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-/*************************************************************************
-** Matrix.cpp **
-** **
-** This file is part of dvisvgm -- a fast DVI to SVG converter **
-** Copyright (C) 2005-2021 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 <algorithm>
-#include <limits>
-#include <sstream>
-#include "Calculator.hpp"
-#include "Matrix.hpp"
-#include "utility.hpp"
-#include "XMLString.hpp"
-
-using namespace std;
-using math::deg2rad;
-
-
-/** 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];
-}
-
-
-/** Creates a diagonal matrix ((d,0,0),(0,d,0),(0,0,d)).
- * @param[in] d value of diagonal elements */
-Matrix::Matrix (double d) {
- set(d);
-}
-
-
-/** 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 (const 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) {
- *this = parse(cmds, calc);
-}
-
-
-Matrix::Matrix (initializer_list<double> initlist) {
- int count=0;
- for (auto it=initlist.begin(); it != initlist.end() && count < 9; ++it) {
- _values[count/3][count%3] = *it;
- count++;
- }
- for (; count < 9; count++)
- _values[count/3][count%3] = (count%4 ? 0 : 1);
-}
-
-
-Matrix& Matrix::set (double d) {
- for (int i=0; i < 3; i++)
- for (int j=0; j < 3; j++)
- _values[i][j] = (i==j ? d : 0);
- return *this;
-}
-
-
-Matrix& Matrix::set (const 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::set (const string &cmds, Calculator &calc) {
- *this = parse(cmds, calc);
- return *this;
-}
-
-
-Matrix& Matrix::translate (double tx, double ty) {
- if (tx != 0 || ty != 0) {
- TranslationMatrix t(tx, ty);
- lmultiply(t);
- }
- return *this;
-}
-
-
-Matrix& Matrix::scale (double sx, double sy) {
- if (sx != 1 || sy != 1) {
- ScalingMatrix s(sx, sy);
- lmultiply(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);
- lmultiply(r);
- return *this;
-}
-
-
-Matrix& Matrix::xskewByAngle (double deg) {
- if (fmod(abs(deg)-90, 180) != 0)
- return xskewByRatio(tan(deg2rad(deg)));
- return *this;
-}
-
-
-Matrix& Matrix::xskewByRatio (double xyratio) {
- if (xyratio != 0) {
- double v[] = {1, xyratio};
- Matrix t(v, 2);
- lmultiply(t);
- }
- return *this;
-}
-
-
-Matrix& Matrix::yskewByAngle (double deg) {
- if (fmod(abs(deg)-90, 180) != 0)
- return yskewByRatio(tan(deg2rad(deg)));
- return *this;
-}
-
-
-Matrix& Matrix::yskewByRatio (double xyratio) {
- if (xyratio != 0) {
- double v[] = {1, 0, 0, xyratio};
- Matrix t(v, 4);
- lmultiply(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);
- lmultiply(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 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] += _values[i][k] * tm._values[k][j];
- return *this = ret;
-}
-
-
-/** 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] += tm._values[i][k] * _values[k][j];
- return *this = ret;
-}
-
-
-Matrix& Matrix::invert () {
- Matrix ret;
- double denom = det(*this);
- if (abs(denom) < 1e-12)
- throw exception();
- for (int i=0; i < 3; ++i) {
- for (int j=0; j < 3; ++j) {
- ret._values[j][i] = det(*this, i, j)/denom;
- if ((i+j)%2 != 0)
- ret._values[j][i] *= -1;
- }
- }
- return *this = ret;
-}
-
-
-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 (std::abs(_values[i][j]-m._values[i][j]) >= numeric_limits<double>::epsilon())
- 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 (std::abs(_values[i][j]-m._values[i][j]) >= numeric_limits<double>::epsilon())
- 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) {
- is >> ws;
- 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 (!isupper(is.peek()) && is.peek() != ',' && is)
- expr += (char)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) {
- Matrix ret(1);
- while (is) {
- is >> ws;
- int cmd = is.get();
- switch (cmd) {
- case 'T': {
- double tx = getArgument(is, calc, 0, false, false);
- double ty = getArgument(is, calc, 0, true, true);
- ret.translate(tx, ty);
- break;
- }
- case 'S': {
- double sx = getArgument(is, calc, 1, false, false);
- double sy = getArgument(is, calc, sx, true, true );
- ret.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);
- ret.translate(-x, -y);
- ret.rotate(a);
- ret.translate(x, y);
- break;
- }
- case 'F': {
- int c = is.get();
- if (c != 'H' && c != 'V')
- throw ParserException("'H' or 'V' expected");
- double a = getArgument(is, calc, 0, false, false);
- ret.flip(c == 'H', a);
- break;
- }
- case 'K': {
- int 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 (std::abs(cos(deg2rad(a))) < numeric_limits<double>::epsilon())
- throw ParserException("illegal skewing angle: " + util::to_string(a) + " degrees");
- if (c == 'X')
- ret.xskewByAngle(a);
- else
- ret.yskewByAngle(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);
- ret.lmultiply(tm);
- break;
- }
- default:
- throw ParserException("transformation command expected (found '" + string(1, cmd) + "' instead)");
- }
- }
- return ret;
-}
-
-
-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::toSVG () const {
- ostringstream oss;
- oss << "matrix(";
- for (int i=0; i < 3; i++) {
- for (int j=0; j < 2; j++)
- oss << XMLString(_values[j][i]) << ' ';
- }
- oss.seekp(-1, ios::cur) << ')'; // overwrite trailing space character
- 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;
-}
-
-
-static const char* ord_suffix (int n) {
- static const char *suffixes[] = {"th", "st", "nd", "rd"};
- if (abs(n) < 4)
- return suffixes[n];
- return suffixes[0];
-}
-
-
-static void skip_comma_wsp (istream &is) {
- is >> ws;
- if (is.peek() == ',') is.get();
- is >> ws;
-}
-
-
-static size_t parse_transform_cmd (istream &is, string cmd, size_t minparams, size_t maxparams, vector<double> &params) {
- for (int i=0; i < int(cmd.length()); i++) {
- if (is.get() != cmd[i]) {
- is.seekg(-i-1, ios::cur);
- return 0;
- }
- }
- params.clear();
- is >> ws;
- if (is.get() != '(')
- throw ParserException("missing '(' after command '"+cmd+"'");
- for (size_t i=1; i <= maxparams; i++) {
- is >> ws;
- double val;
- if (is.fail())
- throw ParserException(to_string(i)+ord_suffix(i)+" parameter of '"+cmd+"' must be a number");
- is >> val;
- params.push_back(val);
- is >> ws;
- if (i == minparams && is.peek() == ')') {
- is.get();
- return i;
- }
- if (i == maxparams) {
- if (is.peek() != ')')
- throw ParserException("missing ')' at end of command '"+cmd+"'");
- is.get();
- }
- skip_comma_wsp(is);
- }
- return maxparams;
-}
-
-
-static bool ne (double x, double y) {return abs(x-y) >= 1e-6;}
-static bool ne_angle (double x, double y) {return abs(x-y) >= 1e-3;}
-
-
-Matrix Matrix::parseSVGTransform (const string &transform) {
- istringstream iss(transform);
- Matrix matrix(1);
- iss >> ws;
- while (iss) {
- vector<double> params;
- if (parse_transform_cmd(iss, "matrix", 6, 6, params)) {
- if (ne(params[0], 1) || ne(params[1], 0) || ne(params[2], 0) || ne(params[3], 1) || ne(params[4], 0) || ne(params[5], 0))
- matrix.rmultiply({params[0], params[2], params[4], params[1], params[3], params[5]});
- }
- else if (parse_transform_cmd(iss, "rotate", 1, 3, params)) {
- if (params.size() == 1) {
- params.push_back(0);
- params.push_back(0);
- }
- if (ne_angle(fmod(params[0], 360), 0)) {
- bool translate = ne(params[1], 0) || ne(params[2], 0);
- if (translate)
- matrix.rmultiply(TranslationMatrix(params[1], params[2]));
- matrix.rmultiply(RotationMatrix(params[0]));
- if (translate)
- matrix.rmultiply(TranslationMatrix(-params[1], -params[2]));
- }
- }
- else if (parse_transform_cmd(iss, "scale", 1, 2, params)) {
- if (params.size() == 1)
- params.push_back(params[0]);
- if (ne(params[0], 1) || ne(params[1], 1))
- matrix.rmultiply(ScalingMatrix(params[0], params[1]));
- }
- else if (parse_transform_cmd(iss, "skewX", 1, 1, params)) {
- if (ne_angle(fmod(abs(params[0])-90, 180), 0))
- matrix.rmultiply(XSkewingMatrix(params[0]));
- }
- else if (parse_transform_cmd(iss, "skewY", 1, 1, params)) {
- if (ne_angle(fmod(abs(params[0])-90, 180), 0))
- matrix.rmultiply(YSkewingMatrix(params[0]));
- }
- else if (parse_transform_cmd(iss, "translate", 1, 2, params)) {
- if (params.size() == 1)
- params.push_back(0);
- if (ne(params[0], 0) || ne(params[1], 0))
- matrix.rmultiply(TranslationMatrix(params[0], params[1]));
- }
- else { // invalid command
- string cmd;
- while (isalpha(iss.peek()))
- cmd += char(iss.get());
- if (cmd.empty())
- throw ParserException("unexpected character in transform attribute: "+to_string(char(iss.get())));
- throw ParserException("invalid command in transform attribute: "+cmd);
- }
- skip_comma_wsp(iss);
- }
- return matrix;
-}
-
-//////////////////////////////////////////////////////////////////
-
-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);
-}
-
-
-XSkewingMatrix::XSkewingMatrix (double deg) {
- double xyratio = tan(deg2rad(deg));
- lmultiply(Matrix({1, xyratio}));
-}
-
-
-YSkewingMatrix::YSkewingMatrix (double deg) {
- double xyratio = tan(deg2rad(deg));
- lmultiply(Matrix({1, 0, 0, xyratio}));
-}