assimp/include/assimp/matrix4x4.inl

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/** @file matrix4x4.inl
 *  @brief Inline implementation of the 4x4 matrix operators
 */
#pragma once
#ifndef AI_MATRIX4X4_INL_INC
#define AI_MATRIX4X4_INL_INC

#ifdef __cplusplus

#include "matrix4x4.h"
#include "matrix3x3.h"
#include "quaternion.h"
#include "MathFunctions.h"

#include <algorithm>
#include <limits>
#include <cmath>

// ----------------------------------------------------------------------------------------
template <typename TReal>
aiMatrix4x4t<TReal>::aiMatrix4x4t() AI_NO_EXCEPT :
        a1(1.0f), a2(), a3(), a4(),
        b1(), b2(1.0f), b3(), b4(),
        c1(), c2(), c3(1.0f), c4(),
        d1(), d2(), d3(), d4(1.0f) {
    // empty
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
aiMatrix4x4t<TReal>::aiMatrix4x4t (TReal _a1, TReal _a2, TReal _a3, TReal _a4,
              TReal _b1, TReal _b2, TReal _b3, TReal _b4,
              TReal _c1, TReal _c2, TReal _c3, TReal _c4,
              TReal _d1, TReal _d2, TReal _d3, TReal _d4) :
        a1(_a1), a2(_a2), a3(_a3), a4(_a4),
        b1(_b1), b2(_b2), b3(_b3), b4(_b4),
        c1(_c1), c2(_c2), c3(_c3), c4(_c4),
        d1(_d1), d2(_d2), d3(_d3), d4(_d4) {
    // empty
}

// ------------------------------------------------------------------------------------------------
template <typename TReal>
template <typename TOther>
aiMatrix4x4t<TReal>::operator aiMatrix4x4t<TOther> () const {
    return aiMatrix4x4t<TOther>(static_cast<TOther>(a1),static_cast<TOther>(a2),static_cast<TOther>(a3),static_cast<TOther>(a4),
        static_cast<TOther>(b1),static_cast<TOther>(b2),static_cast<TOther>(b3),static_cast<TOther>(b4),
        static_cast<TOther>(c1),static_cast<TOther>(c2),static_cast<TOther>(c3),static_cast<TOther>(c4),
        static_cast<TOther>(d1),static_cast<TOther>(d2),static_cast<TOther>(d3),static_cast<TOther>(d4));
}


// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
aiMatrix4x4t<TReal>::aiMatrix4x4t (const aiMatrix3x3t<TReal>& m) {
    a1 = m.a1; a2 = m.a2; a3 = m.a3; a4 = static_cast<TReal>(0.0);
    b1 = m.b1; b2 = m.b2; b3 = m.b3; b4 = static_cast<TReal>(0.0);
    c1 = m.c1; c2 = m.c2; c3 = m.c3; c4 = static_cast<TReal>(0.0);
    d1 = static_cast<TReal>(0.0); d2 = static_cast<TReal>(0.0); d3 = static_cast<TReal>(0.0); d4 = static_cast<TReal>(1.0);
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
aiMatrix4x4t<TReal>::aiMatrix4x4t (const aiVector3t<TReal>& scaling, const aiQuaterniont<TReal>& rotation, const aiVector3t<TReal>& position) {
    // build a 3x3 rotation matrix
    aiMatrix3x3t<TReal> m = rotation.GetMatrix();

    a1 = m.a1 * scaling.x;
    a2 = m.a2 * scaling.x;
    a3 = m.a3 * scaling.x;
    a4 = position.x;

    b1 = m.b1 * scaling.y;
    b2 = m.b2 * scaling.y;
    b3 = m.b3 * scaling.y;
    b4 = position.y;

    c1 = m.c1 * scaling.z;
    c2 = m.c2 * scaling.z;
    c3 = m.c3 * scaling.z;
    c4= position.z;

    d1 = static_cast<TReal>(0.0);
    d2 = static_cast<TReal>(0.0);
    d3 = static_cast<TReal>(0.0);
    d4 = static_cast<TReal>(1.0);
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
aiMatrix4x4t<TReal>& aiMatrix4x4t<TReal>::operator *= (const aiMatrix4x4t<TReal>& m) {
    *this = aiMatrix4x4t<TReal>(
        m.a1 * a1 + m.b1 * a2 + m.c1 * a3 + m.d1 * a4,
        m.a2 * a1 + m.b2 * a2 + m.c2 * a3 + m.d2 * a4,
        m.a3 * a1 + m.b3 * a2 + m.c3 * a3 + m.d3 * a4,
        m.a4 * a1 + m.b4 * a2 + m.c4 * a3 + m.d4 * a4,
        m.a1 * b1 + m.b1 * b2 + m.c1 * b3 + m.d1 * b4,
        m.a2 * b1 + m.b2 * b2 + m.c2 * b3 + m.d2 * b4,
        m.a3 * b1 + m.b3 * b2 + m.c3 * b3 + m.d3 * b4,
        m.a4 * b1 + m.b4 * b2 + m.c4 * b3 + m.d4 * b4,
        m.a1 * c1 + m.b1 * c2 + m.c1 * c3 + m.d1 * c4,
        m.a2 * c1 + m.b2 * c2 + m.c2 * c3 + m.d2 * c4,
        m.a3 * c1 + m.b3 * c2 + m.c3 * c3 + m.d3 * c4,
        m.a4 * c1 + m.b4 * c2 + m.c4 * c3 + m.d4 * c4,
        m.a1 * d1 + m.b1 * d2 + m.c1 * d3 + m.d1 * d4,
        m.a2 * d1 + m.b2 * d2 + m.c2 * d3 + m.d2 * d4,
        m.a3 * d1 + m.b3 * d2 + m.c3 * d3 + m.d3 * d4,
        m.a4 * d1 + m.b4 * d2 + m.c4 * d3 + m.d4 * d4);
    return *this;
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE aiMatrix4x4t<TReal> aiMatrix4x4t<TReal>::operator* (const TReal& aFloat) const {
    aiMatrix4x4t<TReal> temp(
        a1 * aFloat,
        a2 * aFloat,
        a3 * aFloat,
        a4 * aFloat,
        b1 * aFloat,
        b2 * aFloat,
        b3 * aFloat,
        b4 * aFloat,
        c1 * aFloat,
        c2 * aFloat,
        c3 * aFloat,
        c4 * aFloat,
        d1 * aFloat,
        d2 * aFloat,
        d3 * aFloat,
        d4 * aFloat);
    return temp;
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
aiMatrix4x4t<TReal> aiMatrix4x4t<TReal>::operator+ (const aiMatrix4x4t<TReal>& m) const {
    aiMatrix4x4t<TReal> temp(
        m.a1 + a1,
        m.a2 + a2,
        m.a3 + a3,
        m.a4 + a4,
        m.b1 + b1,
        m.b2 + b2,
        m.b3 + b3,
        m.b4 + b4,
        m.c1 + c1,
        m.c2 + c2,
        m.c3 + c3,
        m.c4 + c4,
        m.d1 + d1,
        m.d2 + d2,
        m.d3 + d3,
        m.d4 + d4);
    return temp;
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
aiMatrix4x4t<TReal> aiMatrix4x4t<TReal>::operator* (const aiMatrix4x4t<TReal>& m) const {
    aiMatrix4x4t<TReal> temp( *this);
    temp *= m;
    return temp;
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE aiMatrix4x4t<TReal>& aiMatrix4x4t<TReal>::Transpose() {
    // (TReal&) don't remove, GCC complains cause of packed fields
    std::swap( (TReal&)b1, (TReal&)a2);
    std::swap( (TReal&)c1, (TReal&)a3);
    std::swap( (TReal&)c2, (TReal&)b3);
    std::swap( (TReal&)d1, (TReal&)a4);
    std::swap( (TReal&)d2, (TReal&)b4);
    std::swap( (TReal&)d3, (TReal&)c4);
    return *this;
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
TReal aiMatrix4x4t<TReal>::Determinant() const {
    return a1*b2*c3*d4 - a1*b2*c4*d3 + a1*b3*c4*d2 - a1*b3*c2*d4
        + a1*b4*c2*d3 - a1*b4*c3*d2 - a2*b3*c4*d1 + a2*b3*c1*d4
        - a2*b4*c1*d3 + a2*b4*c3*d1 - a2*b1*c3*d4 + a2*b1*c4*d3
        + a3*b4*c1*d2 - a3*b4*c2*d1 + a3*b1*c2*d4 - a3*b1*c4*d2
        + a3*b2*c4*d1 - a3*b2*c1*d4 - a4*b1*c2*d3 + a4*b1*c3*d2
        - a4*b2*c3*d1 + a4*b2*c1*d3 - a4*b3*c1*d2 + a4*b3*c2*d1;
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
aiMatrix4x4t<TReal>& aiMatrix4x4t<TReal>::Inverse() {
    // Compute the reciprocal determinant
    const TReal det = Determinant();
    if(det == static_cast<TReal>(0.0))
    {
        // Matrix not invertible. Setting all elements to nan is not really
        // correct in a mathematical sense but it is easy to debug for the
        // programmer.
        const TReal nan = std::numeric_limits<TReal>::quiet_NaN();
        *this = aiMatrix4x4t<TReal>(
            nan,nan,nan,nan,
            nan,nan,nan,nan,
            nan,nan,nan,nan,
            nan,nan,nan,nan);

        return *this;
    }

    const TReal invdet = static_cast<TReal>(1.0) / det;

    aiMatrix4x4t<TReal> res;
    res.a1 = invdet  * (b2 * (c3 * d4 - c4 * d3) + b3 * (c4 * d2 - c2 * d4) + b4 * (c2 * d3 - c3 * d2));
    res.a2 = -invdet * (a2 * (c3 * d4 - c4 * d3) + a3 * (c4 * d2 - c2 * d4) + a4 * (c2 * d3 - c3 * d2));
    res.a3 = invdet  * (a2 * (b3 * d4 - b4 * d3) + a3 * (b4 * d2 - b2 * d4) + a4 * (b2 * d3 - b3 * d2));
    res.a4 = -invdet * (a2 * (b3 * c4 - b4 * c3) + a3 * (b4 * c2 - b2 * c4) + a4 * (b2 * c3 - b3 * c2));
    res.b1 = -invdet * (b1 * (c3 * d4 - c4 * d3) + b3 * (c4 * d1 - c1 * d4) + b4 * (c1 * d3 - c3 * d1));
    res.b2 = invdet  * (a1 * (c3 * d4 - c4 * d3) + a3 * (c4 * d1 - c1 * d4) + a4 * (c1 * d3 - c3 * d1));
    res.b3 = -invdet * (a1 * (b3 * d4 - b4 * d3) + a3 * (b4 * d1 - b1 * d4) + a4 * (b1 * d3 - b3 * d1));
    res.b4 = invdet  * (a1 * (b3 * c4 - b4 * c3) + a3 * (b4 * c1 - b1 * c4) + a4 * (b1 * c3 - b3 * c1));
    res.c1 = invdet  * (b1 * (c2 * d4 - c4 * d2) + b2 * (c4 * d1 - c1 * d4) + b4 * (c1 * d2 - c2 * d1));
    res.c2 = -invdet * (a1 * (c2 * d4 - c4 * d2) + a2 * (c4 * d1 - c1 * d4) + a4 * (c1 * d2 - c2 * d1));
    res.c3 = invdet  * (a1 * (b2 * d4 - b4 * d2) + a2 * (b4 * d1 - b1 * d4) + a4 * (b1 * d2 - b2 * d1));
    res.c4 = -invdet * (a1 * (b2 * c4 - b4 * c2) + a2 * (b4 * c1 - b1 * c4) + a4 * (b1 * c2 - b2 * c1));
    res.d1 = -invdet * (b1 * (c2 * d3 - c3 * d2) + b2 * (c3 * d1 - c1 * d3) + b3 * (c1 * d2 - c2 * d1));
    res.d2 = invdet  * (a1 * (c2 * d3 - c3 * d2) + a2 * (c3 * d1 - c1 * d3) + a3 * (c1 * d2 - c2 * d1));
    res.d3 = -invdet * (a1 * (b2 * d3 - b3 * d2) + a2 * (b3 * d1 - b1 * d3) + a3 * (b1 * d2 - b2 * d1));
    res.d4 = invdet  * (a1 * (b2 * c3 - b3 * c2) + a2 * (b3 * c1 - b1 * c3) + a3 * (b1 * c2 - b2 * c1));
    *this = res;

    return *this;
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
TReal* aiMatrix4x4t<TReal>::operator[](unsigned int p_iIndex) {
    if (p_iIndex > 3) {
        return nullptr;
    }
    switch ( p_iIndex ) {
        case 0:
            return &a1;
        case 1:
            return &b1;
        case 2:
            return &c1;
        case 3:
            return &d1;
        default:
            break;
    }
    return &a1;
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
const TReal* aiMatrix4x4t<TReal>::operator[](unsigned int p_iIndex) const {
    if (p_iIndex > 3) {
        return nullptr;
    }

    switch ( p_iIndex ) {
        case 0:
            return &a1;
        case 1:
            return &b1;
        case 2:
            return &c1;
        case 3:
            return &d1;
        default:
            break;
    }
    return &a1;
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
bool aiMatrix4x4t<TReal>::operator== (const aiMatrix4x4t<TReal>& m) const {
    return (a1 == m.a1 && a2 == m.a2 && a3 == m.a3 && a4 == m.a4 &&
            b1 == m.b1 && b2 == m.b2 && b3 == m.b3 && b4 == m.b4 &&
            c1 == m.c1 && c2 == m.c2 && c3 == m.c3 && c4 == m.c4 &&
            d1 == m.d1 && d2 == m.d2 && d3 == m.d3 && d4 == m.d4);
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
bool aiMatrix4x4t<TReal>::operator!= (const aiMatrix4x4t<TReal>& m) const {
    return !(*this == m);
}

// ---------------------------------------------------------------------------
template<typename TReal>
AI_FORCE_INLINE
bool aiMatrix4x4t<TReal>::Equal(const aiMatrix4x4t<TReal>& m, TReal epsilon) const {
    return
        std::abs(a1 - m.a1) <= epsilon &&
        std::abs(a2 - m.a2) <= epsilon &&
        std::abs(a3 - m.a3) <= epsilon &&
        std::abs(a4 - m.a4) <= epsilon &&
        std::abs(b1 - m.b1) <= epsilon &&
        std::abs(b2 - m.b2) <= epsilon &&
        std::abs(b3 - m.b3) <= epsilon &&
        std::abs(b4 - m.b4) <= epsilon &&
        std::abs(c1 - m.c1) <= epsilon &&
        std::abs(c2 - m.c2) <= epsilon &&
        std::abs(c3 - m.c3) <= epsilon &&
        std::abs(c4 - m.c4) <= epsilon &&
        std::abs(d1 - m.d1) <= epsilon &&
        std::abs(d2 - m.d2) <= epsilon &&
        std::abs(d3 - m.d3) <= epsilon &&
        std::abs(d4 - m.d4) <= epsilon;
}

// ----------------------------------------------------------------------------------------

#define ASSIMP_MATRIX4_4_DECOMPOSE_PART		\
	const aiMatrix4x4t<TReal>& _this = *this;/* Create alias for conveniance. */ \
	\
	/* extract translation */ \
	pPosition.x = _this[0][3]; \
	pPosition.y = _this[1][3]; \
	pPosition.z = _this[2][3]; \
	\
	/* extract the columns of the matrix. */ \
	aiVector3t<TReal> vCols[3] = { \
		aiVector3t<TReal>(_this[0][0],_this[1][0],_this[2][0]), \
		aiVector3t<TReal>(_this[0][1],_this[1][1],_this[2][1]), \
		aiVector3t<TReal>(_this[0][2],_this[1][2],_this[2][2]) \
	}; \
	\
	/* extract the scaling factors */ \
	pScaling.x = vCols[0].Length(); \
	pScaling.y = vCols[1].Length(); \
	pScaling.z = vCols[2].Length(); \
	\
	/* and the sign of the scaling */ \
	if (Determinant() < 0) pScaling = -pScaling; \
	\
	/* and remove all scaling from the matrix */ \
	if(pScaling.x) vCols[0] /= pScaling.x; \
	if(pScaling.y) vCols[1] /= pScaling.y; \
	if(pScaling.z) vCols[2] /= pScaling.z; \
	\
	do {} while(false)

template <typename TReal>
AI_FORCE_INLINE
void aiMatrix4x4t<TReal>::Decompose (aiVector3t<TReal>& pScaling, aiQuaterniont<TReal>& pRotation,
        aiVector3t<TReal>& pPosition) const {
	ASSIMP_MATRIX4_4_DECOMPOSE_PART;

    // build a 3x3 rotation matrix
    aiMatrix3x3t<TReal> m(vCols[0].x,vCols[1].x,vCols[2].x,
        vCols[0].y,vCols[1].y,vCols[2].y,
        vCols[0].z,vCols[1].z,vCols[2].z);

    // and generate the rotation quaternion from it
    pRotation = aiQuaterniont<TReal>(m);
}

template <typename TReal>
AI_FORCE_INLINE
void aiMatrix4x4t<TReal>::Decompose(aiVector3t<TReal>& pScaling, aiVector3t<TReal>& pRotation, aiVector3t<TReal>& pPosition) const {
	ASSIMP_MATRIX4_4_DECOMPOSE_PART;

    /*
    assuming a right-handed coordinate system
    and post-multiplication of column vectors,
    the rotation matrix for an euler XYZ rotation is M = Rz * Ry * Rx.
    combining gives:

        |  CE  BDE-AF  ADE+BF  0  |
    M = |  CF  BDF+AE  ADF-BE  0  |
        |  -D    CB      AC    0  |
        |   0     0       0    1  |

    where
	A = cos(angle_x), B = sin(angle_x);
	C = cos(angle_y), D = sin(angle_y);
	E = cos(angle_z), F = sin(angle_z);
	*/

	// Use a small epsilon to solve floating-point inaccuracies
    const TReal epsilon = Assimp::Math::getEpsilon<TReal>();

	pRotation.y  = std::asin(-vCols[0].z);// D. Angle around oY.

	TReal C = std::cos(pRotation.y);

	if(std::fabs(C) > epsilon)
	{
		// Finding angle around oX.
		TReal tan_x = vCols[2].z / C;// A
		TReal tan_y = vCols[1].z / C;// B

		pRotation.x = std::atan2(tan_y, tan_x);
		// Finding angle around oZ.
		tan_x = vCols[0].x / C;// E
		tan_y = vCols[0].y / C;// F
		pRotation.z = std::atan2(tan_y, tan_x);
	}
	else
	{// oY is fixed.
		pRotation.x = 0;// Set angle around oX to 0. => A == 1, B == 0, C == 0, D == 1.

		// And finding angle around oZ.
		TReal tan_x =  vCols[1].y;// BDF+AE => E
		TReal tan_y = -vCols[1].x;// BDE-AF => F

		pRotation.z = std::atan2(tan_y, tan_x);
	}
}

#undef ASSIMP_MATRIX4_4_DECOMPOSE_PART

template <typename TReal>
AI_FORCE_INLINE
void aiMatrix4x4t<TReal>::Decompose(aiVector3t<TReal>& pScaling, aiVector3t<TReal>& pRotationAxis, TReal& pRotationAngle,
											aiVector3t<TReal>& pPosition) const {
    aiQuaterniont<TReal> pRotation;

	Decompose(pScaling, pRotation, pPosition);
	pRotation.Normalize();

	TReal angle_cos = pRotation.w;
	TReal angle_sin = std::sqrt(1.0f - angle_cos * angle_cos);

	pRotationAngle = std::acos(angle_cos) * 2;

	// Use a small epsilon to solve floating-point inaccuracies
    const TReal epsilon = 10e-3f;

	if(std::fabs(angle_sin) < epsilon) angle_sin = 1;

	pRotationAxis.x = pRotation.x / angle_sin;
	pRotationAxis.y = pRotation.y / angle_sin;
	pRotationAxis.z = pRotation.z / angle_sin;
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
void aiMatrix4x4t<TReal>::DecomposeNoScaling (aiQuaterniont<TReal>& rotation,
        aiVector3t<TReal>& position) const {
    const aiMatrix4x4t<TReal>& _this = *this;

    // extract translation
    position.x = _this[0][3];
    position.y = _this[1][3];
    position.z = _this[2][3];

    // extract rotation
    rotation = aiQuaterniont<TReal>((aiMatrix3x3t<TReal>)_this);
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
aiMatrix4x4t<TReal>& aiMatrix4x4t<TReal>::FromEulerAnglesXYZ(const aiVector3t<TReal>& blubb) {
    return FromEulerAnglesXYZ(blubb.x,blubb.y,blubb.z);
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
aiMatrix4x4t<TReal>& aiMatrix4x4t<TReal>::FromEulerAnglesXYZ(TReal x, TReal y, TReal z) {
    aiMatrix4x4t<TReal>& _this = *this;

    TReal cx = std::cos(x);
    TReal sx = std::sin(x);
    TReal cy = std::cos(y);
    TReal sy = std::sin(y);
    TReal cz = std::cos(z);
    TReal sz = std::sin(z);

    // mz*my*mx
    _this.a1 = cz * cy;
    _this.a2 = cz * sy * sx - sz * cx;
    _this.a3 = sz * sx + cz * sy * cx;

    _this.b1 = sz * cy;
    _this.b2 = cz * cx + sz * sy * sx;
    _this.b3 = sz * sy * cx - cz * sx;

    _this.c1 = -sy;
    _this.c2 = cy * sx;
    _this.c3 = cy * cx;

    return *this;
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
bool aiMatrix4x4t<TReal>::IsIdentity() const {
    // Use a small epsilon to solve floating-point inaccuracies
    const static TReal epsilon = 10e-3f;

    return (a2 <= epsilon && a2 >= -epsilon &&
            a3 <= epsilon && a3 >= -epsilon &&
            a4 <= epsilon && a4 >= -epsilon &&
            b1 <= epsilon && b1 >= -epsilon &&
            b3 <= epsilon && b3 >= -epsilon &&
            b4 <= epsilon && b4 >= -epsilon &&
            c1 <= epsilon && c1 >= -epsilon &&
            c2 <= epsilon && c2 >= -epsilon &&
            c4 <= epsilon && c4 >= -epsilon &&
            d1 <= epsilon && d1 >= -epsilon &&
            d2 <= epsilon && d2 >= -epsilon &&
            d3 <= epsilon && d3 >= -epsilon &&
            a1 <= 1.f+epsilon && a1 >= 1.f-epsilon &&
            b2 <= 1.f+epsilon && b2 >= 1.f-epsilon &&
            c3 <= 1.f+epsilon && c3 >= 1.f-epsilon &&
            d4 <= 1.f+epsilon && d4 >= 1.f-epsilon);
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
aiMatrix4x4t<TReal>& aiMatrix4x4t<TReal>::RotationX(TReal a, aiMatrix4x4t<TReal>& out) {
    /*
         |  1  0       0       0 |
     M = |  0  cos(A) -sin(A)  0 |
         |  0  sin(A)  cos(A)  0 |
         |  0  0       0       1 |  */
    out = aiMatrix4x4t<TReal>();
    out.b2 = out.c3 = std::cos(a);
    out.b3 = -(out.c2 = std::sin(a));
    return out;
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
aiMatrix4x4t<TReal>& aiMatrix4x4t<TReal>::RotationY(TReal a, aiMatrix4x4t<TReal>& out) {
    /*
         |  cos(A)  0   sin(A)  0 |
     M = |  0       1   0       0 |
         | -sin(A)  0   cos(A)  0 |
         |  0       0   0       1 |
        */
    out = aiMatrix4x4t<TReal>();
    out.a1 = out.c3 = std::cos(a);
    out.c1 = -(out.a3 = std::sin(a));
    return out;
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
aiMatrix4x4t<TReal>& aiMatrix4x4t<TReal>::RotationZ(TReal a, aiMatrix4x4t<TReal>& out) {
    /*
         |  cos(A)  -sin(A)   0   0 |
     M = |  sin(A)   cos(A)   0   0 |
         |  0        0        1   0 |
         |  0        0        0   1 |   */
    out = aiMatrix4x4t<TReal>();
    out.a1 = out.b2 = std::cos(a);
    out.a2 = -(out.b1 = std::sin(a));
    return out;
}

// ----------------------------------------------------------------------------------------
// Returns a rotation matrix for a rotation around an arbitrary axis.
template <typename TReal>
AI_FORCE_INLINE
aiMatrix4x4t<TReal>& aiMatrix4x4t<TReal>::Rotation( TReal a, const aiVector3t<TReal>& axis, aiMatrix4x4t<TReal>& out) {
    TReal c = std::cos( a), s = std::sin( a), t = 1 - c;
    TReal x = axis.x, y = axis.y, z = axis.z;

    // Many thanks to MathWorld and Wikipedia
    out.a1 = t*x*x + c;   out.a2 = t*x*y - s*z; out.a3 = t*x*z + s*y;
    out.b1 = t*x*y + s*z; out.b2 = t*y*y + c;   out.b3 = t*y*z - s*x;
    out.c1 = t*x*z - s*y; out.c2 = t*y*z + s*x; out.c3 = t*z*z + c;
    out.a4 = out.b4 = out.c4 = static_cast<TReal>(0.0);
    out.d1 = out.d2 = out.d3 = static_cast<TReal>(0.0);
    out.d4 = static_cast<TReal>(1.0);

    return out;
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE aiMatrix4x4t<TReal>& aiMatrix4x4t<TReal>::Translation( const aiVector3t<TReal>& v, aiMatrix4x4t<TReal>& out) {
    out = aiMatrix4x4t<TReal>();
    out.a4 = v.x;
    out.b4 = v.y;
    out.c4 = v.z;
    return out;
}

// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
aiMatrix4x4t<TReal>& aiMatrix4x4t<TReal>::Scaling( const aiVector3t<TReal>& v, aiMatrix4x4t<TReal>& out) {
    out = aiMatrix4x4t<TReal>();
    out.a1 = v.x;
    out.b2 = v.y;
    out.c3 = v.z;
    return out;
}

// ----------------------------------------------------------------------------------------
/** A function for creating a rotation matrix that rotates a vector called
 * "from" into another vector called "to".
 * Input : from[3], to[3] which both must be *normalized* non-zero vectors
 * Output: mtx[3][3] -- a 3x3 matrix in colum-major form
 * Authors: Tomas Möller, John Hughes
 *          "Efficiently Building a Matrix to Rotate One Vector to Another"
 *          Journal of Graphics Tools, 4(4):1-4, 1999
 */
// ----------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
aiMatrix4x4t<TReal>& aiMatrix4x4t<TReal>::FromToMatrix(const aiVector3t<TReal>& from,
        const aiVector3t<TReal>& to, aiMatrix4x4t<TReal>& mtx) {
    aiMatrix3x3t<TReal> m3;
    aiMatrix3x3t<TReal>::FromToMatrix(from,to,m3);
    mtx = aiMatrix4x4t<TReal>(m3);
    return mtx;
}

#endif // __cplusplus
#endif // AI_MATRIX4X4_INL_INC