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/*************************************************************************
** Matrix.cpp **
** **
** This file is part of dvisvgm -- a fast DVI to SVG converter **
** Copyright (C) 2005-2016 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);
}
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