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Diffstat (limited to 'Build/source/texk/dvisvgm/dvisvgm-1.10/src/Matrix.cpp')
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diff --git a/Build/source/texk/dvisvgm/dvisvgm-1.10/src/Matrix.cpp b/Build/source/texk/dvisvgm/dvisvgm-1.10/src/Matrix.cpp new file mode 100644 index 00000000000..06537689c3f --- /dev/null +++ b/Build/source/texk/dvisvgm/dvisvgm-1.10/src/Matrix.cpp @@ -0,0 +1,491 @@ +/************************************************************************* +** Matrix.cpp ** +** ** +** This file is part of dvisvgm -- the DVI to SVG converter ** +** Copyright (C) 2005-2015 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/>. ** +*************************************************************************/ + +#define _USE_MATH_DEFINES +#include <config.h> +#include <algorithm> +#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) { + return M_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) { + 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 (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 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 (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) { + parse(cmds, calc); + 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::xskewByAngle (double deg) { + if (fmod(fabs(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); + rmultiply(t); + } + return *this; +} + + +Matrix& Matrix::yskewByAngle (double deg) { + if (fmod(fabs(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); + 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 += (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) { + *this = Matrix(1); + while (is) { + while (isspace(is.peek())) + is.get(); + int 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': { + int 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': { + 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 (fabs(cos(deg2rad(a))) <= numeric_limits<double>::epsilon()) { + ostringstream oss; + oss << "illegal skewing angle: " << a << " degrees"; + throw ParserException(oss.str()); + } + if (c == 'X') + xskewByAngle(a); + else + 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); + 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); +} + + |