matrix3.h

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#ifndef G3D_MATRIX3_H
#define G3D_MATRIX3_H

#include "G3D/platform.h"
#include "G3D/System.h"
#include "G3D/Vector3.h"
#include "G3D/Vector4.h"

namespace G3D {

/**
  3x3 matrix.  Do not subclass.
 */
class Matrix3 {
private:

    float elt[3][3];

    // Hidden operators
    bool operator<(const Matrix3&) const;
    bool operator>(const Matrix3&) const;
    bool operator<=(const Matrix3&) const;
    bool operator>=(const Matrix3&) const;

public:

    /** Initial values are undefined for performance.  See also 
        Matrix3::zero(), Matrix3::identity(), Matrix3::fromAxisAngle, etc.*/
    inline Matrix3() {}

    Matrix3 (const float aafEntry[3][3]);
    Matrix3 (const Matrix3& rkMatrix);
    Matrix3 (float fEntry00, float fEntry01, float fEntry02,
             float fEntry10, float fEntry11, float fEntry12,
             float fEntry20, float fEntry21, float fEntry22);

    bool fuzzyEq(const Matrix3& b) const;

    /** Constructs a matrix from a quaternion.
        @cite Graphics Gems II, p. 351--354
 	    @cite Implementation from Watt and Watt, pg 362*/
    Matrix3(const class Quat& q);


    /**
     Sets all elements.
     */
    void set(float fEntry00, float fEntry01, float fEntry02,
             float fEntry10, float fEntry11, float fEntry12,
             float fEntry20, float fEntry21, float fEntry22);

    /**
     * member access, allows use of construct mat[r][c]
     */
    inline float* operator[] (int iRow) {
        debugAssert(iRow >= 0);
        debugAssert(iRow < 3);
        return (float*)&elt[iRow][0];
    }

    inline const float* operator[] (int iRow) const {
        debugAssert(iRow >= 0);
        debugAssert(iRow < 3);
        return (const float*)&elt[iRow][0];
    }

    inline operator float* () {
        return (float*)&elt[0][0];
    }

    inline operator const float* () const{
        return (const float*)&elt[0][0];
    }

    Vector3 getColumn (int iCol) const;
    Vector3 getRow (int iRow) const;
    void setColumn(int iCol, const Vector3 &vector);
    void setRow(int iRow, const Vector3 &vector);

    // assignment and comparison
    inline Matrix3& operator= (const Matrix3& rkMatrix) {
        System::memcpy(elt, rkMatrix.elt, 9 * sizeof(float));
        return *this;
    }

    bool operator== (const Matrix3& rkMatrix) const;
    bool operator!= (const Matrix3& rkMatrix) const;

    // arithmetic operations
    Matrix3 operator+ (const Matrix3& rkMatrix) const;
    Matrix3 operator- (const Matrix3& rkMatrix) const;
    /** Matrix-matrix multiply */
    Matrix3 operator* (const Matrix3& rkMatrix) const;
    Matrix3 operator- () const;

    Matrix3& operator+= (const Matrix3& rkMatrix);
    Matrix3& operator-= (const Matrix3& rkMatrix);
    Matrix3& operator*= (const Matrix3& rkMatrix);

    /**
     * matrix * vector [3x3 * 3x1 = 3x1]
     */
    inline Vector3 operator* (const Vector3& v) const {
        Vector3 kProd;

        for (int r = 0; r < 3; ++r) {
            kProd[r] =
                elt[r][0] * v[0] +
                elt[r][1] * v[1] +
                elt[r][2] * v[2];
        }

        return kProd;
    }


    /**
     * vector * matrix [1x3 * 3x3 = 1x3]
     */
    friend Vector3 operator* (const Vector3& rkVector,
                              const Matrix3& rkMatrix);

    /**
     * matrix * scalar
     */
    Matrix3 operator* (float fScalar) const;

    /** scalar * matrix */
    friend Matrix3 operator* (double fScalar, const Matrix3& rkMatrix);
    friend Matrix3 operator* (float fScalar, const Matrix3& rkMatrix);
    friend Matrix3 operator* (int fScalar, const Matrix3& rkMatrix);

private:
    /** Multiplication where out != A and out != B */
    static void _mul(const Matrix3& A, const Matrix3& B, Matrix3& out);
public:

    /** Optimized implementation of out = A * B.  It is safe (but slow) to call 
        with A, B, and out possibly pointer equal to one another.*/
    // This is a static method so that it is not ambiguous whether "this"
    // is an input or output argument.
    inline static void mul(const Matrix3& A, const Matrix3& B, Matrix3& out) {
        if ((&out == &A) || (&out == &B)) {
            // We need a temporary anyway, so revert to the stack method.
            out = A * B;
        } else {
            // Optimized in-place multiplication.
            _mul(A, B, out);
        }
    }

private:
    static void _transpose(const Matrix3& A, Matrix3& out);
public:

    /** Optimized implementation of out = A.transpose().  It is safe (but slow) to call 
        with A and out possibly pointer equal to one another.
    
        Note that <CODE>A.transpose() * v</CODE> can be computed 
        more efficiently as <CODE>v * A</CODE>.
    */
    inline static void transpose(const Matrix3& A, Matrix3& out) {
        if (&A == &out) {
            out = A.transpose();
        } else {
            _transpose(A, out);
        }
    }

    /** Returns true if the rows and column L2 norms are 1.0 and the rows are orthogonal. */
    bool isOrthonormal() const;

    Matrix3 transpose () const;
    bool inverse (Matrix3& rkInverse, float fTolerance = 1e-06) const;
    Matrix3 inverse (float fTolerance = 1e-06) const;
    float determinant () const;

    /** singular value decomposition */
    void singularValueDecomposition (Matrix3& rkL, Vector3& rkS,
                                     Matrix3& rkR) const;
    /** singular value decomposition */
    void singularValueComposition (const Matrix3& rkL,
                                   const Vector3& rkS, const Matrix3& rkR);

    /** Gram-Schmidt orthonormalization (applied to columns of rotation matrix) */
    void orthonormalize();

    /** orthogonal Q, diagonal D, upper triangular U stored as (u01,u02,u12) */
    void qDUDecomposition (Matrix3& rkQ, Vector3& rkD,
                           Vector3& rkU) const;

    float spectralNorm () const;

    /** matrix must be orthonormal */
    void toAxisAngle(Vector3& rkAxis, float& rfRadians) const;

    static Matrix3 fromAxisAngle(const Vector3& rkAxis, float fRadians);

    /**
     * The matrix must be orthonormal.  The decomposition is yaw*pitch*roll
     * where yaw is rotation about the Up vector, pitch is rotation about the
     * right axis, and roll is rotation about the Direction axis.
     */
    bool toEulerAnglesXYZ (float& rfYAngle, float& rfPAngle,
                           float& rfRAngle) const;
    bool toEulerAnglesXZY (float& rfYAngle, float& rfPAngle,
                           float& rfRAngle) const;
    bool toEulerAnglesYXZ (float& rfYAngle, float& rfPAngle,
                           float& rfRAngle) const;
    bool toEulerAnglesYZX (float& rfYAngle, float& rfPAngle,
                           float& rfRAngle) const;
    bool toEulerAnglesZXY (float& rfYAngle, float& rfPAngle,
                           float& rfRAngle) const;
    bool toEulerAnglesZYX (float& rfYAngle, float& rfPAngle,
                           float& rfRAngle) const;
    static Matrix3 fromEulerAnglesXYZ (float fYAngle, float fPAngle, float fRAngle);
    static Matrix3 fromEulerAnglesXZY (float fYAngle, float fPAngle, float fRAngle);
    static Matrix3 fromEulerAnglesYXZ (float fYAngle, float fPAngle, float fRAngle);
    static Matrix3 fromEulerAnglesYZX (float fYAngle, float fPAngle, float fRAngle);
    static Matrix3 fromEulerAnglesZXY (float fYAngle, float fPAngle, float fRAngle);
    static Matrix3 fromEulerAnglesZYX (float fYAngle, float fPAngle, float fRAngle);

    /** eigensolver, matrix must be symmetric */
    void eigenSolveSymmetric (float afEigenvalue[3],
                              Vector3 akEigenvector[3]) const;

    static void tensorProduct (const Vector3& rkU, const Vector3& rkV,
                               Matrix3& rkProduct);
	std::string toString() const;

    static const float EPSILON; 

    // Special values.
    // The unguaranteed order of initialization of static variables across 
    // translation units can be a source of annoying bugs, so now the static
    // special values (like Vector3::ZERO, Color3::WHITE, ...) are wrapped
    // inside static functions that return references to them. 
    // These functions are intentionally not inlined, because: 
    // "You might be tempted to write [...] them as inline functions 
    // inside their respective header files, but this is something you 
    // must definitely not do. An inline function can be duplicated 
    // in every file in which it appears ?and this duplication 
    // includes the static object definition. Because inline functions 
    // automatically default to internal linkage, this would result in 
    // having multiple static objects across the various translation 
    // units, which would certainly cause problems. So you must 
    // ensure that there is only one definition of each wrapping 
    // function, and this means not making the wrapping functions inline",
    // according to Chapter 10 of "Thinking in C++, 2nd ed. Volume 1" by Bruce Eckel, 
    // http://www.mindview.net/
    static const Matrix3& zero();
    static const Matrix3& identity(); 

    // Deprecated. 
    /** @deprecated Use Matrix3::zero() */
    static const Matrix3 ZERO;
    /** @deprecated Use Matrix3::identity() */
    static const Matrix3 IDENTITY;

protected:
    // support for eigensolver
    void tridiagonal (float afDiag[3], float afSubDiag[3]);
    bool qLAlgorithm (float afDiag[3], float afSubDiag[3]);

    // support for singular value decomposition
    static const float ms_fSvdEpsilon;
    static const int ms_iSvdMaxIterations;
    static void bidiagonalize (Matrix3& kA, Matrix3& kL,
                               Matrix3& kR);
    static void golubKahanStep (Matrix3& kA, Matrix3& kL,
                                Matrix3& kR);

    // support for spectral norm
    static float maxCubicRoot (float afCoeff[3]);

};


//----------------------------------------------------------------------------
/**  <code>v * M == M.transpose() * v</code> */
inline Vector3 operator* (const Vector3& rkPoint, const Matrix3& rkMatrix) {
    Vector3 kProd;

    for (int r = 0; r < 3; ++r) {
        kProd[r] =
            rkPoint[0] * rkMatrix.elt[0][r] +
            rkPoint[1] * rkMatrix.elt[1][r] +
            rkPoint[2] * rkMatrix.elt[2][r];
    }

    return kProd;
}


} // namespace

#endif