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+/*************************************************************************
+** Matrix.cpp **
+** **
+** This file is part of dvisvgm -- the DVI to SVG converter **
+** Copyright (C) 2005-2013 Martin Gieseking <martin.gieseking@uos.de> **
+** **
+** This program is free software; you can redistribute it and/or **
+** modify it under the terms of the GNU General Public License as **
+** published by the Free Software Foundation; either version 3 of **
+** the License, or (at your option) any later version. **
+** **
+** This program is distributed in the hope that it will be useful, but **
+** WITHOUT ANY WARRANTY; without even the implied warranty of **
+** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the **
+** GNU General Public License for more details. **
+** **
+** You should have received a copy of the GNU General Public License **
+** along with this program; if not, see <http://www.gnu.org/licenses/>. **
+*************************************************************************/
+
+#include <cmath>
+#include <limits>
+#include <sstream>
+#include "Calculator.h"
+#include "Matrix.h"
+#include "XMLString.h"
+
+using namespace std;
+
+
+
+/** Computes the determinant of a given matrix */
+double det (const Matrix &m) {
+ double sum=0;
+ for (int i=0; i < 3; ++i) {
+ sum += m._values[0][i] * m._values[1][(i+1)%3] * m._values[2][(i+2)%3]
+ - m._values[0][2-i] * m._values[1][(4-i)%3] * m._values[2][(3-i)%3];
+ }
+ return sum;
+}
+
+
+/** Computes the determinant of the 2x2 submatrix of m where a given
+ * row and column were removed.
+ * @param[in] m base matrix
+ * @param[in] row row to remove
+ * @param[in] col column to remove */
+double det (const Matrix &m, int row, int col) {
+ int c1 = (col+1)%3, c2 = (col+2)%3;
+ int r1 = (row+1)%3, r2 = (row+2)%3;
+ if (c1 > c2)
+ swap(c1, c2);
+ if (r1 > r2)
+ swap(r1, r2);
+ return m._values[r1][c1] * m._values[r2][c2]
+ - m._values[r1][c2] * m._values[r2][c1];
+}
+
+
+static inline double deg2rad (double deg) {
+ const double PI = acos(-1.0);
+ return PI*deg/180.0;
+}
+
+
+/** Creates a diagonal matrix ((d,0,0),(0,d,0),(0,0,d)).
+ * @param[in] d value of diagonal elements */
+Matrix::Matrix (double d) {
+ for (int i=0; i < 3; i++)
+ for (int j=0; j < 3; j++)
+ _values[i][j] = (i==j ? d : 0);
+}
+
+
+/** Creates the matrix ((v0,v1,v2),(v3,v4,v5),(v6,v7,v8)).
+ * Expects that array v consists of 'size' elements. If size is less than 9, the
+ * remaining matrix components will be set to those of the identity matrix.
+ * @param[in] v array containing the matrix components
+ * @param[in] size size of array v */
+Matrix::Matrix (double v[], unsigned size) {
+ set(v, size);
+}
+
+
+/** Creates the matrix ((v0,v1,v2),(v3,v4,v5),(v6,v7,v8)).
+ * If vector v has less than 9 elements, the remaining matrix components will be set to
+ * those of the identity matrix.
+ * @param[in] v array containing the matrix components
+ * @param[in] start use vector components start,...,start+8 */
+Matrix::Matrix (const std::vector<double> &v, int start) {
+ set(v, start);
+}
+
+
+Matrix::Matrix (const string &cmds, Calculator &calc) {
+ parse(cmds, calc);
+}
+
+
+Matrix& Matrix::set (double v[], unsigned size) {
+ size = min(size, 9u);
+ for (unsigned i=0; i < size; i++)
+ _values[i/3][i%3] = v[i];
+ for (unsigned i=size; i < 9; i++)
+ _values[i/3][i%3] = (i%4 ? 0 : 1);
+ return *this;
+}
+
+
+/** Set matrix values ((v0,v1,v2),(v3,v4,v5),(v6,v7,v8)).
+ * If vector v has less than 9 elements, the remaining matrix components will be set to
+ * those of the identity matrix.
+ * @param[in] v array containing the matrix components
+ * @param[in] start use vector components start,...,start+8 */
+Matrix& Matrix::set (const vector<double> &v, int start) {
+ unsigned size = min((unsigned)v.size()-start, 9u);
+ for (unsigned i=0; i < size; i++)
+ _values[i/3][i%3] = v[i+start];
+ for (unsigned i=size; i < 9; i++)
+ _values[i/3][i%3] = (i%4 ? 0 : 1);
+ return *this;
+}
+
+
+Matrix& Matrix::translate (double tx, double ty) {
+ if (tx != 0 || ty != 0) {
+ TranslationMatrix t(tx, ty);
+ rmultiply(t);
+ }
+ return *this;
+}
+
+
+Matrix& Matrix::scale (double sx, double sy) {
+ if (sx != 1 || sy != 1) {
+ ScalingMatrix s(sx, sy);
+ rmultiply(s);
+ }
+ return *this;
+}
+
+
+/** Multiplies this matrix by ((cos d, -sin d, 0), (sin d, cos d, 0), (0,0,1)) that
+ * describes an anti-clockwise rotation by d degrees.
+ * @param[in] deg rotation angle in degrees */
+Matrix& Matrix::rotate (double deg) {
+ RotationMatrix r(deg);
+ rmultiply(r);
+ return *this;
+}
+
+
+Matrix& Matrix::xskew (double deg) {
+ double t = tan(deg2rad(deg));
+ if (t != 0) {
+ double v[] = {1, t};
+ Matrix t(v, 2);
+ rmultiply(t);
+ }
+ return *this;
+}
+
+
+Matrix& Matrix::yskew (double deg) {
+ double t = tan(deg2rad(deg));
+ if (t != 0) {
+ double v[] = {1, 0, 0, t};
+ Matrix t(v, 4);
+ rmultiply(t);
+ }
+ return *this;
+}
+
+
+Matrix& Matrix::flip (bool haxis, double a) {
+ double s = 1;
+ if (haxis) // mirror at horizontal axis?
+ s = -1;
+ double v[] = {-s, 0, (haxis ? 0 : 2*a), 0, s, (haxis ? 2*a : 0), 0, 0, 1};
+ Matrix t(v);
+ rmultiply(t);
+ return *this;
+}
+
+
+/** Swaps rows and columns of the matrix. */
+Matrix& Matrix::transpose () {
+ for (int i=0; i < 3; i++)
+ for (int j=i+1; j < 3; j++)
+ swap(_values[i][j], _values[j][i]);
+ return *this;
+}
+
+
+/** Multiplies this matrix M with matrix tm (tm is the factor on the left side): M := tm * M */
+Matrix& Matrix::lmultiply (const Matrix &tm) {
+ Matrix ret;
+ for (int i=0; i < 3; i++)
+ for (int j=0; j < 3; j++)
+ for (int k=0; k < 3; k++)
+ ret._values[i][j] += _values[i][k] * tm._values[k][j];
+ return *this = ret;
+}
+
+
+/** Multiplies this matrix M with matrix tm (tm is the factor on the right side): M := M * tm */
+Matrix& Matrix::rmultiply (const Matrix &tm) {
+ Matrix ret;
+ for (int i=0; i < 3; i++)
+ for (int j=0; j < 3; j++)
+ for (int k=0; k < 3; k++)
+ ret._values[i][j] += tm._values[i][k] * _values[k][j];
+ return *this = ret;
+}
+
+
+Matrix& Matrix::invert () {
+ Matrix ret;
+ if (double denom = det(*this)) {
+ for (int i=0; i < 3; ++i) {
+ for (int j=0; j < 3; ++j) {
+ ret._values[i][j] = det(*this, i, j)/denom;
+ if ((i+j)%2 != 0)
+ ret._values[i][j] *= -1;
+ }
+ }
+ return *this = ret;
+ }
+ throw exception();
+}
+
+
+Matrix& Matrix::operator *= (double c) {
+ for (int i=0; i < 3; i++)
+ for (int j=0; j < 3; j++)
+ _values[i][j] *= c;
+ return *this;
+}
+
+
+DPair Matrix::operator * (const DPair &p) const {
+ double pp[] = {p.x(), p.y(), 1};
+ double ret[]= {0, 0};
+ for (int i=0; i < 2; i++)
+ for (int j=0; j < 3; j++)
+ ret[i] += _values[i][j] * pp[j];
+ return DPair(ret[0], ret[1]);
+}
+
+
+/** Returns true if this matrix equals. Checks equality by comparing the matrix components. */
+bool Matrix::operator == (const Matrix &m) const {
+ for (int i=0; i < 2; i++)
+ for (int j=0; j < 3; j++)
+ if (_values[i][j] != m._values[i][j])
+ return false;
+ return true;
+}
+
+
+/** Returns true if this matrix doesn't equal m. Checks inequality by comparing the matrix components. */
+bool Matrix::operator != (const Matrix &m) const {
+ for (int i=0; i < 2; i++)
+ for (int j=0; j < 3; j++)
+ if (_values[i][j] != m._values[i][j])
+ return true;
+ return false;
+}
+
+
+/** Returns true if this matrix is the identity matrix ((1,0,0),(0,1,0),(0,0,1)). */
+bool Matrix::isIdentity() const {
+ for (int i=0; i < 2; i++)
+ for (int j=0; j < 3; j++) {
+ const double &v = _values[i][j];
+ if ((i == j && v != 1) || (i != j && v != 0))
+ return false;
+ }
+ return true;
+}
+
+
+/** Checks whether this matrix describes a plain translation (without any other transformations).
+ * If so, the parameters tx and ty are filled with the translation components.
+ * @param[out] tx horizontal translation
+ * @param[out] ty vertical translation
+ * @return true if matrix describes a pure translation */
+bool Matrix::isTranslation (double &tx, double &ty) const {
+ tx = _values[0][2];
+ ty = _values[1][2];
+ for (int i=0; i < 3; i++)
+ for (int j=0; j < 2; j++) {
+ const double &v = _values[i][j];
+ if ((i == j && v != 1) || (i != j && v != 0))
+ return false;
+ }
+ return _values[2][2] == 1;
+}
+
+
+/** Gets a parameter for the transformation command.
+ * @param[in] is parameter chars are read from this stream
+ * @param[in] calc parameters can be arithmetic expressions, so we need a calculator to evaluate them
+ * @param[in] def default value if parameter is optional
+ * @param[in] optional true if parameter is optional
+ * @param[in] leadingComma true if first non-blank must be a comma
+ * @return value of argument */
+static double getArgument (istream &is, Calculator &calc, double def, bool optional, bool leadingComma) {
+ while (isspace(is.peek()))
+ is.get();
+ if (!optional && leadingComma && is.peek() != ',')
+ throw ParserException("',' expected");
+ if (is.peek() == ',') {
+ is.get(); // skip comma
+ optional = false; // now we expect a parameter
+ }
+ string expr;
+ while (is && !isupper(is.peek()) && is.peek() != ',')
+ expr += is.get();
+ if (expr.length() == 0) {
+ if (optional)
+ return def;
+ else
+ throw ParserException("parameter expected");
+ }
+ return calc.eval(expr);
+}
+
+
+Matrix& Matrix::parse (istream &is, Calculator &calc) {
+ *this = Matrix(1);
+ while (is) {
+ while (isspace(is.peek()))
+ is.get();
+ char cmd = is.get();
+ switch (cmd) {
+ case 'T': {
+ double tx = getArgument(is, calc, 0, false, false);
+ double ty = getArgument(is, calc, 0, true, true);
+ translate(tx, ty);
+ break;
+ }
+ case 'S': {
+ double sx = getArgument(is, calc, 1, false, false);
+ double sy = getArgument(is, calc, sx, true, true );
+ scale(sx, sy);
+ break;
+ }
+ case 'R': {
+ double a = getArgument(is, calc, 0, false, false);
+ double x = getArgument(is, calc, calc.getVariable("ux")+calc.getVariable("w")/2, true, true);
+ double y = getArgument(is, calc, calc.getVariable("uy")+calc.getVariable("h")/2, true, true);
+ translate(-x, -y);
+ rotate(a);
+ translate(x, y);
+ break;
+ }
+ case 'F': {
+ char c = is.get();
+ if (c != 'H' && c != 'V')
+ throw ParserException("'H' or 'V' expected");
+ double a = getArgument(is, calc, 0, false, false);
+ flip(c == 'H', a);
+ break;
+ }
+ case 'K': {
+ char c = is.get();
+ if (c != 'X' && c != 'Y')
+ throw ParserException("transformation command 'K' must be followed by 'X' or 'Y'");
+ double a = getArgument(is, calc, 0, false, false);
+ if (fabs(cos(deg2rad(a))) <= numeric_limits<double>::epsilon()) {
+ ostringstream oss;
+ oss << "illegal skewing angle: " << a << " degrees";
+ throw ParserException(oss.str());
+ }
+ if (c == 'X')
+ xskew(a);
+ else
+ yskew(a);
+ break;
+ }
+ case 'M': {
+ double v[9];
+ for (int i=0; i < 6; i++)
+ v[i] = getArgument(is, calc, i%4 ? 0 : 1, i!=0, i!=0);
+ // third row (0, 0, 1)
+ v[6] = v[7] = 0;
+ v[8] = 1;
+ Matrix tm(v);
+ rmultiply(tm);
+ break;
+ }
+ default:
+ ostringstream oss;
+ oss << "transformation command expected (found '" << cmd << "' instead)";
+ throw ParserException(oss.str());
+ }
+ }
+ return *this;
+}
+
+
+Matrix& Matrix::parse (const string &cmds, Calculator &calc) {
+ istringstream iss;
+ iss.str(cmds);
+ return parse(iss, calc);
+}
+
+
+/** Returns an SVG matrix expression that can be used in transform attributes.
+ * ((a,b,c),(d,e,f),(0,0,1)) => matrix(a d b e c f) */
+string Matrix::getSVG () const {
+ ostringstream oss;
+ oss << "matrix(";
+ for (int i=0; i < 3; i++) {
+ for (int j=0; j < 2; j++) {
+ if (i > 0 || j > 0)
+ oss << ' ';
+ oss << XMLString(_values[j][i]);
+ }
+ }
+ oss << ')';
+ return oss.str();
+}
+
+
+ostream& Matrix::write (ostream &os) const {
+ os << '(';
+ for (int i=0; i < 3; i++) {
+ os << '(' << _values[i][0];
+ for (int j=1; j < 3; j++)
+ os << ',' << _values[i][j];
+ os << ')';
+ if (i < 2)
+ os << ',';
+ }
+ os << ')';
+ return os;
+}
+
+
+//////////////////////////////////////////////////////////////////
+
+
+TranslationMatrix::TranslationMatrix (double tx, double ty) {
+ double v[] = {1, 0, tx, 0, 1, ty};
+ set(v, 6);
+}
+
+
+ScalingMatrix::ScalingMatrix (double sx, double sy) {
+ double v[] = {sx, 0, 0, 0, sy};
+ set(v, 5);
+}
+
+
+RotationMatrix::RotationMatrix (double deg) {
+ double rad = deg2rad(deg);
+ double c = cos(rad);
+ double s = sin(rad);
+ double v[] = {c, -s, 0, s, c};
+ set(v, 5);
+}
+
+