];
	temp[8] = M[8] + other[8];
	temp[9] = M[9] + other[9];
	temp[10] = M[10] + other[10];
	temp[11] = M[11] + other[11];
	temp[12] = M[12] + other[12];
	temp[13] = M[13] + other[13];
	temp[14] = M[14] + other[14];
	temp[15] = M[15] + other[15];

	return temp;
}

//! Add another matrix.
template <class T>
inline CMatrix4<T> &CMatrix4<T>::operator+=(const CMatrix4<T> &other)
{
	M[0] += other[0];
	M[1] += other[1];
	M[2] += other[2];
	M[3] += other[3];
	M[4] += other[4];
	M[5] += other[5];
	M[6] += other[6];
	M[7] += other[7];
	M[8] += other[8];
	M[9] += other[9];
	M[10] += other[10];
	M[11] += other[11];
	M[12] += other[12];
	M[13] += other[13];
	M[14] += other[14];
	M[15] += other[15];

	return *this;
}

//! Subtract another matrix.
template <class T>
inline CMatrix4<T> CMatrix4<T>::operator-(const CMatrix4<T> &other) const
{
	CMatrix4<T> temp(EM4CONST_NOTHING);

	temp[0] = M[0] - other[0];
	temp[1] = M[1] - other[1];
	temp[2] = M[2] - other[2];
	temp[3] = M[3] - other[3];
	temp[4] = M[4] - other[4];
	temp[5] = M[5] - other[5];
	temp[6] = M[6] - other[6];
	temp[7] = M[7] - other[7];
	temp[8] = M[8] - other[8];
	temp[9] = M[9] - other[9];
	temp[10] = M[10] - other[10];
	temp[11] = M[11] - other[11];
	temp[12] = M[12] - other[12];
	temp[13] = M[13] - other[13];
	temp[14] = M[14] - other[14];
	temp[15] = M[15] - other[15];

	return temp;
}

//! Subtract another matrix.
template <class T>
inline CMatrix4<T> &CMatrix4<T>::operator-=(const CMatrix4<T> &other)
{
	M[0] -= other[0];
	M[1] -= other[1];
	M[2] -= other[2];
	M[3] -= other[3];
	M[4] -= other[4];
	M[5] -= other[5];
	M[6] -= other[6];
	M[7] -= other[7];
	M[8] -= other[8];
	M[9] -= other[9];
	M[10] -= other[10];
	M[11] -= other[11];
	M[12] -= other[12];
	M[13] -= other[13];
	M[14] -= other[14];
	M[15] -= other[15];

	return *this;
}

//! Multiply by scalar.
template <class T>
inline CMatrix4<T> CMatrix4<T>::operator*(const T &scalar) const
{
	CMatrix4<T> temp(EM4CONST_NOTHING);

	temp[0] = M[0] * scalar;
	temp[1] = M[1] * scalar;
	temp[2] = M[2] * scalar;
	temp[3] = M[3] * scalar;
	temp[4] = M[4] * scalar;
	temp[5] = M[5] * scalar;
	temp[6] = M[6] * scalar;
	temp[7] = M[7] * scalar;
	temp[8] = M[8] * scalar;
	temp[9] = M[9] * scalar;
	temp[10] = M[10] * scalar;
	temp[11] = M[11] * scalar;
	temp[12] = M[12] * scalar;
	temp[13] = M[13] * scalar;
	temp[14] = M[14] * scalar;
	temp[15] = M[15] * scalar;

	return temp;
}

//! Multiply by scalar.
template <class T>
inline CMatrix4<T> &CMatrix4<T>::operator*=(const T &scalar)
{
	M[0] *= scalar;
	M[1] *= scalar;
	M[2] *= scalar;
	M[3] *= scalar;
	M[4] *= scalar;
	M[5] *= scalar;
	M[6] *= scalar;
	M[7] *= scalar;
	M[8] *= scalar;
	M[9] *= scalar;
	M[10] *= scalar;
	M[11] *= scalar;
	M[12] *= scalar;
	M[13] *= scalar;
	M[14] *= scalar;
	M[15] *= scalar;

	return *this;
}

//! Multiply by another matrix.
template <class T>
inline CMatrix4<T> &CMatrix4<T>::operator*=(const CMatrix4<T> &other)
{
#if defined(USE_MATRIX_TEST)
	// do checks on your own in order to avoid copy creation
	if (!other.isIdentity()) {
		if (this->isIdentity()) {
			return (*this = other);
		} else {
			CMatrix4<T> temp(*this);
			return setbyproduct_nocheck(temp, other);
		}
	}
	return *this;
#else
	CMatrix4<T> temp(*this);
	return setbyproduct_nocheck(temp, other);
#endif
}

//! multiply by another matrix
// set this matrix to the product of two other matrices
// goal is to reduce stack use and copy
template <class T>
inline CMatrix4<T> &CMatrix4<T>::setbyproduct_nocheck(const CMatrix4<T> &other_a, const CMatrix4<T> &other_b)
{
	const T *m1 = other_a.M;
	const T *m2 = other_b.M;

	M[0] = m1[0] * m2[0] + m1[4] * m2[1] + m1[8] * m2[2] + m1[12] * m2[3];
	M[1] = m1[1] * m2[0] + m1[5] * m2[1] + m1[9] * m2[2] + m1[13] * m2[3];
	M[2] = m1[2] * m2[0] + m1[6] * m2[1] + m1[10] * m2[2] + m1[14] * m2[3];
	M[3] = m1[3] * m2[0] + m1[7] * m2[1] + m1[11] * m2[2] + m1[15] * m2[3];

	M[4] = m1[0] * m2[4] + m1[4] * m2[5] + m1[8] * m2[6] + m1[12] * m2[7];
	M[5] = m1[1] * m2[4] + m1[5] * m2[5] + m1[9] * m2[6] + m1[13] * m2[7];
	M[6] = m1[2] * m2[4] + m1[6] * m2[5] + m1[10] * m2[6] + m1[14] * m2[7];
	M[7] = m1[3] * m2[4] + m1[7] * m2[5] + m1[11] * m2[6] + m1[15] * m2[7];

	M[8] = m1[0] * m2[8] + m1[4] * m2[9] + m1[8] * m2[10] + m1[12] * m2[11];
	M[9] = m1[1] * m2[8] + m1[5] * m2[9] + m1[9] * m2[10] + m1[13] * m2[11];
	M[10] = m1[2] * m2[8] + m1[6] * m2[9] + m1[10] * m2[10] + m1[14] * m2[11];
	M[11] = m1[3] * m2[8] + m1[7] * m2[9] + m1[11] * m2[10] + m1[15] * m2[11];

	M[12] = m1[0] * m2[12] + m1[4] * m2[13] + m1[8] * m2[14] + m1[12] * m2[15];
	M[13] = m1[1] * m2[12] + m1[5] * m2[13] + m1[9] * m2[14] + m1[13] * m2[15];
	M[14] = m1[2] * m2[12] + m1[6] * m2[13] + m1[10] * m2[14] + m1[14] * m2[15];
	M[15] = m1[3] * m2[12] + m1[7] * m2[13] + m1[11] * m2[14] + m1[15] * m2[15];
#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
	return *this;
}

//! multiply by another matrix
// set this matrix to the product of two other matrices
// goal is to reduce stack use and copy
template <class T>
inline CMatrix4<T> &CMatrix4<T>::setbyproduct(const CMatrix4<T> &other_a, const CMatrix4<T> &other_b)
{
#if defined(USE_MATRIX_TEST)
	if (other_a.isIdentity())
		return (*this = other_b);
	else if (other_b.isIdentity())
		return (*this = other_a);
	else
		return setbyproduct_nocheck(other_a, other_b);
#else
	return setbyproduct_nocheck(other_a, other_b);
#endif
}

//! multiply by another matrix
template <class T>
inline CMatrix4<T> CMatrix4<T>::operator*(const CMatrix4<T> &m2) const
{
#if defined(USE_MATRIX_TEST)
	// Testing purpose..
	if (this->isIdentity())
		return m2;
	if (m2.isIdentity())
		return *this;
#endif

	CMatrix4<T> m3(EM4CONST_NOTHING);

	const T *m1 = M;

	m3[0] = m1[0] * m2[0] + m1[4] * m2[1] + m1[8] * m2[2] + m1[12] * m2[3];
	m3[1] = m1[1] * m2[0] + m1[5] * m2[1] + m1[9] * m2[2] + m1[13] * m2[3];
	m3[2] = m1[2] * m2[0] + m1[6] * m2[1] + m1[10] * m2[2] + m1[14] * m2[3];
	m3[3] = m1[3] * m2[0] + m1[7] * m2[1] + m1[11] * m2[2] + m1[15] * m2[3];

	m3[4] = m1[0] * m2[4] + m1[4] * m2[5] + m1[8] * m2[6] + m1[12] * m2[7];
	m3[5] = m1[1] * m2[4] + m1[5] * m2[5] + m1[9] * m2[6] + m1[13] * m2[7];
	m3[6] = m1[2] * m2[4] + m1[6] * m2[5] + m1[10] * m2[6] + m1[14] * m2[7];
	m3[7] = m1[3] * m2[4] + m1[7] * m2[5] + m1[11] * m2[6] + m1[15] * m2[7];

	m3[8] = m1[0] * m2[8] + m1[4] * m2[9] + m1[8] * m2[10] + m1[12] * m2[11];
	m3[9] = m1[1] * m2[8] + m1[5] * m2[9] + m1[9] * m2[10] + m1[13] * m2[11];
	m3[10] = m1[2] * m2[8] + m1[6] * m2[9] + m1[10] * m2[10] + m1[14] * m2[11];
	m3[11] = m1[3] * m2[8] + m1[7] * m2[9] + m1[11] * m2[10] + m1[15] * m2[11];

	m3[12] = m1[0] * m2[12] + m1[4] * m2[13] + m1[8] * m2[14] + m1[12] * m2[15];
	m3[13] = m1[1] * m2[12] + m1[5] * m2[13] + m1[9] * m2[14] + m1[13] * m2[15];
	m3[14] = m1[2] * m2[12] + m1[6] * m2[13] + m1[10] * m2[14] + m1[14] * m2[15];
	m3[15] = m1[3] * m2[12] + m1[7] * m2[13] + m1[11] * m2[14] + m1[15] * m2[15];
	return m3;
}

template <class T>
inline vector3d<T> CMatrix4<T>::getTranslation() const
{
	return vector3d<T>(M[12], M[13], M[14]);
}

template <class T>
inline CMatrix4<T> &CMatrix4<T>::setTranslation(const vector3d<T> &translation)
{
	M[12] = translation.X;
	M[13] = translation.Y;
	M[14] = translation.Z;
#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
	return *this;
}

template <class T>
inline CMatrix4<T> &CMatrix4<T>::setInverseTranslation(const vector3d<T> &translation)
{
	M[12] = -translation.X;
	M[13] = -translation.Y;
	M[14] = -translation.Z;
#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
	return *this;
}

template <class T>
inline CMatrix4<T> &CMatrix4<T>::setScale(const vector3d<T> &scale)
{
	M[0] = scale.X;
	M[5] = scale.Y;
	M[10] = scale.Z;
#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
	return *this;
}

//! Returns the absolute values of the scales of the matrix.
/**
Note: You only get back original values if the matrix only set the scale.
Otherwise the result is a scale you can use to normalize the matrix axes,
but it's usually no longer what you did set with setScale.
*/
template <class T>
inline vector3d<T> CMatrix4<T>::getScale() const
{
	// See http://www.robertblum.com/articles/2005/02/14/decomposing-matrices

	// Deal with the 0 rotation case first
	// Prior to Irrlicht 1.6, we always returned this value.
	if (core::iszero(M[1]) && core::iszero(M[2]) &&
			core::iszero(M[4]) && core::iszero(M[6]) &&
			core::iszero(M[8]) && core::iszero(M[9]))
		return vector3d<T>(M[0], M[5], M[10]);

	// We have to do the full calculation.
	return vector3d<T>(sqrtf(M[0] * M[0] + M[1] * M[1] + M[2] * M[2]),
			sqrtf(M[4] * M[4] + M[5] * M[5] + M[6] * M[6]),
			sqrtf(M[8] * M[8] + M[9] * M[9] + M[10] * M[10]));
}

template <class T>
inline CMatrix4<T> &CMatrix4<T>::setRotationDegrees(const vector3d<T> &rotation)
{
	return setRotationRadians(rotation * core::DEGTORAD);
}

template <class T>
inline CMatrix4<T> &CMatrix4<T>::setInverseRotationDegrees(const vector3d<T> &rotation)
{
	return setInverseRotationRadians(rotation * core::DEGTORAD);
}

template <class T>
inline CMatrix4<T> &CMatrix4<T>::setRotationRadians(const vector3d<T> &rotation)
{
	const f64 cr = cos(rotation.X);
	const f64 sr = sin(rotation.X);
	const f64 cp = cos(rotation.Y);
	const f64 sp = sin(rotation.Y);
	const f64 cy = cos(rotation.Z);
	const f64 sy = sin(rotation.Z);

	M[0] = (T)(cp * cy);
	M[1] = (T)(cp * sy);
	M[2] = (T)(-sp);

	const f64 srsp = sr * sp;
	const f64 crsp = cr * sp;

	M[4] = (T)(srsp * cy - cr * sy);
	M[5] = (T)(srsp * sy + cr * cy);
	M[6] = (T)(sr * cp);

	M[8] = (T)(crsp * cy + sr * sy);
	M[9] = (T)(crsp * sy - sr * cy);
	M[10] = (T)(cr * cp);
#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
	return *this;
}

//! Returns a rotation which (mostly) works in combination with the given scale
/**
This code was originally written by by Chev (assuming no scaling back then,
we can be blamed for all problems added by regarding scale)
*/
template <class T>
inline core::vector3d<T> CMatrix4<T>::getRotationDegrees(const vector3d<T> &scale_) const
{
	const CMatrix4<T> &mat = *this;
	const core::vector3d<f64> scale(core::iszero(scale_.X) ? FLT_MAX : scale_.X, core::iszero(scale_.Y) ? FLT_MAX : scale_.Y, core::iszero(scale_.Z) ? FLT_MAX : scale_.Z);
	const core::vector3d<f64> invScale(core::reciprocal(scale.X), core::reciprocal(scale.Y), core::reciprocal(scale.Z));

	f64 Y = -asin(core::clamp(mat[2] * invScale.X, -1.0, 1.0));
	const f64 C = cos(Y);
	Y *= RADTODEG64;

	f64 rotx, roty, X, Z;

	if (!core::iszero((T)C)) {
		const f64 invC = core::reciprocal(C);
		rotx = mat[10] * invC * invScale.Z;
		roty = mat[6] * invC * invScale.Y;
		X = atan2(roty, rotx) * RADTODEG64;
		rotx = mat[0] * invC * invScale.X;
		roty = mat[1] * invC * invScale.X;
		Z = atan2(roty, rotx) * RADTODEG64;
	} else {
		X = 0.0;
		rotx = mat[5] * invScale.Y;
		roty = -mat[4] * invScale.Y;
		Z = atan2(roty, rotx) * RADTODEG64;
	}

	// fix values that get below zero
	if (X < 0.0)
		X += 360.0;
	if (Y < 0.0)
		Y += 360.0;
	if (Z < 0.0)
		Z += 360.0;

	return vector3d<T>((T)X, (T)Y, (T)Z);
}

//! Returns a rotation that is equivalent to that set by setRotationDegrees().
template <class T>
inline core::vector3d<T> CMatrix4<T>::getRotationDegrees() const
{
	// Note: Using getScale() here make it look like it could do matrix decomposition.
	// It can't! It works (or should work) as long as rotation doesn't flip the handedness
	// aka scale swapping 1 or 3 axes. (I think we could catch that as well by comparing
	// crossproduct of first 2 axes to direction of third axis, but TODO)
	// And maybe it should also offer the solution for the simple calculation
	// without regarding scaling as Irrlicht did before 1.7
	core::vector3d<T> scale(getScale());

	// We assume the matrix uses rotations instead of negative scaling 2 axes.
	// Otherwise it fails even for some simple cases, like rotating around
	// 2 axes by 180° which getScale thinks is a negative scaling.
	if (scale.Y < 0 && scale.Z < 0) {
		scale.Y = -scale.Y;
		scale.Z = -scale.Z;
	} else if (scale.X < 0 && scale.Z < 0) {
		scale.X = -scale.X;
		scale.Z = -scale.Z;
	} else if (scale.X < 0 && scale.Y < 0) {
		scale.X = -scale.X;
		scale.Y = -scale.Y;
	}

	return getRotationDegrees(scale);
}

//! Sets matrix to rotation matrix of inverse angles given as parameters
template <class T>
inline CMatrix4<T> &CMatrix4<T>::setInverseRotationRadians(const vector3d<T> &rotation)
{
	f64 cr = cos(rotation.X);
	f64 sr = sin(rotation.X);
	f64 cp = cos(rotation.Y);
	f64 sp = sin(rotation.Y);
	f64 cy = cos(rotation.Z);
	f64 sy = sin(rotation.Z);

	M[0] = (T)(cp * cy);
	M[4] = (T)(cp * sy);
	M[8] = (T)(-sp);

	f64 srsp = sr * sp;
	f64 crsp = cr * sp;

	M[1] = (T)(srsp * cy - cr * sy);
	M[5] = (T)(srsp * sy + cr * cy);
	M[9] = (T)(sr * cp);

	M[2] = (T)(crsp * cy + sr * sy);
	M[6] = (T)(crsp * sy - sr * cy);
	M[10] = (T)(cr * cp);
#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
	return *this;
}

//! Sets matrix to rotation matrix defined by axis and angle, assuming LH rotation
template <class T>
inline CMatrix4<T> &CMatrix4<T>::setRotationAxisRadians(const T &angle, const vector3d<T> &axis)
{
	const f64 c = cos(angle);
	const f64 s = sin(angle);
	const f64 t = 1.0 - c;

	const f64 tx = t * axis.X;
	const f64 ty = t * axis.Y;
	const f64 tz = t * axis.Z;

	const f64 sx = s * axis.X;
	const f64 sy = s * axis.Y;
	const f64 sz = s * axis.Z;

	M[0] = (T)(tx * axis.X + c);
	M[1] = (T)(tx * axis.Y + sz);
	M[2] = (T)(tx * axis.Z - sy);

	M[4] = (T)(ty * axis.X - sz);
	M[5] = (T)(ty * axis.Y + c);
	M[6] = (T)(ty * axis.Z + sx);

	M[8] = (T)(tz * axis.X + sy);
	M[9] = (T)(tz * axis.Y - sx);
	M[10] = (T)(tz * axis.Z + c);

#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
	return *this;
}

/*!
 */
template <class T>
inline CMatrix4<T> &CMatrix4<T>::makeIdentity()
{
	memset(M, 0, 16 * sizeof(T));
	M[0] = M[5] = M[10] = M[15] = (T)1;
#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = true;
#endif
	return *this;
}

/*
	check identity with epsilon
	solve floating range problems..
*/
template <class T>
inline bool CMatrix4<T>::isIdentity() const
{
#if defined(USE_MATRIX_TEST)
	if (definitelyIdentityMatrix)
		return true;
#endif
	if (!core::equals(M[12], (T)0) || !core::equals(M[13], (T)0) || !core::equals(M[14], (T)0) || !core::equals(M[15], (T)1))
		return false;

	if (!core::equals(M[0], (T)1) || !core::equals(M[1], (T)0) || !core::equals(M[2], (T)0) || !core::equals(M[3], (T)0))
		return false;

	if (!core::equals(M[4], (T)0) || !core::equals(M[5], (T)1) || !core::equals(M[6], (T)0) || !core::equals(M[7], (T)0))
		return false;

	if (!core::equals(M[8], (T)0) || !core::equals(M[9], (T)0) || !core::equals(M[10], (T)1) || !core::equals(M[11], (T)0))
		return false;
/*
		if (!core::equals( M[ 0], (T)1 ) ||
			!core::equals( M[ 5], (T)1 ) ||
			!core::equals( M[10], (T)1 ) ||
			!core::equals( M[15], (T)1 ))
			return false;

		for (s32 i=0; i<4; ++i)
			for (s32 j=0; j<4; ++j)
				if ((j != i) && (!iszero((*this)(i,j))))
					return false;
*/
#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = true;
#endif
	return true;
}

/* Check orthogonality of matrix. */
template <class T>
inline bool CMatrix4<T>::isOrthogonal() const
{
	T dp = M[0] * M[4] + M[1] * M[5] + M[2] * M[6] + M[3] * M[7];
	if (!iszero(dp))
		return false;
	dp = M[0] * M[8] + M[1] * M[9] + M[2] * M[10] + M[3] * M[11];
	if (!iszero(dp))
		return false;
	dp = M[0] * M[12] + M[1] * M[13] + M[2] * M[14] + M[3] * M[15];
	if (!iszero(dp))
		return false;
	dp = M[4] * M[8] + M[5] * M[9] + M[6] * M[10] + M[7] * M[11];
	if (!iszero(dp))
		return false;
	dp = M[4] * M[12] + M[5] * M[13] + M[6] * M[14] + M[7] * M[15];
	if (!iszero(dp))
		return false;
	dp = M[8] * M[12] + M[9] * M[13] + M[10] * M[14] + M[11] * M[15];
	return (iszero(dp));
}

/*
	doesn't solve floating range problems..
	but takes care on +/- 0 on translation because we are changing it..
	reducing floating point branches
	but it needs the floats in memory..
*/
template <class T>
inline bool CMatrix4<T>::isIdentity_integer_base() const
{
#if defined(USE_MATRIX_TEST)
	if (definitelyIdentityMatrix)
		return true;
#endif
	if (IR(M[0]) != F32_VALUE_1)
		return false;
	if (IR(M[1]) != 0)
		return false;
	if (IR(M[2]) != 0)
		return false;
	if (IR(M[3]) != 0)
		return false;

	if (IR(M[4]) != 0)
		return false;
	if (IR(M[5]) != F32_VALUE_1)
		return false;
	if (IR(M[6]) != 0)
		return false;
	if (IR(M[7]) != 0)
		return false;

	if (IR(M[8]) != 0)
		return false;
	if (IR(M[9]) != 0)
		return false;
	if (IR(M[10]) != F32_VALUE_1)
		return false;
	if (IR(M[11]) != 0)
		return false;

	if (IR(M[12]) != 0)
		return false;
	if (IR(M[13]) != 0)
		return false;
	if (IR(M[13]) != 0)
		return false;
	if (IR(M[15]) != F32_VALUE_1)
		return false;

#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = true;
#endif
	return true;
}

template <class T>
inline vector3d<T> CMatrix4<T>::rotateAndScaleVect(const vector3d<T> &v) const
{
	return {
		v.X * M[0] + v.Y * M[4] + v.Z * M[8],
		v.X * M[1] + v.Y * M[5] + v.Z * M[9],
		v.X * M[2] + v.Y * M[6] + v.Z * M[10]
	};
}

template <class T>
inline vector3d<T> CMatrix4<T>::scaleThenInvRotVect(const vector3d<T> &v) const
{
	return {
		v.X * M[0] + v.Y * M[1] + v.Z * M[2],
		v.X * M[4] + v.Y * M[5] + v.Z * M[6],
		v.X * M[8] + v.Y * M[9] + v.Z * M[10]
	};
}

template <class T>
inline void CMatrix4<T>::transformVect(vector3df &vect) const
{
	T vector[3];

	vector[0] = vect.X * M[0] + vect.Y * M[4] + vect.Z * M[8] + M[12];
	vector[1] = vect.X * M[1] + vect.Y * M[5] + vect.Z * M[9] + M[13];
	vector[2] = vect.X * M[2] + vect.Y * M[6] + vect.Z * M[10] + M[14];

	vect.X = static_cast<f32>(vector[0]);
	vect.Y = static_cast<f32>(vector[1]);
	vect.Z = static_cast<f32>(vector[2]);
}

template <class T>
inline void CMatrix4<T>::transformVect(vector3df &out, const vector3df &in) const
{
	out.X = in.X * M[0] + in.Y * M[4] + in.Z * M[8] + M[12];
	out.Y = in.X * M[1] + in.Y * M[5] + in.Z * M[9] + M[13];
	out.Z = in.X * M[2] + in.Y * M[6] + in.Z * M[10] + M[14];
}

template <class T>
inline void CMatrix4<T>::transformVect(T *out, const core::vector3df &in) const
{
	out[0] = in.X * M[0] + in.Y * M[4] + in.Z * M[8] + M[12];
	out[1] = in.X * M[1] + in.Y * M[5] + in.Z * M[9] + M[13];
	out[2] = in.X * M[2] + in.Y * M[6] + in.Z * M[10] + M[14];
	out[3] = in.X * M[3] + in.Y * M[7] + in.Z * M[11] + M[15];
}

template <class T>
inline void CMatrix4<T>::transformVec3(T *out, const T *in) const
{
	out[0] = in[0] * M[0] + in[1] * M[4] + in[2] * M[8] + M[12];
	out[1] = in[0] * M[1] + in[1] * M[5] + in[2] * M[9] + M[13];
	out[2] = in[0] * M[2] + in[1] * M[6] + in[2] * M[10] + M[14];
}

template <class T>
inline void CMatrix4<T>::transformVec4(T *out, const T *in) const
{
	out[0] = in[0] * M[0] + in[1] * M[4] + in[2] * M[8] + in[3] * M[12];
	out[1] = in[0] * M[1] + in[1] * M[5] + in[2] * M[9] + in[3] * M[13];
	out[2] = in[0] * M[2] + in[1] * M[6] + in[2] * M[10] + in[3] * M[14];
	out[3] = in[0] * M[3] + in[1] * M[7] + in[2] * M[11] + in[3] * M[15];
}

//! Transforms a plane by this matrix
template <class T>
inline void CMatrix4<T>::transformPlane(core::plane3d<f32> &plane) const
{
	vector3df member;
	// Transform the plane member point, i.e. rotate, translate and scale it.
	transformVect(member, plane.getMemberPoint());

	// Transform the normal by the transposed inverse of the matrix
	CMatrix4<T> transposedInverse(*this, EM4CONST_INVERSE_TRANSPOSED);
	vector3df normal = transposedInverse.rotateAndScaleVect(plane.Normal);
	plane.setPlane(member, normal.normalize());
}

//! Transforms a plane by this matrix
template <class T>
inline void CMatrix4<T>::transformPlane(const core::plane3d<f32> &in, core::plane3d<f32> &out) const
{
	out = in;
	transformPlane(out);
}

//! Transforms a axis aligned bounding box more accurately than transformBox()
template <class T>
inline void CMatrix4<T>::transformBoxEx(core::aabbox3d<f32> &box) const
{
#if defined(USE_MATRIX_TEST)
	if (isIdentity())
		return;
#endif

	const f32 Amin[3] = {box.MinEdge.X, box.MinEdge.Y, box.MinEdge.Z};
	const f32 Amax[3] = {box.MaxEdge.X, box.MaxEdge.Y, box.MaxEdge.Z};

	f32 Bmin[3];
	f32 Bmax[3];

	Bmin[0] = Bmax[0] = M[12];
	Bmin[1] = Bmax[1] = M[13];
	Bmin[2] = Bmax[2] = M[14];

	const CMatrix4<T> &m = *this;

	for (u32 i = 0; i < 3; ++i) {
		for (u32 j = 0; j < 3; ++j) {
			const f32 a = m(j, i) * Amin[j];
			const f32 b = m(j, i) * Amax[j];

			if (a < b) {
				Bmin[i] += a;
				Bmax[i] += b;
			} else {
				Bmin[i] += b;
				Bmax[i] += a;
			}
		}
	}

	box.MinEdge.X = Bmin[0];
	box.MinEdge.Y = Bmin[1];
	box.MinEdge.Z = Bmin[2];

	box.MaxEdge.X = Bmax[0];
	box.MaxEdge.Y = Bmax[1];
	box.MaxEdge.Z = Bmax[2];
}

//! Multiplies this matrix by a 1x4 matrix
template <class T>
inline void CMatrix4<T>::multiplyWith1x4Matrix(T *matrix) const
{
	/*
	0  1  2  3
	4  5  6  7
	8  9  10 11
	12 13 14 15
	*/

	T mat[4];
	mat[0] = matrix[0];
	mat[1] = matrix[1];
	mat[2] = matrix[2];
	mat[3] = matrix[3];

	matrix[0] = M[0] * mat[0] + M[4] * mat[1] + M[8] * mat[2] + M[12] * mat[3];
	matrix[1] = M[1] * mat[0] + M[5] * mat[1] + M[9] * mat[2] + M[13] * mat[3];
	matrix[2] = M[2] * mat[0] + M[6] * mat[1] + M[10] * mat[2] + M[14] * mat[3];
	matrix[3] = M[3] * mat[0] + M[7] * mat[1] + M[11] * mat[2] + M[15] * mat[3];
}

template <class T>
inline void CMatrix4<T>::inverseTranslateVect(vector3df &vect) const
{
	vect.X = vect.X - M[12];
	vect.Y = vect.Y - M[13];
	vect.Z = vect.Z - M[14];
}

template <class T>
inline void CMatrix4<T>::translateVect(vector3df &vect) const
{
	vect.X = vect.X + M[12];
	vect.Y = vect.Y + M[13];
	vect.Z = vect.Z + M[14];
}

template <class T>
inline bool CMatrix4<T>::getInverse(CMatrix4<T> &out) const
{
	/// Calculates the inverse of this Matrix
	/// The inverse is calculated using Cramers rule.
	/// If no inverse exists then 'false' is returned.

#if defined(USE_MATRIX_TEST)
	if (this->isIdentity()) {
		out = *this;
		return true;
	}
#endif
	const CMatrix4<T> &m = *this;

	f32 d = (m[0] * m[5] - m[1] * m[4]) * (m[10] * m[15] - m[11] * m[14]) -
			(m[0] * m[6] - m[2] * m[4]) * (m[9] * m[15] - m[11] * m[13]) +
			(m[0] * m[7] - m[3] * m[4]) * (m[9] * m[14] - m[10] * m[13]) +
			(m[1] * m[6] - m[2] * m[5]) * (m[8] * m[15] - m[11] * m[12]) -
			(m[1] * m[7] - m[3] * m[5]) * (m[8] * m[14] - m[10] * m[12]) +
			(m[2] * m[7] - m[3] * m[6]) * (m[8] * m[13] - m[9] * m[12]);

	if (core::iszero(d, FLT_MIN))
		return false;

	d = core::reciprocal(d);

	out[0] = d * (m[5] * (m[10] * m[15] - m[11] * m[14]) +
						 m[6] * (m[11] * m[13] - m[9] * m[15]) +
						 m[7] * (m[9] * m[14] - m[10] * m[13]));
	out[1] = d * (m[9] * (m[2] * m[15] - m[3] * m[14]) +
						 m[10] * (m[3] * m[13] - m[1] * m[15]) +
						 m[11] * (m[1] * m[14] - m[2] * m[13]));
	out[2] = d * (m[13] * (m[2] * m[7] - m[3] * m[6]) +
						 m[14] * (m[3] * m[5] - m[1] * m[7]) +
						 m[15] * (m[1] * m[6] - m[2] * m[5]));
	out[3] = d * (m[1] * (m[7] * m[10] - m[6] * m[11]) +
						 m[2] * (m[5] * m[11] - m[7] * m[9]) +
						 m[3] * (m[6] * m[9] - m[5] * m[10]));
	out[4] = d * (m[6] * (m[8] * m[15] - m[11] * m[12]) +
						 m[7] * (m[10] * m[12] - m[8] * m[14]) +
						 m[4] * (m[11] * m[14] - m[10] * m[15]));
	out[5] = d * (m[10] * (m[0] * m[15] - m[3] * m[12]) +
						 m[11] * (m[2] * m[12] - m[0] * m[14]) +
						 m[8] * (m[3] * m[14] - m[2] * m[15]));
	out[6] = d * (m[14] * (m[0] * m[7] - m[3] * m[4]) +
						 m[15] * (m[2] * m[4] - m[0] * m[6]) +
						 m[12] * (m[3] * m[6] - m[2] * m[7]));
	out[7] = d * (m[2] * (m[7] * m[8] - m[4] * m[11]) +
						 m[3] * (m[4] * m[10] - m[6] * m[8]) +
						 m[0] * (m[6] * m[11] - m[7] * m[10]));
	out[8] = d * (m[7] * (m[8] * m[13] - m[9] * m[12]) +
						 m[4] * (m[9] * m[15] - m[11] * m[13]) +
						 m[5] * (m[11] * m[12] - m[8] * m[15]));
	out[9] = d * (m[11] * (m[0] * m[13] - m[1] * m[12]) +
						 m[8] * (m[1] * m[15] - m[3] * m[13]) +
						 m[9] * (m[3] * m[12] - m[0] * m[15]));
	out[10] = d * (m[15] * (m[0] * m[5] - m[1] * m[4]) +
						  m[12] * (m[1] * m[7] - m[3] * m[5]) +
						  m[13] * (m[3] * m[4] - m[0] * m[7]));
	out[11] = d * (m[3] * (m[5] * m[8] - m[4] * m[9]) +
						  m[0] * (m[7] * m[9] - m[5] * m[11]) +
						  m[1] * (m[4] * m[11] - m[7] * m[8]));
	out[12] = d * (m[4] * (m[10] * m[13] - m[9] * m[14]) +
						  m[5] * (m[8] * m[14] - m[10] * m[12]) +
						  m[6] * (m[9] * m[12] - m[8] * m[13]));
	out[13] = d * (m[8] * (m[2] * m[13] - m[1] * m[14]) +
						  m[9] * (m[0] * m[14] - m[2] * m[12]) +
						  m[10] * (m[1] * m[12] - m[0] * m[13]));
	out[14] = d * (m[12] * (m[2] * m[5] - m[1] * m[6]) +
						  m[13] * (m[0] * m[6] - m[2] * m[4]) +
						  m[14] * (m[1] * m[4] - m[0] * m[5]));
	out[15] = d * (m[0] * (m[5] * m[10] - m[6] * m[9]) +
						  m[1] * (m[6] * m[8] - m[4] * m[10]) +
						  m[2] * (m[4] * m[9] - m[5] * m[8]));

#if defined(USE_MATRIX_TEST)
	out.definitelyIdentityMatrix = definitelyIdentityMatrix;
#endif
	return true;
}

//! Inverts a primitive matrix which only contains a translation and a rotation
//! \param out: where result matrix is written to.
template <class T>
inline bool CMatrix4<T>::getInversePrimitive(CMatrix4<T> &out) const
{
	out.M[0] = M[0];
	out.M[1] = M[4];
	out.M[2] = M[8];
	out.M[3] = 0;

	out.M[4] = M[1];
	out.M[5] = M[5];
	out.M[6] = M[9];
	out.M[7] = 0;

	out.M[8] = M[2];
	out.M[9] = M[6];
	out.M[10] = M[10];
	out.M[11] = 0;

	out.M[12] = (T) - (M[12] * M[0] + M[13] * M[1] + M[14] * M[2]);
	out.M[13] = (T) - (M[12] * M[4] + M[13] * M[5] + M[14] * M[6]);
	out.M[14] = (T) - (M[12] * M[8] + M[13] * M[9] + M[14] * M[10]);
	out.M[15] = 1;

#if defined(USE_MATRIX_TEST)
	out.definitelyIdentityMatrix = definitelyIdentityMatrix;
#endif
	return true;
}

/*!
 */
template <class T>
inline bool CMatrix4<T>::makeInverse()
{
#if defined(USE_MATRIX_TEST)
	if (definitelyIdentityMatrix)
		return true;
#endif
	CMatrix4<T> temp(EM4CONST_NOTHING);

	if (getInverse(temp)) {
		*this = temp;
		return true;
	}

	return false;
}

template <class T>
inline CMatrix4<T> &CMatrix4<T>::operator=(const T &scalar)
{
	for (s32 i = 0; i < 16; ++i)
		M[i] = scalar;

#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
	return *this;
}

// Builds a right-handed perspective projection matrix based on a field of view
template <class T>
inline CMatrix4<T> &CMatrix4<T>::buildProjectionMatrixPerspectiveFovRH(
		f32 fieldOfViewRadians, f32 aspectRatio, f32 zNear, f32 zFar, bool zClipFromZero)
{
	const f64 h = reciprocal(tan(fieldOfViewRadians * 0.5));
	_IRR_DEBUG_BREAK_IF(aspectRatio == 0.f); // divide by zero
	const T w = static_cast<T>(h / aspectRatio);

	_IRR_DEBUG_BREAK_IF(zNear == zFar); // divide by zero
	M[0] = w;
	M[1] = 0;
	M[2] = 0;
	M[3] = 0;

	M[4] = 0;
	M[5] = (T)h;
	M[6] = 0;
	M[7] = 0;

	M[8] = 0;
	M[9] = 0;
	// M[10]
	M[11] = -1;

	M[12] = 0;
	M[13] = 0;
	// M[14]
	M[15] = 0;

	if (zClipFromZero) { // DirectX version
		M[10] = (T)(zFar / (zNear - zFar));
		M[14] = (T)(zNear * zFar / (zNear - zFar));
	} else // OpenGL version
	{
		M[10] = (T)((zFar + zNear) / (zNear - zFar));
		M[14] = (T)(2.0f * zNear * zFar / (zNear - zFar));
	}

#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
	return *this;
}

// Builds a left-handed perspective projection matrix based on a field of view
template <class T>
inline CMatrix4<T> &CMatrix4<T>::buildProjectionMatrixPerspectiveFovLH(
		f32 fieldOfViewRadians, f32 aspectRatio, f32 zNear, f32 zFar, bool zClipFromZero)
{
	const f64 h = reciprocal(tan(fieldOfViewRadians * 0.5));
	_IRR_DEBUG_BREAK_IF(aspectRatio == 0.f); // divide by zero
	const T w = static_cast<T>(h / aspectRatio);

	_IRR_DEBUG_BREAK_IF(zNear == zFar); // divide by zero
	M[0] = w;
	M[1] = 0;
	M[2] = 0;
	M[3] = 0;

	M[4] = 0;
	M[5] = (T)h;
	M[6] = 0;
	M[7] = 0;

	M[8] = 0;
	M[9] = 0;
	// M[10]
	M[11] = 1;

	M[12] = 0;
	M[13] = 0;
	// M[14]
	M[15] = 0;

	if (zClipFromZero) { // DirectX version
		M[10] = (T)(zFar / (zFar - zNear));
		M[14] = (T)(-zNear * zFar / (zFar - zNear));
	} else // OpenGL version
	{
		M[10] = (T)((zFar + zNear) / (zFar - zNear));
		M[14] = (T)(2.0f * zNear * zFar / (zNear - zFar));
	}

#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
	return *this;
}

// Builds a left-handed perspective projection matrix based on a field of view, with far plane culling at infinity
template <class T>
inline CMatrix4<T> &CMatrix4<T>::buildProjectionMatrixPerspectiveFovInfinityLH(
		f32 fieldOfViewRadians, f32 aspectRatio, f32 zNear, f32 epsilon)
{
	const f64 h = reciprocal(tan(fieldOfViewRadians * 0.5));
	_IRR_DEBUG_BREAK_IF(aspectRatio == 0.f); // divide by zero
	const T w = static_cast<T>(h / aspectRatio);

	M[0] = w;
	M[1] = 0;
	M[2] = 0;
	M[3] = 0;

	M[4] = 0;
	M[5] = (T)h;
	M[6] = 0;
	M[7] = 0;

	M[8] = 0;
	M[9] = 0;
	M[10] = (T)(1.f - epsilon);
	M[11] = 1;

	M[12] = 0;
	M[13] = 0;
	M[14] = (T)(zNear * (epsilon - 1.f));
	M[15] = 0;

#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
	return *this;
}

// Builds a left-handed orthogonal projection matrix.
template <class T>
inline CMatrix4<T> &CMatrix4<T>::buildProjectionMatrixOrthoLH(
		f32 widthOfViewVolume, f32 heightOfViewVolume, f32 zNear, f32 zFar, bool zClipFromZero)
{
	_IRR_DEBUG_BREAK_IF(widthOfViewVolume == 0.f);  // divide by zero
	_IRR_DEBUG_BREAK_IF(heightOfViewVolume == 0.f); // divide by zero
	_IRR_DEBUG_BREAK_IF(zNear == zFar);             // divide by zero
	M[0] = (T)(2 / widthOfViewVolume);
	M[1] = 0;
	M[2] = 0;
	M[3] = 0;

	M[4] = 0;
	M[5] = (T)(2 / heightOfViewVolume);
	M[6] = 0;
	M[7] = 0;

	M[8] = 0;
	M[9] = 0;
	// M[10]
	M[11] = 0;

	M[12] = 0;
	M[13] = 0;
	// M[14]
	M[15] = 1;

	if (zClipFromZero) {
		M[10] = (T)(1 / (zFar - zNear));
		M[14] = (T)(zNear / (zNear - zFar));
	} else {
		M[10] = (T)(2 / (zFar - zNear));
		M[14] = (T) - (zFar + zNear) / (zFar - zNear);
	}

#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
	return *this;
}

// Builds a right-handed orthogonal projection matrix.
template <class T>
inline CMatrix4<T> &CMatrix4<T>::buildProjectionMatrixOrthoRH(
		f32 widthOfViewVolume, f32 heightOfViewVolume, f32 zNear, f32 zFar, bool zClipFromZero)
{
	_IRR_DEBUG_BREAK_IF(widthOfViewVolume == 0.f);  // divide by zero
	_IRR_DEBUG_BREAK_IF(heightOfViewVolume == 0.f); // divide by zero
	_IRR_DEBUG_BREAK_IF(zNear == zFar);             // divide by zero
	M[0] = (T)(2 / widthOfViewVolume);
	M[1] = 0;
	M[2] = 0;
	M[3] = 0;

	M[4] = 0;
	M[5] = (T)(2 / heightOfViewVolume);
	M[6] = 0;
	M[7] = 0;

	M[8] = 0;
	M[9] = 0;
	// M[10]
	M[11] = 0;

	M[12] = 0;
	M[13] = 0;
	// M[14]
	M[15] = 1;

	if (zClipFromZero) {
		M[10] = (T)(1 / (zNear - zFar));
		M[14] = (T)(zNear / (zNear - zFar));
	} else {
		M[10] = (T)(2 / (zNear - zFar));
		M[14] = (T) - (zFar + zNear) / (zFar - zNear);
	}

#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
	return *this;
}

// Builds a right-handed perspective projection matrix.
template <class T>
inline CMatrix4<T> &CMatrix4<T>::buildProjectionMatrixPerspectiveRH(
		f32 widthOfViewVolume, f32 heightOfViewVolume, f32 zNear, f32 zFar, bool zClipFromZero)
{
	_IRR_DEBUG_BREAK_IF(widthOfViewVolume == 0.f);  // divide by zero
	_IRR_DEBUG_BREAK_IF(heightOfViewVolume == 0.f); // divide by zero
	_IRR_DEBUG_BREAK_IF(zNear == zFar);             // divide by zero
	M[0] = (T)(2 * zNear / widthOfViewVolume);
	M[1] = 0;
	M[2] = 0;
	M[3] = 0;

	M[4] = 0;
	M[5] = (T)(2 * zNear / heightOfViewVolume);
	M[6] = 0;
	M[7] = 0;

	M[8] = 0;
	M[9] = 0;
	// M[10]
	M[11] = -1;

	M[12] = 0;
	M[13] = 0;
	// M[14]
	M[15] = 0;

	if (zClipFromZero) { // DirectX version
		M[10] = (T)(zFar / (zNear - zFar));
		M[14] = (T)(zNear * zFar / (zNear - zFar));
	} else // OpenGL version
	{
		M[10] = (T)((zFar + zNear) / (zNear - zFar));
		M[14] = (T)(2.0f * zNear * zFar / (zNear - zFar));
	}

#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
	return *this;
}

// Builds a left-handed perspective projection matrix.
template <class T>
inline CMatrix4<T> &CMatrix4<T>::buildProjectionMatrixPerspectiveLH(
		f32 widthOfViewVolume, f32 heightOfViewVolume, f32 zNear, f32 zFar, bool zClipFromZero)
{
	_IRR_DEBUG_BREAK_IF(widthOfViewVolume == 0.f);  // divide by zero
	_IRR_DEBUG_BREAK_IF(heightOfViewVolume == 0.f); // divide by zero
	_IRR_DEBUG_BREAK_IF(zNear == zFar);             // divide by zero
	M[0] = (T)(2 * zNear / widthOfViewVolume);
	M[1] = 0;
	M[2] = 0;
	M[3] = 0;

	M[4] = 0;
	M[5] = (T)(2 * zNear / heightOfViewVolume);
	M[6] = 0;
	M[7] = 0;

	M[8] = 0;
	M[9] = 0;
	// M[10]
	M[11] = 1;

	M[12] = 0;
	M[13] = 0;
	// M[14] = (T)(zNear*zFar/(zNear-zFar));
	M[15] = 0;

	if (zClipFromZero) { // DirectX version
		M[10] = (T)(zFar / (zFar - zNear));
		M[14] = (T)(zNear * zFar / (zNear - zFar));
	} else // OpenGL version
	{
		M[10] = (T)((zFar + zNear) / (zFar - zNear));
		M[14] = (T)(2.0f * zNear * zFar / (zNear - zFar));
	}

#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
	return *this;
}

// Builds a matrix that flattens geometry into a plane.
template <class T>
inline CMatrix4<T> &CMatrix4<T>::buildShadowMatrix(const core::vector3df &light, core::plane3df plane, f32 point)
{
	plane.Normal.normalize();
	const f32 d = plane.Normal.dotProduct(light);

	M[0] = (T)(-plane.Normal.X * light.X + d);
	M[1] = (T)(-plane.Normal.X * light.Y);
	M[2] = (T)(-plane.Normal.X * light.Z);
	M[3] = (T)(-plane.Normal.X * point);

	M[4] = (T)(-plane.Normal.Y * light.X);
	M[5] = (T)(-plane.Normal.Y * light.Y + d);
	M[6] = (T)(-plane.Normal.Y * light.Z);
	M[7] = (T)(-plane.Normal.Y * point);

	M[8] = (T)(-plane.Normal.Z * light.X);
	M[9] = (T)(-plane.Normal.Z * light.Y);
	M[10] = (T)(-plane.Normal.Z * light.Z + d);
	M[11] = (T)(-plane.Normal.Z * point);

	M[12] = (T)(-plane.D * light.X);
	M[13] = (T)(-plane.D * light.Y);
	M[14] = (T)(-plane.D * light.Z);
	M[15] = (T)(-plane.D * point + d);
#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
	return *this;
}

// Builds a left-handed look-at matrix.
template <class T>
inline CMatrix4<T> &CMatrix4<T>::buildCameraLookAtMatrixLH(
		const vector3df &position,
		const vector3df &target,
		const vector3df &upVector)
{
	vector3df zaxis = target - position;
	zaxis.normalize();

	vector3df xaxis = upVector.crossProduct(zaxis);
	xaxis.normalize();

	vector3df yaxis = zaxis.crossProduct(xaxis);

	M[0] = (T)xaxis.X;
	M[1] = (T)yaxis.X;
	M[2] = (T)zaxis.X;
	M[3] = 0;

	M[4] = (T)xaxis.Y;
	M[5] = (T)yaxis.Y;
	M[6] = (T)zaxis.Y;
	M[7] = 0;

	M[8] = (T)xaxis.Z;
	M[9] = (T)yaxis.Z;
	M[10] = (T)zaxis.Z;
	M[11] = 0;

	M[12] = (T)-xaxis.dotProduct(position);
	M[13] = (T)-yaxis.dotProduct(position);
	M[14] = (T)-zaxis.dotProduct(position);
	M[15] = 1;
#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
	return *this;
}

// Builds a right-handed look-at matrix.
template <class T>
inline CMatrix4<T> &CMatrix4<T>::buildCameraLookAtMatrixRH(
		const vector3df &position,
		const vector3df &target,
		const vector3df &upVector)
{
	vector3df zaxis = position - target;
	zaxis.normalize();

	vector3df xaxis = upVector.crossProduct(zaxis);
	xaxis.normalize();

	vector3df yaxis = zaxis.crossProduct(xaxis);

	M[0] = (T)xaxis.X;
	M[1] = (T)yaxis.X;
	M[2] = (T)zaxis.X;
	M[3] = 0;

	M[4] = (T)xaxis.Y;
	M[5] = (T)yaxis.Y;
	M[6] = (T)zaxis.Y;
	M[7] = 0;

	M[8] = (T)xaxis.Z;
	M[9] = (T)yaxis.Z;
	M[10] = (T)zaxis.Z;
	M[11] = 0;

	M[12] = (T)-xaxis.dotProduct(position);
	M[13] = (T)-yaxis.dotProduct(position);
	M[14] = (T)-zaxis.dotProduct(position);
	M[15] = 1;
#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
	return *this;
}

// creates a new matrix as interpolated matrix from this and the passed one.
template <class T>
inline CMatrix4<T> CMatrix4<T>::interpolate(const core::CMatrix4<T> &b, f32 time) const
{
	CMatrix4<T> mat(EM4CONST_NOTHING);

	for (u32 i = 0; i < 16; i += 4) {
		mat.M[i + 0] = (T)(M[i + 0] + (b.M[i + 0] - M[i + 0]) * time);
		mat.M[i + 1] = (T)(M[i + 1] + (b.M[i + 1] - M[i + 1]) * time);
		mat.M[i + 2] = (T)(M[i + 2] + (b.M[i + 2] - M[i + 2]) * time);
		mat.M[i + 3] = (T)(M[i + 3] + (b.M[i + 3] - M[i + 3]) * time);
	}
	return mat;
}

// returns transposed matrix
template <class T>
inline CMatrix4<T> CMatrix4<T>::getTransposed() const
{
	CMatrix4<T> t(EM4CONST_NOTHING);
	getTransposed(t);
	return t;
}

// returns transposed matrix
template <class T>
inline void CMatrix4<T>::getTransposed(CMatrix4<T> &o) const
{
	o[0] = M[0];
	o[1] = M[4];
	o[2] = M[8];
	o[3] = M[12];

	o[4] = M[1];
	o[5] = M[5];
	o[6] = M[9];
	o[7] = M[13];

	o[8] = M[2];
	o[9] = M[6];
	o[10] = M[10];
	o[11] = M[14];

	o[12] = M[3];
	o[13] = M[7];
	o[14] = M[11];
	o[15] = M[15];
#if defined(USE_MATRIX_TEST)
	o.definitelyIdentityMatrix = definitelyIdentityMatrix;
#endif
}

// used to scale <-1,-1><1,1> to viewport
template <class T>
inline CMatrix4<T> &CMatrix4<T>::buildNDCToDCMatrix(const core::rect<s32> &viewport, f32 zScale)
{
	const f32 scaleX = (viewport.getWidth() - 0.75f) * 0.5f;
	const f32 scaleY = -(viewport.getHeight() - 0.75f) * 0.5f;

	const f32 dx = -0.5f + ((viewport.UpperLeftCorner.X + viewport.LowerRightCorner.X) * 0.5f);
	const f32 dy = -0.5f + ((viewport.UpperLeftCorner.Y + viewport.LowerRightCorner.Y) * 0.5f);

	makeIdentity();
	M[12] = (T)dx;
	M[13] = (T)dy;
	return setScale(core::vector3d<T>((T)scaleX, (T)scaleY, (T)zScale));
}

//! Builds a matrix that rotates from one vector to another
/** \param from: vector to rotate from
\param to: vector to rotate to

	http://www.euclideanspace.com/maths/geometry/rotations/conversions/angleToMatrix/index.htm
 */
template <class T>
inline CMatrix4<T> &CMatrix4<T>::buildRotateFromTo(const core::vector3df &from, const core::vector3df &to)
{
	// unit vectors
	core::vector3df f(from);
	core::vector3df t(to);
	f.normalize();
	t.normalize();

	// axis multiplication by sin
	core::vector3df vs(t.crossProduct(f));

	// axis of rotation
	core::vector3df v(vs);
	v.normalize();

	// cosine angle
	T ca = f.dotProduct(t);

	core::vector3df vt(v * (1 - ca));

	M[0] = vt.X * v.X + ca;
	M[5] = vt.Y * v.Y + ca;
	M[10] = vt.Z * v.Z + ca;

	vt.X *= v.Y;
	vt.Z *= v.X;
	vt.Y *= v.Z;

	M[1] = vt.X - vs.Z;
	M[2] = vt.Z + vs.Y;
	M[3] = 0;

	M[4] = vt.X + vs.Z;
	M[6] = vt.Y - vs.X;
	M[7] = 0;

	M[8] = vt.Z - vs.Y;
	M[9] = vt.Y + vs.X;
	M[11] = 0;

	M[12] = 0;
	M[13] = 0;
	M[14] = 0;
	M[15] = 1;

	return *this;
}

//! Builds a matrix which rotates a source vector to a look vector over an arbitrary axis
/** \param camPos: viewer position in world coord
\param center: object position in world-coord, rotation pivot
\param translation: object final translation from center
\param axis: axis to rotate about
\param from: source vector to rotate from
 */
template <class T>
inline void CMatrix4<T>::buildAxisAlignedBillboard(
		const core::vector3df &camPos,
		const core::vector3df &center,
		const core::vector3df &translation,
		const core::vector3df &axis,
		const core::vector3df &from)
{
	// axis of rotation
	core::vector3df up = axis;
	up.normalize();
	const core::vector3df forward = (camPos - center).normalize();
	const core::vector3df right = up.crossProduct(forward).normalize();

	// correct look vector
	const core::vector3df look = right.crossProduct(up);

	// rotate from to
	// axis multiplication by sin
	const core::vector3df vs = look.crossProduct(from);

	// cosine angle
	const f32 ca = from.dotProduct(look);

	core::vector3df vt(up * (1.f - ca));

	M[0] = static_cast<T>(vt.X * up.X + ca);
	M[5] = static_cast<T>(vt.Y * up.Y + ca);
	M[10] = static_cast<T>(vt.Z * up.Z + ca);

	vt.X *= up.Y;
	vt.Z *= up.X;
	vt.Y *= up.Z;

	M[1] = static_cast<T>(vt.X - vs.Z);
	M[2] = static_cast<T>(vt.Z + vs.Y);
	M[3] = 0;

	M[4] = static_cast<T>(vt.X + vs.Z);
	M[6] = static_cast<T>(vt.Y - vs.X);
	M[7] = 0;

	M[8] = static_cast<T>(vt.Z - vs.Y);
	M[9] = static_cast<T>(vt.Y + vs.X);
	M[11] = 0;

	setRotationCenter(center, translation);
}

//! Builds a combined matrix which translate to a center before rotation and translate afterward
template <class T>
inline void CMatrix4<T>::setRotationCenter(const core::vector3df &center, const core::vector3df &translation)
{
	M[12] = -M[0] * center.X - M[4] * center.Y - M[8] * center.Z + (center.X - translation.X);
	M[13] = -M[1] * center.X - M[5] * center.Y - M[9] * center.Z + (center.Y - translation.Y);
	M[14] = -M[2] * center.X - M[6] * center.Y - M[10] * center.Z + (center.Z - translation.Z);
	M[15] = (T)1.0;
#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
}

/*!
	Generate texture coordinates as linear functions so that:
		u = Ux*x + Uy*y + Uz*z + Uw
		v = Vx*x + Vy*y + Vz*z + Vw
	The matrix M for this case is:
		Ux  Vx  0  0
		Uy  Vy  0  0
		Uz  Vz  0  0
		Uw  Vw  0  0
*/

template <class T>
inline CMatrix4<T> &CMatrix4<T>::buildTextureTransform(f32 rotateRad,
		const core::vector2df &rotatecenter,
		const core::vector2df &translate,
		const core::vector2df &scale)
{
	const f32 c = cosf(rotateRad);
	const f32 s = sinf(rotateRad);

	M[0] = (T)(c * scale.X);
	M[1] = (T)(s * scale.Y);
	M[2] = 0;
	M[3] = 0;

	M[4] = (T)(-s * scale.X);
	M[5] = (T)(c * scale.Y);
	M[6] = 0;
	M[7] = 0;

	M[8] = (T)(c * scale.X * rotatecenter.X + -s * rotatecenter.Y + translate.X);
	M[9] = (T)(s * scale.Y * rotatecenter.X + c * rotatecenter.Y + translate.Y);
	M[10] = 1;
	M[11] = 0;

	M[12] = 0;
	M[13] = 0;
	M[14] = 0;
	M[15] = 1;
#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
	return *this;
}

// rotate about z axis, center ( 0.5, 0.5 )
template <class T>
inline CMatrix4<T> &CMatrix4<T>::setTextureRotationCenter(f32 rotateRad)
{
	const f32 c = cosf(rotateRad);
	const f32 s = sinf(rotateRad);
	M[0] = (T)c;
	M[1] = (T)s;

	M[4] = (T)-s;
	M[5] = (T)c;

	M[8] = (T)(0.5f * (s - c) + 0.5f);
	M[9] = (T)(-0.5f * (s + c) + 0.5f);

#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = definitelyIdentityMatrix && (rotateRad == 0.0f);
#endif
	return *this;
}

template <class T>
inline CMatrix4<T> &CMatrix4<T>::setTextureTranslate(f32 x, f32 y)
{
	M[8] = (T)x;
	M[9] = (T)y;

#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = definitelyIdentityMatrix && (x == 0.0f) && (y == 0.0f);
#endif
	return *this;
}

template <class T>
inline void CMatrix4<T>::getTextureTranslate(f32 &x, f32 &y) const
{
	x = (f32)M[8];
	y = (f32)M[9];
}

template <class T>
inline CMatrix4<T> &CMatrix4<T>::setTextureTranslateTransposed(f32 x, f32 y)
{
	M[2] = (T)x;
	M[6] = (T)y;

#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = definitelyIdentityMatrix && (x == 0.0f) && (y == 0.0f);
#endif
	return *this;
}

template <class T>
inline CMatrix4<T> &CMatrix4<T>::setTextureScale(f32 sx, f32 sy)
{
	M[0] = (T)sx;
	M[5] = (T)sy;
#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = definitelyIdentityMatrix && (sx == 1.0f) && (sy == 1.0f);
#endif
	return *this;
}

template <class T>
inline void CMatrix4<T>::getTextureScale(f32 &sx, f32 &sy) const
{
	sx = (f32)M[0];
	sy = (f32)M[5];
}

template <class T>
inline CMatrix4<T> &CMatrix4<T>::setTextureScaleCenter(f32 sx, f32 sy)
{
	M[0] = (T)sx;
	M[5] = (T)sy;
	M[8] = (T)(0.5f - 0.5f * sx);
	M[9] = (T)(0.5f - 0.5f * sy);

#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = definitelyIdentityMatrix && (sx == 1.0f) && (sy == 1.0f);
#endif
	return *this;
}

// sets all matrix data members at once
template <class T>
inline CMatrix4<T> &CMatrix4<T>::setM(const T *data)
{
	memcpy(M, data, 16 * sizeof(T));

#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = false;
#endif
	return *this;
}

// sets if the matrix is definitely identity matrix
template <class T>
inline void CMatrix4<T>::setDefinitelyIdentityMatrix(bool isDefinitelyIdentityMatrix)
{
#if defined(USE_MATRIX_TEST)
	definitelyIdentityMatrix = isDefinitelyIdentityMatrix;
#else
	(void)isDefinitelyIdentityMatrix; // prevent compiler warning
#endif
}

// gets if the matrix is definitely identity matrix
template <class T>
inline bool CMatrix4<T>::getDefinitelyIdentityMatrix() const
{
#if defined(USE_MATRIX_TEST)
	return definitelyIdentityMatrix;
#else
	return false;
#endif
}

//! Compare two matrices using the equal method
template <class T>
inline bool CMatrix4<T>::equals(const core::CMatrix4<T> &other, const T tolerance) const
{
#if defined(USE_MATRIX_TEST)
	if (definitelyIdentityMatrix && other.definitelyIdentityMatrix)
		return true;
#endif
	for (s32 i = 0; i < 16; ++i)
		if (!core::equals(M[i], other.M[i], tolerance))
			return false;

	return true;
}

// Multiply by scalar.
template <class T>
inline CMatrix4<T> operator*(const T scalar, const CMatrix4<T> &mat)
{
	return mat * scalar;
}

//! Typedef for f32 matrix
typedef CMatrix4<f32> matrix4;

//! global const identity matrix
IRRLICHT_API extern const matrix4 IdentityMatrix;

} // end namespace core
} // end namespace irr