implement inverse, determinant
git-svn-id: http://skia.googlecode.com/svn/trunk@507 2bbb7eff-a529-9590-31e7-b0007b416f81
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reed@android.com
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@ -1,99 +1,208 @@
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typedef float SkMScalar;
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static const SkMScalar SK_MScalar1 = 1;
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struct SkVector4 {
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SkScalar fData[4];
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};
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class SkMatrix44 {
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public:
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SkMatrix44();
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explicit SkMatrix44(const SkMatrix44&);
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SkMatrix44(const SkMatrix44& a, const SkMatrix44& b);
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void setIdentity();
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void setTranslate(SkMScalar dx, SkMScalar dy, SkMScalar dz);
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void preTranslate(SkMScalar dx, SkMScalar dy, SkMScalar dz);
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void postTranslate(SkMScalar dx, SkMScalar dy, SkMScalar dz);
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void setConcat(const SkMatrix44& a, const SkMatrix44& b);
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void map(const SkScalar src[4], SkScalar dst[4]);
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SkVector4 operator*(const SkVector4& src) {
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SkVector4 dst;
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this->map(src.fData, dst.fData);
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return dst;
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}
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friend SkMatrix44* operator*(const SkMatrix44& a, const SkMatrix44& b) {
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return SkMatrix(a, b);
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}
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private:
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SkMScalar fMat[4][4];
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};
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SkMatrix44::SkMatrix44() {
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this->setIdentity();
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}
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SkMatrix44::SkMatrix44(const SkMatrix44& src) {
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memcpy(this, &src, sizeof(src));
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}
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SkMatrix44::SkMatrix44(const SkMatrix44& a, const SkMatrix44& b) {
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this->setConcat(a, b);
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}
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void SkMatrix44:setIdentity() {
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sk_bzero(fMat, sizeof(fMat));
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fMat[0][0] = fMat[1][1] = fMat[2][2] = fMat[3][3] = SK_MScalar1;
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}
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void SkMatrix44::setTranslate(SkMScalar tx, SkMScalar ty, SkMScalar tz) {
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sk_bzero(fMat, sizeof(fMat));
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fMat[3][0] = tx;
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fMat[3][1] = ty;
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fMat[3][2] = tz;
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fMat[3][3] = SK_MScalar1;
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}
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void SkMatrix44::preTranslate(SkMScalar dx, SkMScalar dy, SkMScalar dz) {
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SkMatrix44 mat;
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mat.setTranslate(dx, dy, dz);
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this->preConcat(mat);
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}
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void SkMatrix44::postTranslate(SkMScalar dx, SkMScalar dy, SkMScalar dz) {
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fMat[3][0] += dx;
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fMat[3][1] += dy;
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fMat[3][2] += dz;
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}
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void SkMatrix44::map(const SkScalar src[4], SkScalar dst[4]) {
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SkScalar result[4];
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for (int i = 0; i < 4; i++) {
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SkMScalar value = 0;
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for (int j = 0; j < 4; j++) {
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value += fMat[j][i] * src[j];
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}
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result[i] = value;
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}
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memcpy(dst, result, sizeof(result));
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}
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void SkMatrix44::setConcat(const SkMatrix44& a, const SkMatrix44& b) {
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SkMScalar result[4][4];
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for (int i = 0; i < 4; i++) {
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for (int j = 0; j < 4; j++) {
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SkMScalar value = 0;
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for (int k = 0; k < 4; k++) {
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value += a.fMat[k][j] * b.fMat[i][k];
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}
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result[j][i] = value;
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}
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}
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memcpy(fMat, result, sizeof(result));
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}
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#include "SkMatrix44.h"
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SkMatrix44::SkMatrix44() {
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this->setIdentity();
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}
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SkMatrix44::SkMatrix44(const SkMatrix44& src) {
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memcpy(this, &src, sizeof(src));
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}
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SkMatrix44::SkMatrix44(const SkMatrix44& a, const SkMatrix44& b) {
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this->setConcat(a, b);
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}
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///////////////////////////////////////////////////////////////////////////////
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void SkMatrix44::setIdentity() {
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sk_bzero(fMat, sizeof(fMat));
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fMat[0][0] = fMat[1][1] = fMat[2][2] = fMat[3][3] = SK_MScalar1;
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}
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void SkMatrix44::setTranslate(SkMScalar tx, SkMScalar ty, SkMScalar tz) {
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sk_bzero(fMat, sizeof(fMat));
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fMat[3][0] = tx;
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fMat[3][1] = ty;
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fMat[3][2] = tz;
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fMat[3][3] = SK_MScalar1;
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}
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void SkMatrix44::preTranslate(SkMScalar dx, SkMScalar dy, SkMScalar dz) {
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SkMatrix44 mat;
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mat.setTranslate(dx, dy, dz);
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this->preConcat(mat);
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}
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void SkMatrix44::postTranslate(SkMScalar dx, SkMScalar dy, SkMScalar dz) {
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fMat[3][0] += dx;
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fMat[3][1] += dy;
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fMat[3][2] += dz;
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}
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///////////////////////////////////////////////////////////////////////////////
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void SkMatrix44::setScale(SkMScalar sx, SkMScalar sy, SkMScalar sz) {
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sk_bzero(fMat, sizeof(fMat));
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fMat[0][0] = sx;
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fMat[1][1] = sy;
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fMat[2][2] = sz;
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fMat[3][3] = SK_MScalar1;
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}
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void SkMatrix44::preScale(SkMScalar sx, SkMScalar sy, SkMScalar sz) {
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SkMatrix44 tmp;
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tmp.setScale(sx, sy, sz);
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this->preConcat(tmp);
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}
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void SkMatrix44::postScale(SkMScalar sx, SkMScalar sy, SkMScalar sz) {
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for (int i = 0; i < 4; i++) {
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fMat[i][0] *= sx;
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fMat[i][1] *= sy;
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fMat[i][2] *= sz;
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}
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}
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///////////////////////////////////////////////////////////////////////////////
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void SkMatrix44::setConcat(const SkMatrix44& a, const SkMatrix44& b) {
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SkMScalar result[4][4];
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for (int i = 0; i < 4; i++) {
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for (int j = 0; j < 4; j++) {
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double value = 0;
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for (int k = 0; k < 4; k++) {
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value += (double)a.fMat[k][j] * b.fMat[i][k];
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}
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result[j][i] = SkDoubleToMScalar(value);
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}
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}
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memcpy(fMat, result, sizeof(result));
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}
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///////////////////////////////////////////////////////////////////////////////
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static inline SkMScalar det2x2(double m00, double m01, double m10, double m11) {
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return m00 * m11 - m10 * m01;
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}
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static inline double det3x3(double m00, double m01, double m02,
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double m10, double m11, double m12,
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double m20, double m21, double m22) {
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return m00 * det2x2(m11, m12, m21, m22) -
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m10 * det2x2(m01, m02, m21, m22) +
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m20 * det2x2(m01, m02, m11, m12);
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}
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/** We always perform the calculation in doubles, to avoid prematurely losing
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precision along the way. This relies on the compiler automatically
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promoting our SkMScalar values to double (if needed).
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*/
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double SkMatrix44::determinant() const {
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return fMat[0][0] * det3x3(fMat[1][1], fMat[1][2], fMat[1][3],
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fMat[2][1], fMat[2][2], fMat[2][3],
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fMat[3][1], fMat[3][2], fMat[3][3]) -
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fMat[1][0] * det3x3(fMat[0][1], fMat[0][2], fMat[0][3],
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fMat[2][1], fMat[2][2], fMat[2][3],
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fMat[3][1], fMat[3][2], fMat[3][3]) +
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fMat[2][0] * det3x3(fMat[0][1], fMat[0][2], fMat[0][3],
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fMat[1][1], fMat[1][2], fMat[1][3],
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fMat[3][1], fMat[3][2], fMat[3][3]) -
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fMat[3][0] * det3x3(fMat[0][1], fMat[0][2], fMat[0][3],
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fMat[1][1], fMat[1][2], fMat[1][3],
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fMat[2][1], fMat[2][2], fMat[2][3]);
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}
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///////////////////////////////////////////////////////////////////////////////
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// just picked a small value. not sure how to pick the "right" one
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#define TOO_SMALL_FOR_DETERMINANT (1.e-8)
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static inline double dabs(double x) {
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if (x < 0) {
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x = -x;
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}
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return x;
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}
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bool SkMatrix44::invert(SkMatrix44* inverse) const {
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double det = this->determinant();
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if (dabs(det) < TOO_SMALL_FOR_DETERMINANT) {
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return false;
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}
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if (NULL == inverse) {
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return true;
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}
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// we explicitly promote to doubles to keep the intermediate values in
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// higher precision (assuming SkMScalar isn't already a double)
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double m00 = fMat[0][0];
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double m01 = fMat[0][1];
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double m02 = fMat[0][2];
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double m03 = fMat[0][3];
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double m10 = fMat[1][0];
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double m11 = fMat[1][1];
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double m12 = fMat[1][2];
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double m13 = fMat[1][3];
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double m20 = fMat[2][0];
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double m21 = fMat[2][1];
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double m22 = fMat[2][2];
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double m23 = fMat[2][3];
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double m30 = fMat[3][0];
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double m31 = fMat[3][1];
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double m32 = fMat[3][2];
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double m33 = fMat[3][3];
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double tmp[4][4];
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tmp[0][0] = m12*m23*m31 - m13*m22*m31 + m13*m21*m32 - m11*m23*m32 - m12*m21*m33 + m11*m22*m33;
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tmp[0][1] = m03*m22*m31 - m02*m23*m31 - m03*m21*m32 + m01*m23*m32 + m02*m21*m33 - m01*m22*m33;
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tmp[0][2] = m02*m13*m31 - m03*m12*m31 + m03*m11*m32 - m01*m13*m32 - m02*m11*m33 + m01*m12*m33;
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tmp[0][3] = m03*m12*m21 - m02*m13*m21 - m03*m11*m22 + m01*m13*m22 + m02*m11*m23 - m01*m12*m23;
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tmp[1][0] = m13*m22*m30 - m12*m23*m30 - m13*m20*m32 + m10*m23*m32 + m12*m20*m33 - m10*m22*m33;
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tmp[1][1] = m02*m23*m30 - m03*m22*m30 + m03*m20*m32 - m00*m23*m32 - m02*m20*m33 + m00*m22*m33;
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tmp[1][2] = m03*m12*m30 - m02*m13*m30 - m03*m10*m32 + m00*m13*m32 + m02*m10*m33 - m00*m12*m33;
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tmp[1][3] = m02*m13*m20 - m03*m12*m20 + m03*m10*m22 - m00*m13*m22 - m02*m10*m23 + m00*m12*m23;
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tmp[2][0] = m11*m23*m30 - m13*m21*m30 + m13*m20*m31 - m10*m23*m31 - m11*m20*m33 + m10*m21*m33;
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tmp[2][1] = m03*m21*m30 - m01*m23*m30 - m03*m20*m31 + m00*m23*m31 + m01*m20*m33 - m00*m21*m33;
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tmp[2][2] = m01*m13*m30 - m03*m11*m30 + m03*m10*m31 - m00*m13*m31 - m01*m10*m33 + m00*m11*m33;
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tmp[2][3] = m03*m11*m20 - m01*m13*m20 - m03*m10*m21 + m00*m13*m21 + m01*m10*m23 - m00*m11*m23;
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tmp[3][0] = m12*m21*m30 - m11*m22*m30 - m12*m20*m31 + m10*m22*m31 + m11*m20*m32 - m10*m21*m32;
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tmp[3][1] = m01*m22*m30 - m02*m21*m30 + m02*m20*m31 - m00*m22*m31 - m01*m20*m32 + m00*m21*m32;
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tmp[3][2] = m02*m11*m30 - m01*m12*m30 - m02*m10*m31 + m00*m12*m31 + m01*m10*m32 - m00*m11*m32;
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tmp[3][3] = m01*m12*m20 - m02*m11*m20 + m02*m10*m21 - m00*m12*m21 - m01*m10*m22 + m00*m11*m22;
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double invDet = 1.0 / det;
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for (int i = 0; i < 4; i++) {
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for (int j = 0; j < 4; j++) {
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inverse->fMat[i][j] = SkDoubleToMScalar(tmp[i][j] * invDet);
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}
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}
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return true;
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}
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///////////////////////////////////////////////////////////////////////////////
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void SkMatrix44::map(const SkScalar src[4], SkScalar dst[4]) const {
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SkScalar result[4];
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for (int i = 0; i < 4; i++) {
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SkMScalar value = 0;
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for (int j = 0; j < 4; j++) {
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value += fMat[j][i] * src[j];
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}
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result[i] = value;
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}
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memcpy(dst, result, sizeof(result));
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}
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///////////////////////////////////////////////////////////////////////////////
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void SkMatrix44::dump() const {
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SkDebugf("[%g %g %g %g][%g %g %g %g][%g %g %g %g][%g %g %g %g]\n",
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fMat[0][0], fMat[0][1], fMat[0][2], fMat[0][3],
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fMat[1][0], fMat[1][1], fMat[1][2], fMat[1][3],
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fMat[2][0], fMat[2][1], fMat[2][2], fMat[2][3],
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fMat[3][0], fMat[3][1], fMat[3][2], fMat[3][3]);
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}
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85
experimental/SkMatrix44.h
Normal file
85
experimental/SkMatrix44.h
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@ -0,0 +1,85 @@
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#ifndef SkMatrix44_DEFINED
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#define SkMatrix44_DEFINED
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#include "SkScalar.h"
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typedef float SkMScalar;
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static const SkMScalar SK_MScalar1 = 1;
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static inline SkMScalar SkDoubleToMScalar(double x) {
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return static_cast<float>(x);
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}
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struct SkVector4 {
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SkScalar fData[4];
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};
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class SkMatrix44 {
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public:
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SkMatrix44();
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SkMatrix44(const SkMatrix44&);
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SkMatrix44(const SkMatrix44& a, const SkMatrix44& b);
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void setIdentity();
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void setTranslate(SkMScalar dx, SkMScalar dy, SkMScalar dz);
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void preTranslate(SkMScalar dx, SkMScalar dy, SkMScalar dz);
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void postTranslate(SkMScalar dx, SkMScalar dy, SkMScalar dz);
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void setScale(SkMScalar sx, SkMScalar sx, SkMScalar sx);
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void preScale(SkMScalar sx, SkMScalar sx, SkMScalar sx);
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void postScale(SkMScalar sx, SkMScalar sx, SkMScalar sx);
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void setScale(SkMScalar scale) {
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this->setScale(scale, scale, scale);
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}
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void preScale(SkMScalar scale) {
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this->preScale(scale, scale, scale);
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}
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void postScale(SkMScalar scale) {
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this->postScale(scale, scale, scale);
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}
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void setConcat(const SkMatrix44& a, const SkMatrix44& b);
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void preConcat(const SkMatrix44& m) {
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this->setConcat(*this, m);
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}
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void postConcat(const SkMatrix44& m) {
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this->setConcat(m, *this);
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}
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friend SkMatrix44 operator*(const SkMatrix44& a, const SkMatrix44& b) {
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return SkMatrix44(a, b);
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}
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/** If this is invertible, return that in inverse and return true. If it is
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not invertible, return false and ignore the inverse parameter.
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*/
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bool invert(SkMatrix44* inverse) const;
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/** Apply the matrix to the src vector, returning the new vector in dst.
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It is legal for src and dst to point to the same memory.
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*/
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void map(const SkScalar src[4], SkScalar dst[4]) const;
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void map(SkScalar vec[4]) const {
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this->map(vec, vec);
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}
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friend SkVector4 operator*(const SkMatrix44& m, const SkVector4& src) {
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SkVector4 dst;
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m.map(src.fData, dst.fData);
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return dst;
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}
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void dump() const;
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private:
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/* Stored in the same order as opengl:
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[3][0] = tx
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[3][1] = ty
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[3][2] = tz
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*/
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SkMScalar fMat[4][4];
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double determinant() const;
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};
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#endif
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