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btMatrix3x3.h

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/*
Copyright (c) 2003-2006 Gino van den Bergen / Erwin Coumans  http://continuousphysics.com/Bullet/

This software is provided 'as-is', without any express or implied warranty.
In no event will the authors be held liable for any damages arising from the use of this software.
Permission is granted to anyone to use this software for any purpose, 
including commercial applications, and to alter it and redistribute it freely, 
subject to the following restrictions:

1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required.
2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
3. This notice may not be removed or altered from any source distribution.
*/


#ifndef BT_MATRIX3x3_H
#define BT_MATRIX3x3_H

#include "btVector3.h"
#include "btQuaternion.h"

#ifdef BT_USE_DOUBLE_PRECISION
#define btMatrix3x3Data btMatrix3x3DoubleData 
#else
#define btMatrix3x3Data btMatrix3x3FloatData
#endif //BT_USE_DOUBLE_PRECISION


class btMatrix3x3 {

        btVector3 m_el[3];

public:
        btMatrix3x3 () {}

        //              explicit btMatrix3x3(const btScalar *m) { setFromOpenGLSubMatrix(m); }

        explicit btMatrix3x3(const btQuaternion& q) { setRotation(q); }
        /*
        template <typename btScalar>
        Matrix3x3(const btScalar& yaw, const btScalar& pitch, const btScalar& roll)
        { 
        setEulerYPR(yaw, pitch, roll);
        }
        */
        btMatrix3x3(const btScalar& xx, const btScalar& xy, const btScalar& xz,
                const btScalar& yx, const btScalar& yy, const btScalar& yz,
                const btScalar& zx, const btScalar& zy, const btScalar& zz)
        { 
                setValue(xx, xy, xz, 
                        yx, yy, yz, 
                        zx, zy, zz);
        }
        SIMD_FORCE_INLINE btMatrix3x3 (const btMatrix3x3& other)
        {
                m_el[0] = other.m_el[0];
                m_el[1] = other.m_el[1];
                m_el[2] = other.m_el[2];
        }
        SIMD_FORCE_INLINE btMatrix3x3& operator=(const btMatrix3x3& other)
        {
                m_el[0] = other.m_el[0];
                m_el[1] = other.m_el[1];
                m_el[2] = other.m_el[2];
                return *this;
        }

        SIMD_FORCE_INLINE btVector3 getColumn(int i) const
        {
                return btVector3(m_el[0][i],m_el[1][i],m_el[2][i]);
        }


        SIMD_FORCE_INLINE const btVector3& getRow(int i) const
        {
                btFullAssert(0 <= i && i < 3);
                return m_el[i];
        }

        SIMD_FORCE_INLINE btVector3&  operator[](int i)
        { 
                btFullAssert(0 <= i && i < 3);
                return m_el[i]; 
        }

        SIMD_FORCE_INLINE const btVector3& operator[](int i) const
        {
                btFullAssert(0 <= i && i < 3);
                return m_el[i]; 
        }

        btMatrix3x3& operator*=(const btMatrix3x3& m); 

        void setFromOpenGLSubMatrix(const btScalar *m)
        {
                m_el[0].setValue(m[0],m[4],m[8]);
                m_el[1].setValue(m[1],m[5],m[9]);
                m_el[2].setValue(m[2],m[6],m[10]);

        }
        void setValue(const btScalar& xx, const btScalar& xy, const btScalar& xz, 
                const btScalar& yx, const btScalar& yy, const btScalar& yz, 
                const btScalar& zx, const btScalar& zy, const btScalar& zz)
        {
                m_el[0].setValue(xx,xy,xz);
                m_el[1].setValue(yx,yy,yz);
                m_el[2].setValue(zx,zy,zz);
        }

        void setRotation(const btQuaternion& q) 
        {
                btScalar d = q.length2();
                btFullAssert(d != btScalar(0.0));
                btScalar s = btScalar(2.0) / d;
                btScalar xs = q.x() * s,   ys = q.y() * s,   zs = q.z() * s;
                btScalar wx = q.w() * xs,  wy = q.w() * ys,  wz = q.w() * zs;
                btScalar xx = q.x() * xs,  xy = q.x() * ys,  xz = q.x() * zs;
                btScalar yy = q.y() * ys,  yz = q.y() * zs,  zz = q.z() * zs;
                setValue(btScalar(1.0) - (yy + zz), xy - wz, xz + wy,
                        xy + wz, btScalar(1.0) - (xx + zz), yz - wx,
                        xz - wy, yz + wx, btScalar(1.0) - (xx + yy));
        }


        void setEulerZYX(const btScalar& yaw, const btScalar& pitch, const btScalar& roll) __attribute__((deprecated))
        {
                setEulerYPR(yaw, pitch, roll);
        }

        void setEulerYPR(btScalar eulerZ, btScalar eulerY,btScalar eulerX)  { 
                btScalar ci ( btCos(eulerX)); 
                btScalar cj ( btCos(eulerY)); 
                btScalar ch ( btCos(eulerZ)); 
                btScalar si ( btSin(eulerX)); 
                btScalar sj ( btSin(eulerY)); 
                btScalar sh ( btSin(eulerZ)); 
                btScalar cc = ci * ch; 
                btScalar cs = ci * sh; 
                btScalar sc = si * ch; 
                btScalar ss = si * sh;

                setValue(cj * ch, sj * sc - cs, sj * cc + ss,
                        cj * sh, sj * ss + cc, sj * cs - sc, 
                        -sj,      cj * si,      cj * ci);
        }

        void setRPY(btScalar roll, btScalar pitch,btScalar yaw) { 
               setEulerYPR(yaw, pitch, roll);
        }

        void setIdentity()
        { 
                setValue(btScalar(1.0), btScalar(0.0), btScalar(0.0), 
                        btScalar(0.0), btScalar(1.0), btScalar(0.0), 
                        btScalar(0.0), btScalar(0.0), btScalar(1.0)); 
        }

        static const btMatrix3x3&       getIdentity()
        {
                static const btMatrix3x3 identityMatrix(btScalar(1.0), btScalar(0.0), btScalar(0.0), 
                        btScalar(0.0), btScalar(1.0), btScalar(0.0), 
                        btScalar(0.0), btScalar(0.0), btScalar(1.0));
                return identityMatrix;
        }

        void getOpenGLSubMatrix(btScalar *m) const 
        {
                m[0]  = btScalar(m_el[0].x()); 
                m[1]  = btScalar(m_el[1].x());
                m[2]  = btScalar(m_el[2].x());
                m[3]  = btScalar(0.0); 
                m[4]  = btScalar(m_el[0].y());
                m[5]  = btScalar(m_el[1].y());
                m[6]  = btScalar(m_el[2].y());
                m[7]  = btScalar(0.0); 
                m[8]  = btScalar(m_el[0].z()); 
                m[9]  = btScalar(m_el[1].z());
                m[10] = btScalar(m_el[2].z());
                m[11] = btScalar(0.0); 
        }

        void getRotation(btQuaternion& q) const
        {
                btScalar trace = m_el[0].x() + m_el[1].y() + m_el[2].z();
                btScalar temp[4];

                if (trace > btScalar(0.0)) 
                {
                        btScalar s = btSqrt(trace + btScalar(1.0));
                        temp[3]=(s * btScalar(0.5));
                        s = btScalar(0.5) / s;

                        temp[0]=((m_el[2].y() - m_el[1].z()) * s);
                        temp[1]=((m_el[0].z() - m_el[2].x()) * s);
                        temp[2]=((m_el[1].x() - m_el[0].y()) * s);
                } 
                else 
                {
                        int i = m_el[0].x() < m_el[1].y() ? 
                                (m_el[1].y() < m_el[2].z() ? 2 : 1) :
                                (m_el[0].x() < m_el[2].z() ? 2 : 0); 
                        int j = (i + 1) % 3;  
                        int k = (i + 2) % 3;

                        btScalar s = btSqrt(m_el[i][i] - m_el[j][j] - m_el[k][k] + btScalar(1.0));
                        temp[i] = s * btScalar(0.5);
                        s = btScalar(0.5) / s;

                        temp[3] = (m_el[k][j] - m_el[j][k]) * s;
                        temp[j] = (m_el[j][i] + m_el[i][j]) * s;
                        temp[k] = (m_el[k][i] + m_el[i][k]) * s;
                }
                q.setValue(temp[0],temp[1],temp[2],temp[3]);
        }

        __attribute__((deprecated)) void getEulerZYX(btScalar& yaw, btScalar& pitch, btScalar& roll, unsigned int solution_number = 1) const
        {
                getEulerYPR(yaw, pitch, roll, solution_number);
        };


        void getEulerYPR(btScalar& yaw, btScalar& pitch, btScalar& roll, unsigned int solution_number = 1) const
        {
                struct Euler
                {
                        btScalar yaw;
                        btScalar pitch;
                        btScalar roll;
                };

                Euler euler_out;
                Euler euler_out2; //second solution
                //get the pointer to the raw data

                // Check that pitch is not at a singularity
                // Check that pitch is not at a singularity
                if (btFabs(m_el[2].x()) >= 1)
                {
                        euler_out.yaw = 0;
                        euler_out2.yaw = 0;
        
                        // From difference of angles formula
                        btScalar delta = btAtan2(m_el[2].y(),m_el[2].z());
                        if (m_el[2].x() < 0)  //gimbal locked down
                        {
                                euler_out.pitch = SIMD_PI / btScalar(2.0);
                                euler_out2.pitch = SIMD_PI / btScalar(2.0);
                                euler_out.roll = delta;
                                euler_out2.roll = delta;
                        }
                        else // gimbal locked up
                        {
                                euler_out.pitch = -SIMD_PI / btScalar(2.0);
                                euler_out2.pitch = -SIMD_PI / btScalar(2.0);
                                euler_out.roll = delta;
                                euler_out2.roll = delta;
                        }
                }
                else
                {
                        euler_out.pitch = - btAsin(m_el[2].x());
                        euler_out2.pitch = SIMD_PI - euler_out.pitch;

                        euler_out.roll = btAtan2(m_el[2].y()/btCos(euler_out.pitch), 
                                m_el[2].z()/btCos(euler_out.pitch));
                        euler_out2.roll = btAtan2(m_el[2].y()/btCos(euler_out2.pitch), 
                                m_el[2].z()/btCos(euler_out2.pitch));

                        euler_out.yaw = btAtan2(m_el[1].x()/btCos(euler_out.pitch), 
                                m_el[0].x()/btCos(euler_out.pitch));
                        euler_out2.yaw = btAtan2(m_el[1].x()/btCos(euler_out2.pitch), 
                                m_el[0].x()/btCos(euler_out2.pitch));
                }

                if (solution_number == 1)
                { 
                        yaw = euler_out.yaw; 
                        pitch = euler_out.pitch;
                        roll = euler_out.roll;
                }
                else
                { 
                        yaw = euler_out2.yaw; 
                        pitch = euler_out2.pitch;
                        roll = euler_out2.roll;
                }
        }

        void getRPY(btScalar& roll, btScalar& pitch, btScalar& yaw, unsigned int solution_number = 1) const
        {
        getEulerYPR(yaw, pitch, roll, solution_number);
        }

        btMatrix3x3 scaled(const btVector3& s) const
        {
                return btMatrix3x3(m_el[0].x() * s.x(), m_el[0].y() * s.y(), m_el[0].z() * s.z(),
                        m_el[1].x() * s.x(), m_el[1].y() * s.y(), m_el[1].z() * s.z(),
                        m_el[2].x() * s.x(), m_el[2].y() * s.y(), m_el[2].z() * s.z());
        }

        btScalar            determinant() const;
        btMatrix3x3 adjoint() const;
        btMatrix3x3 absolute() const;
        btMatrix3x3 transpose() const;
        btMatrix3x3 inverse() const; 

        btMatrix3x3 transposeTimes(const btMatrix3x3& m) const;
        btMatrix3x3 timesTranspose(const btMatrix3x3& m) const;

        SIMD_FORCE_INLINE btScalar tdotx(const btVector3& v) const 
        {
                return m_el[0].x() * v.x() + m_el[1].x() * v.y() + m_el[2].x() * v.z();
        }
        SIMD_FORCE_INLINE btScalar tdoty(const btVector3& v) const 
        {
                return m_el[0].y() * v.x() + m_el[1].y() * v.y() + m_el[2].y() * v.z();
        }
        SIMD_FORCE_INLINE btScalar tdotz(const btVector3& v) const 
        {
                return m_el[0].z() * v.x() + m_el[1].z() * v.y() + m_el[2].z() * v.z();
        }


        void diagonalize(btMatrix3x3& rot, btScalar threshold, int maxSteps)
        {
                rot.setIdentity();
                for (int step = maxSteps; step > 0; step--)
                {
                        // find off-diagonal element [p][q] with largest magnitude
                        int p = 0;
                        int q = 1;
                        int r = 2;
                        btScalar max = btFabs(m_el[0][1]);
                        btScalar v = btFabs(m_el[0][2]);
                        if (v > max)
                        {
                                q = 2;
                                r = 1;
                                max = v;
                        }
                        v = btFabs(m_el[1][2]);
                        if (v > max)
                        {
                                p = 1;
                                q = 2;
                                r = 0;
                                max = v;
                        }

                        btScalar t = threshold * (btFabs(m_el[0][0]) + btFabs(m_el[1][1]) + btFabs(m_el[2][2]));
                        if (max <= t)
                        {
                                if (max <= SIMD_EPSILON * t)
                                {
                                        return;
                                }
                                step = 1;
                        }

                        // compute Jacobi rotation J which leads to a zero for element [p][q] 
                        btScalar mpq = m_el[p][q];
                        btScalar theta = (m_el[q][q] - m_el[p][p]) / (2 * mpq);
                        btScalar theta2 = theta * theta;
                        btScalar cos;
                        btScalar sin;
                        if (theta2 * theta2 < btScalar(10 / SIMD_EPSILON))
                        {
                                t = (theta >= 0) ? 1 / (theta + btSqrt(1 + theta2))
                                        : 1 / (theta - btSqrt(1 + theta2));
                                cos = 1 / btSqrt(1 + t * t);
                                sin = cos * t;
                        }
                        else
                        {
                                // approximation for large theta-value, i.e., a nearly diagonal matrix
                                t = 1 / (theta * (2 + btScalar(0.5) / theta2));
                                cos = 1 - btScalar(0.5) * t * t;
                                sin = cos * t;
                        }

                        // apply rotation to matrix (this = J^T * this * J)
                        m_el[p][q] = m_el[q][p] = 0;
                        m_el[p][p] -= t * mpq;
                        m_el[q][q] += t * mpq;
                        btScalar mrp = m_el[r][p];
                        btScalar mrq = m_el[r][q];
                        m_el[r][p] = m_el[p][r] = cos * mrp - sin * mrq;
                        m_el[r][q] = m_el[q][r] = cos * mrq + sin * mrp;

                        // apply rotation to rot (rot = rot * J)
                        for (int i = 0; i < 3; i++)
                        {
                                btVector3& row = rot[i];
                                mrp = row[p];
                                mrq = row[q];
                                row[p] = cos * mrp - sin * mrq;
                                row[q] = cos * mrq + sin * mrp;
                        }
                }
        }




        btScalar cofac(int r1, int c1, int r2, int c2) const 
        {
                return m_el[r1][c1] * m_el[r2][c2] - m_el[r1][c2] * m_el[r2][c1];
        }

        void    serialize(struct        btMatrix3x3Data& dataOut) const;

        void    serializeFloat(struct   btMatrix3x3FloatData& dataOut) const;

        void    deSerialize(const struct        btMatrix3x3Data& dataIn);

        void    deSerializeFloat(const struct   btMatrix3x3FloatData& dataIn);

        void    deSerializeDouble(const struct  btMatrix3x3DoubleData& dataIn);

};


SIMD_FORCE_INLINE btMatrix3x3& 
btMatrix3x3::operator*=(const btMatrix3x3& m)
{
        setValue(m.tdotx(m_el[0]), m.tdoty(m_el[0]), m.tdotz(m_el[0]),
                m.tdotx(m_el[1]), m.tdoty(m_el[1]), m.tdotz(m_el[1]),
                m.tdotx(m_el[2]), m.tdoty(m_el[2]), m.tdotz(m_el[2]));
        return *this;
}

SIMD_FORCE_INLINE btScalar 
btMatrix3x3::determinant() const
{ 
        return btTriple((*this)[0], (*this)[1], (*this)[2]);
}


SIMD_FORCE_INLINE btMatrix3x3 
btMatrix3x3::absolute() const
{
        return btMatrix3x3(
                btFabs(m_el[0].x()), btFabs(m_el[0].y()), btFabs(m_el[0].z()),
                btFabs(m_el[1].x()), btFabs(m_el[1].y()), btFabs(m_el[1].z()),
                btFabs(m_el[2].x()), btFabs(m_el[2].y()), btFabs(m_el[2].z()));
}

SIMD_FORCE_INLINE btMatrix3x3 
btMatrix3x3::transpose() const 
{
        return btMatrix3x3(m_el[0].x(), m_el[1].x(), m_el[2].x(),
                m_el[0].y(), m_el[1].y(), m_el[2].y(),
                m_el[0].z(), m_el[1].z(), m_el[2].z());
}

SIMD_FORCE_INLINE btMatrix3x3 
btMatrix3x3::adjoint() const 
{
        return btMatrix3x3(cofac(1, 1, 2, 2), cofac(0, 2, 2, 1), cofac(0, 1, 1, 2),
                cofac(1, 2, 2, 0), cofac(0, 0, 2, 2), cofac(0, 2, 1, 0),
                cofac(1, 0, 2, 1), cofac(0, 1, 2, 0), cofac(0, 0, 1, 1));
}

SIMD_FORCE_INLINE btMatrix3x3 
btMatrix3x3::inverse() const
{
        btVector3 co(cofac(1, 1, 2, 2), cofac(1, 2, 2, 0), cofac(1, 0, 2, 1));
        btScalar det = (*this)[0].dot(co);
        btFullAssert(det != btScalar(0.0));
        btScalar s = btScalar(1.0) / det;
        return btMatrix3x3(co.x() * s, cofac(0, 2, 2, 1) * s, cofac(0, 1, 1, 2) * s,
                co.y() * s, cofac(0, 0, 2, 2) * s, cofac(0, 2, 1, 0) * s,
                co.z() * s, cofac(0, 1, 2, 0) * s, cofac(0, 0, 1, 1) * s);
}

SIMD_FORCE_INLINE btMatrix3x3 
btMatrix3x3::transposeTimes(const btMatrix3x3& m) const
{
        return btMatrix3x3(
                m_el[0].x() * m[0].x() + m_el[1].x() * m[1].x() + m_el[2].x() * m[2].x(),
                m_el[0].x() * m[0].y() + m_el[1].x() * m[1].y() + m_el[2].x() * m[2].y(),
                m_el[0].x() * m[0].z() + m_el[1].x() * m[1].z() + m_el[2].x() * m[2].z(),
                m_el[0].y() * m[0].x() + m_el[1].y() * m[1].x() + m_el[2].y() * m[2].x(),
                m_el[0].y() * m[0].y() + m_el[1].y() * m[1].y() + m_el[2].y() * m[2].y(),
                m_el[0].y() * m[0].z() + m_el[1].y() * m[1].z() + m_el[2].y() * m[2].z(),
                m_el[0].z() * m[0].x() + m_el[1].z() * m[1].x() + m_el[2].z() * m[2].x(),
                m_el[0].z() * m[0].y() + m_el[1].z() * m[1].y() + m_el[2].z() * m[2].y(),
                m_el[0].z() * m[0].z() + m_el[1].z() * m[1].z() + m_el[2].z() * m[2].z());
}

SIMD_FORCE_INLINE btMatrix3x3 
btMatrix3x3::timesTranspose(const btMatrix3x3& m) const
{
        return btMatrix3x3(
                m_el[0].dot(m[0]), m_el[0].dot(m[1]), m_el[0].dot(m[2]),
                m_el[1].dot(m[0]), m_el[1].dot(m[1]), m_el[1].dot(m[2]),
                m_el[2].dot(m[0]), m_el[2].dot(m[1]), m_el[2].dot(m[2]));

}

SIMD_FORCE_INLINE btVector3 
operator*(const btMatrix3x3& m, const btVector3& v) 
{
        return btVector3(m[0].dot(v), m[1].dot(v), m[2].dot(v));
}


SIMD_FORCE_INLINE btVector3
operator*(const btVector3& v, const btMatrix3x3& m)
{
        return btVector3(m.tdotx(v), m.tdoty(v), m.tdotz(v));
}

SIMD_FORCE_INLINE btMatrix3x3 
operator*(const btMatrix3x3& m1, const btMatrix3x3& m2)
{
        return btMatrix3x3(
                m2.tdotx( m1[0]), m2.tdoty( m1[0]), m2.tdotz( m1[0]),
                m2.tdotx( m1[1]), m2.tdoty( m1[1]), m2.tdotz( m1[1]),
                m2.tdotx( m1[2]), m2.tdoty( m1[2]), m2.tdotz( m1[2]));
}

/*
SIMD_FORCE_INLINE btMatrix3x3 btMultTransposeLeft(const btMatrix3x3& m1, const btMatrix3x3& m2) {
return btMatrix3x3(
m1[0][0] * m2[0][0] + m1[1][0] * m2[1][0] + m1[2][0] * m2[2][0],
m1[0][0] * m2[0][1] + m1[1][0] * m2[1][1] + m1[2][0] * m2[2][1],
m1[0][0] * m2[0][2] + m1[1][0] * m2[1][2] + m1[2][0] * m2[2][2],
m1[0][1] * m2[0][0] + m1[1][1] * m2[1][0] + m1[2][1] * m2[2][0],
m1[0][1] * m2[0][1] + m1[1][1] * m2[1][1] + m1[2][1] * m2[2][1],
m1[0][1] * m2[0][2] + m1[1][1] * m2[1][2] + m1[2][1] * m2[2][2],
m1[0][2] * m2[0][0] + m1[1][2] * m2[1][0] + m1[2][2] * m2[2][0],
m1[0][2] * m2[0][1] + m1[1][2] * m2[1][1] + m1[2][2] * m2[2][1],
m1[0][2] * m2[0][2] + m1[1][2] * m2[1][2] + m1[2][2] * m2[2][2]);
}
*/

SIMD_FORCE_INLINE bool operator==(const btMatrix3x3& m1, const btMatrix3x3& m2)
{
        return ( m1[0][0] == m2[0][0] && m1[1][0] == m2[1][0] && m1[2][0] == m2[2][0] &&
                m1[0][1] == m2[0][1] && m1[1][1] == m2[1][1] && m1[2][1] == m2[2][1] &&
                m1[0][2] == m2[0][2] && m1[1][2] == m2[1][2] && m1[2][2] == m2[2][2] );
}

struct  btMatrix3x3FloatData
{
        btVector3FloatData m_el[3];
};

struct  btMatrix3x3DoubleData
{
        btVector3DoubleData m_el[3];
};


        

SIMD_FORCE_INLINE       void    btMatrix3x3::serialize(struct   btMatrix3x3Data& dataOut) const
{
        for (int i=0;i<3;i++)
                m_el[i].serialize(dataOut.m_el[i]);
}

SIMD_FORCE_INLINE       void    btMatrix3x3::serializeFloat(struct      btMatrix3x3FloatData& dataOut) const
{
        for (int i=0;i<3;i++)
                m_el[i].serializeFloat(dataOut.m_el[i]);
}


SIMD_FORCE_INLINE       void    btMatrix3x3::deSerialize(const struct   btMatrix3x3Data& dataIn)
{
        for (int i=0;i<3;i++)
                m_el[i].deSerialize(dataIn.m_el[i]);
}

SIMD_FORCE_INLINE       void    btMatrix3x3::deSerializeFloat(const struct      btMatrix3x3FloatData& dataIn)
{
        for (int i=0;i<3;i++)
                m_el[i].deSerializeFloat(dataIn.m_el[i]);
}

SIMD_FORCE_INLINE       void    btMatrix3x3::deSerializeDouble(const struct     btMatrix3x3DoubleData& dataIn)
{
        for (int i=0;i<3;i++)
                m_el[i].deSerializeDouble(dataIn.m_el[i]);
}

#endif //BT_MATRIX3x3_H

---

tf2
Author(s): Tully Foote, Wim Meeussen, Eitan Marder-Eppstein
autogenerated on Tue Mar 5 11:58:42 2013