experimental/SkMatrix44.cpp

#include "SkMatrix44.h"

SkMatrix44::SkMatrix44() {
	this->setIdentity();
}

SkMatrix44::SkMatrix44(const SkMatrix44& src) {
	memcpy(this, &src, sizeof(src));
}

SkMatrix44::SkMatrix44(const SkMatrix44& a, const SkMatrix44& b) {
	this->setConcat(a, b);
}

///////////////////////////////////////////////////////////////////////////////

static const SkMatrix44 gIdentity44;

bool SkMatrix44::isIdentity() const {
    return *this == gIdentity44;
}

///////////////////////////////////////////////////////////////////////////////

void SkMatrix44::setIdentity() {
	sk_bzero(fMat, sizeof(fMat));
	fMat[0][0] = fMat[1][1] = fMat[2][2] = fMat[3][3] = 1;
}

void SkMatrix44::set3x3(SkMScalar m00, SkMScalar m01, SkMScalar m02,
                        SkMScalar m10, SkMScalar m11, SkMScalar m12,
                        SkMScalar m20, SkMScalar m21, SkMScalar m22) {
	sk_bzero(fMat, sizeof(fMat));
	fMat[0][0] = m00; fMat[0][1] = m01; fMat[0][2] = m02; fMat[0][3] = 0;
	fMat[1][0] = m10; fMat[1][1] = m11; fMat[1][2] = m12; fMat[1][3] = 0;
	fMat[2][0] = m20; fMat[2][1] = m21; fMat[2][2] = m22; fMat[2][3] = 0;
    fMat[3][0] = 0;   fMat[3][1] = 0;   fMat[3][2] = 0;   fMat[3][3] = 1;
}

///////////////////////////////////////////////////////////////////////////////

void SkMatrix44::setTranslate(SkMScalar tx, SkMScalar ty, SkMScalar tz) {
	this->setIdentity();
	fMat[3][0] = tx;
	fMat[3][1] = ty;
	fMat[3][2] = tz;
	fMat[3][3] = 1;
}

void SkMatrix44::preTranslate(SkMScalar dx, SkMScalar dy, SkMScalar dz) {
	SkMatrix44 mat;
	mat.setTranslate(dx, dy, dz);
	this->preConcat(mat);
}

void SkMatrix44::postTranslate(SkMScalar dx, SkMScalar dy, SkMScalar dz) {
	fMat[3][0] += dx;
	fMat[3][1] += dy;
	fMat[3][2] += dz;
}

///////////////////////////////////////////////////////////////////////////////

void SkMatrix44::setScale(SkMScalar sx, SkMScalar sy, SkMScalar sz) {
	sk_bzero(fMat, sizeof(fMat));
	fMat[0][0] = sx;
    fMat[1][1] = sy;
    fMat[2][2] = sz;
    fMat[3][3] = 1;
}

void SkMatrix44::preScale(SkMScalar sx, SkMScalar sy, SkMScalar sz) {
    SkMatrix44 tmp;
    tmp.setScale(sx, sy, sz);
    this->preConcat(tmp);
}

void SkMatrix44::postScale(SkMScalar sx, SkMScalar sy, SkMScalar sz) {
    for (int i = 0; i < 4; i++) {
        fMat[i][0] *= sx;
        fMat[i][1] *= sy;
        fMat[i][2] *= sz;
    }
}

///////////////////////////////////////////////////////////////////////////////

void SkMatrix44::setRotateAbout(SkMScalar x, SkMScalar y, SkMScalar z,
                                SkMScalar radians) {
    double len2 = x * x + y * y + z * z;
    if (len2 != 1) {
        if (len2 == 0) {
            this->setIdentity();
            return;
        }
        double scale = 1 / sqrt(len2);
        x *= scale;
        y *= scale;
        z *= scale;
    }
    this->setRotateAboutUnit(x, y, z, radians);
}

void SkMatrix44::setRotateAboutUnit(SkMScalar x, SkMScalar y, SkMScalar z,
                                    SkMScalar radians) {
    double c = cos(radians);
    double s = sin(radians);
    double C = 1 - c;
    double xs = x * s;
    double ys = y * s;
    double zs = z * s;
    double xC = x * C;
    double yC = y * C;
    double zC = z * C;
    double xyC = x * yC;
    double yzC = y * zC;
    double zxC = z * xC;

    this->set3x3(x * xC + c,    xyC - zs,       zxC + ys,
                 xyC + zs,      y * yC + c,     yzC - xs,
                 zxC - ys,      yzC + xs,       z * zC + c);
}

///////////////////////////////////////////////////////////////////////////////

void SkMatrix44::setConcat(const SkMatrix44& a, const SkMatrix44& b) {
	SkMScalar result[4][4];
	for (int i = 0; i < 4; i++) {
		for (int j = 0; j < 4; j++) {
			double value = 0;
			for (int k = 0; k < 4; k++) {
				value += SkMScalarToDouble(a.fMat[k][i]) * b.fMat[j][k];
			}
			result[j][i] = SkDoubleToMScalar(value);
		}
	}
	memcpy(fMat, result, sizeof(result));
}

///////////////////////////////////////////////////////////////////////////////

static inline SkMScalar det2x2(double m00, double m01, double m10, double m11) {
    return m00 * m11 - m10 * m01;
}

static inline double det3x3(double m00, double m01, double m02,
                            double m10, double m11, double m12,
                            double m20, double m21, double m22) {
    return  m00 * det2x2(m11, m12, m21, m22) -
            m10 * det2x2(m01, m02, m21, m22) +
            m20 * det2x2(m01, m02, m11, m12);
}

/** We always perform the calculation in doubles, to avoid prematurely losing
    precision along the way. This relies on the compiler automatically
    promoting our SkMScalar values to double (if needed).
 */
double SkMatrix44::determinant() const {
    return  fMat[0][0] * det3x3(fMat[1][1], fMat[1][2], fMat[1][3],
                                fMat[2][1], fMat[2][2], fMat[2][3],
                                fMat[3][1], fMat[3][2], fMat[3][3]) -
            fMat[1][0] * det3x3(fMat[0][1], fMat[0][2], fMat[0][3],
                                fMat[2][1], fMat[2][2], fMat[2][3],
                                fMat[3][1], fMat[3][2], fMat[3][3]) +
            fMat[2][0] * det3x3(fMat[0][1], fMat[0][2], fMat[0][3],
                                fMat[1][1], fMat[1][2], fMat[1][3],
                                fMat[3][1], fMat[3][2], fMat[3][3]) -
            fMat[3][0] * det3x3(fMat[0][1], fMat[0][2], fMat[0][3],
                                fMat[1][1], fMat[1][2], fMat[1][3],
                                fMat[2][1], fMat[2][2], fMat[2][3]);
}

///////////////////////////////////////////////////////////////////////////////

// just picked a small value. not sure how to pick the "right" one
#define TOO_SMALL_FOR_DETERMINANT   (1.e-8)

static inline double dabs(double x) {
    if (x < 0) {
        x = -x;
    }
    return x;
}

bool SkMatrix44::invert(SkMatrix44* inverse) const {
    double det = this->determinant();
    if (dabs(det) < TOO_SMALL_FOR_DETERMINANT) {
        return false;
    }
    if (NULL == inverse) {
        return true;
    }

    // we explicitly promote to doubles to keep the intermediate values in
    // higher precision (assuming SkMScalar isn't already a double)
    double m00 = fMat[0][0];
    double m01 = fMat[0][1];
    double m02 = fMat[0][2];
    double m03 = fMat[0][3];
    double m10 = fMat[1][0];
    double m11 = fMat[1][1];
    double m12 = fMat[1][2];
    double m13 = fMat[1][3];
    double m20 = fMat[2][0];
    double m21 = fMat[2][1];
    double m22 = fMat[2][2];
    double m23 = fMat[2][3];
    double m30 = fMat[3][0];
    double m31 = fMat[3][1];
    double m32 = fMat[3][2];
    double m33 = fMat[3][3];
    
    double tmp[4][4];

    tmp[0][0] = m12*m23*m31 - m13*m22*m31 + m13*m21*m32 - m11*m23*m32 - m12*m21*m33 + m11*m22*m33;
    tmp[0][1] = m03*m22*m31 - m02*m23*m31 - m03*m21*m32 + m01*m23*m32 + m02*m21*m33 - m01*m22*m33;
    tmp[0][2] = m02*m13*m31 - m03*m12*m31 + m03*m11*m32 - m01*m13*m32 - m02*m11*m33 + m01*m12*m33;
    tmp[0][3] = m03*m12*m21 - m02*m13*m21 - m03*m11*m22 + m01*m13*m22 + m02*m11*m23 - m01*m12*m23;
    tmp[1][0] = m13*m22*m30 - m12*m23*m30 - m13*m20*m32 + m10*m23*m32 + m12*m20*m33 - m10*m22*m33;
    tmp[1][1] = m02*m23*m30 - m03*m22*m30 + m03*m20*m32 - m00*m23*m32 - m02*m20*m33 + m00*m22*m33;
    tmp[1][2] = m03*m12*m30 - m02*m13*m30 - m03*m10*m32 + m00*m13*m32 + m02*m10*m33 - m00*m12*m33;
    tmp[1][3] = m02*m13*m20 - m03*m12*m20 + m03*m10*m22 - m00*m13*m22 - m02*m10*m23 + m00*m12*m23;
    tmp[2][0] = m11*m23*m30 - m13*m21*m30 + m13*m20*m31 - m10*m23*m31 - m11*m20*m33 + m10*m21*m33;
    tmp[2][1] = m03*m21*m30 - m01*m23*m30 - m03*m20*m31 + m00*m23*m31 + m01*m20*m33 - m00*m21*m33;
    tmp[2][2] = m01*m13*m30 - m03*m11*m30 + m03*m10*m31 - m00*m13*m31 - m01*m10*m33 + m00*m11*m33;
    tmp[2][3] = m03*m11*m20 - m01*m13*m20 - m03*m10*m21 + m00*m13*m21 + m01*m10*m23 - m00*m11*m23;
    tmp[3][0] = m12*m21*m30 - m11*m22*m30 - m12*m20*m31 + m10*m22*m31 + m11*m20*m32 - m10*m21*m32;
    tmp[3][1] = m01*m22*m30 - m02*m21*m30 + m02*m20*m31 - m00*m22*m31 - m01*m20*m32 + m00*m21*m32;
    tmp[3][2] = m02*m11*m30 - m01*m12*m30 - m02*m10*m31 + m00*m12*m31 + m01*m10*m32 - m00*m11*m32;
    tmp[3][3] = m01*m12*m20 - m02*m11*m20 + m02*m10*m21 - m00*m12*m21 - m01*m10*m22 + m00*m11*m22;

    double invDet = 1.0 / det;
    for (int i = 0; i < 4; i++) {
        for (int j = 0; j < 4; j++) {
            inverse->fMat[i][j] = SkDoubleToMScalar(tmp[i][j] * invDet);
        }
    }
    return true;
}

///////////////////////////////////////////////////////////////////////////////

void SkMatrix44::map(const SkScalar src[4], SkScalar dst[4]) const {
	SkScalar result[4];
	for (int i = 0; i < 4; i++) {
		SkMScalar value = 0;
		for (int j = 0; j < 4; j++) {
			value += fMat[j][i] * src[j];
		}
		result[i] = value;
	}
	memcpy(dst, result, sizeof(result));
}

///////////////////////////////////////////////////////////////////////////////

void SkMatrix44::dump() const {
    SkDebugf("[%g %g %g %g][%g %g %g %g][%g %g %g %g][%g %g %g %g]\n",
#if 0
             fMat[0][0], fMat[0][1], fMat[0][2], fMat[0][3],
             fMat[1][0], fMat[1][1], fMat[1][2], fMat[1][3],
             fMat[2][0], fMat[2][1], fMat[2][2], fMat[2][3],
             fMat[3][0], fMat[3][1], fMat[3][2], fMat[3][3]);
#else
            fMat[0][0], fMat[1][0], fMat[2][0], fMat[3][0],
            fMat[0][1], fMat[1][1], fMat[2][1], fMat[3][1],
            fMat[0][2], fMat[1][2], fMat[2][2], fMat[3][2],
            fMat[0][3], fMat[1][3], fMat[2][3], fMat[3][3]);
#endif
}

///////////////////////////////////////////////////////////////////////////////

static void initFromMatrix(SkMScalar dst[4][4], const SkMatrix& src) {
	sk_bzero(dst, 16 * sizeof(SkMScalar));
    dst[0][0] = src[SkMatrix::kMScaleX];
    dst[1][0] = src[SkMatrix::kMSkewX];
    dst[3][0] = src[SkMatrix::kMTransX];
    dst[0][1] = src[SkMatrix::kMSkewY];
    dst[1][1] = src[SkMatrix::kMScaleY];
    dst[3][1] = src[SkMatrix::kMTransY];
    dst[2][2] = dst[3][3] = 1;
}

SkMatrix44::SkMatrix44(const SkMatrix& src) {
    initFromMatrix(fMat, src);
}

SkMatrix44& SkMatrix44::operator=(const SkMatrix& src) {
    initFromMatrix(fMat, src);
    return *this;
}

SkMatrix44::operator SkMatrix() const {
    SkMatrix dst;
    dst.reset();    // setup our perspective correctly for identity

    dst[SkMatrix::kMScaleX]  = SkMScalarToFloat(fMat[0][0]);
    dst[SkMatrix::kMSkewX]  = SkMScalarToFloat(fMat[1][0]);
    dst[SkMatrix::kMTransX] = SkMScalarToFloat(fMat[3][0]);

    dst[SkMatrix::kMSkewY]  = SkMScalarToFloat(fMat[0][1]);
    dst[SkMatrix::kMScaleY] = SkMScalarToFloat(fMat[1][1]);
    dst[SkMatrix::kMTransY] = SkMScalarToFloat(fMat[3][1]);

    return dst;
}