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/*************************************************************************
** PathClipper.cpp **
** **
** This file is part of dvisvgm -- a fast DVI to SVG converter **
** Copyright (C) 2005-2018 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 "Bezier.hpp"
#include "PathClipper.hpp"
using namespace std;
using namespace ClipperLib;
using Polygon = ClipperLib::Path;
using Polygons = ClipperLib::Paths;
using CurvedPath = PathClipper::CurvedPath;
const int SCALE_FACTOR = 1000;
inline cInt to_cInt (double x) {
if (x < 0)
return static_cast<cInt>(x*SCALE_FACTOR - 0.5);
return static_cast<cInt>(x*SCALE_FACTOR + 0.5);
}
inline double to_double (cInt x) {
return static_cast<double>(x)/SCALE_FACTOR;
}
inline DPair to_DPair (const IntPoint &p) {
return DPair(to_double(p.X), to_double(p.Y));
}
/** In order to flatten a curved path, all path segements are processed sequentially.
* Depending on the type of the segment, one of the methods provided by this class
* is called. */
class FlattenActions : public CurvedPath::Actions {
public:
FlattenActions (vector<Bezier> &curves, Polygons &polygons, int &numLines)
: _polygons(polygons), _curves(curves), _numLines(numLines) {}
void moveto (const CurvedPath::Point &p) override {
if (p == _currentPoint && !_currentPoly.empty())
return;
closepath();
_currentPoly.emplace_back(IntPoint(to_cInt(p.x()), to_cInt(p.y()), 0));
_currentPoint = _startPoint = p;
}
void lineto (const CurvedPath::Point &p) override {
if (p == _currentPoint && !_currentPoly.empty())
return;
if (_currentPoly.empty()) // this shouldn't happen but in case it does...
_currentPoly.emplace_back(IntPoint(0, 0, 0)); // ...add a start point first
_numLines--;
_currentPoly.back().Z.label2 = _numLines;
_currentPoly.emplace_back(IntPoint(to_cInt(p.x()), to_cInt(p.y()), ZType(_numLines, 0)));
_currentPoint = p;
}
void conicto (const CurvedPath::Point &p1, const CurvedPath::Point &p2) override {
Bezier bezier(_currentPoint, p1, p2);
addCurvePoints(bezier);
}
void cubicto (const CurvedPath::Point &p1, const CurvedPath::Point &p2, const CurvedPath::Point &p3) override {
Bezier bezier(_currentPoint, p1, p2, p3);
addCurvePoints(bezier);
}
void closepath () override {
if (_currentPoly.empty())
return;
_numLines--;
_currentPoly.back().Z.label2 = ZLabel(_numLines, 0);
_currentPoly.front().Z.label1 = ZLabel(_numLines, 0);
_polygons.push_back(_currentPoly);
_currentPoly.clear();
}
void finished () override {
closepath();
}
protected:
void addCurvePoints (const Bezier &bezier) {
if (_currentPoly.empty()) // this shouldn't happen but in case it does, ...
_currentPoly.emplace_back(IntPoint(0, 0, 0)); // ...add a start point first
vector<DPair> points; // points of flattened curve
vector<double> t; // corresponding 'time' parameters
bezier.approximate(0.01, points, &t);
if (points.size() < 2)
return;
_curves.push_back(bezier);
for (size_t i=1; i < points.size(); i++) {
const DPair &p = points[i];
if (p == _currentPoint)
continue;
_currentPoly.back().Z.label2 = ZLabel(_curves.size(), t[i-1]);
ZLabel label(_curves.size(), t[i]);
_currentPoly.emplace_back(IntPoint(to_cInt(p.x()), to_cInt(p.y()), ZType(label, label)));
_currentPoint = p;
}
}
private:
CurvedPath::Point _startPoint, _currentPoint;
Polygon _currentPoly; ///< polygon being created
Polygons &_polygons; ///< all polygons created
vector<Bezier> &_curves;
int &_numLines;
};
/** Removes adjacent polygon vertices that equal their predecessor. */
static void remove_redundant_vertices (Polygon &polygon) {
Polygon::iterator it1=polygon.begin();
while (it1 != polygon.end()) {
Polygon::iterator it2 = it1+1;
if (it2 == polygon.end())
it2 = polygon.begin();
if (it1 == it2)
return;
if (*it1 != *it2)
++it1;
else {
it1->Z.label2 = it2->Z.label2;
polygon.erase(it2);
}
}
}
/** Approximates a curved path by a set of polygons and stores information
* to reconstruct the curved segments later. The z component of each
* polygon vertex holds two integers representing information about the two
* adjacent edges the vertex belongs to. This is required to identify the
* affected edges and thus the former (curve/line) segment of the path during
* the intersection process.
* @param[in] curvedPath curved path to be flattened
* @param[out] polygons the flattened path (set of polygons) */
void PathClipper::flatten (const CurvedPath &curvedPath, Polygons &polygons) {
FlattenActions flattenActions(_curves, polygons, _numLines);
curvedPath.iterate(flattenActions, false);
for (size_t i=0; i < polygons.size(); i++)
remove_redundant_vertices(polygons[i]);
}
/** Returns the ID of the path segment the polygon edge defined by its start
* and end point belongs to. The z component of a polygon vertex holds a pair
* of labels that allows to identify the original path segments the point belongs to.
* Since always two adjacent segments share a point, each point gets two values assigned.
* Negative numbers denote line segments, positive ones Bézier curves.
* There are only these two segment types, so we don't need further flags in
* order to distinguish them. By comparing the labels of two adjacent polygon
* vertexes it's possible to identify the original path segment the corresponding
* edge belongs to.
* @param[in] p1 first of two adjacent vertices
* @param[in] p2 second of two adjacent vertices
* @param[out] t1 time parameter of p1
* @param[out] t2 time parameter of p2
* @return id of edge between p1 and p2, or 0 if it's not possible to identify the segment */
static int32_t segment_id (const IntPoint &p1, const IntPoint &p2, double &t1, double &t2) {
const ZType &z1=p1.Z, &z2=p2.Z;
if (z1 == z2 && z1.minLabel().id < 0) return z1.minLabel().id;
if (z1.label1 == z2.label2) {t1=z1.label1.t; t2=z2.label2.t; return z1.label1.id;}
if (z1.label2 == z2.label1) {t1=z1.label2.t; t2=z2.label1.t; return z1.label2.id;}
if (z1.label1 == z2.label1) {t1=z1.label1.t; t2=z2.label1.t; return z1.label1.id;}
if (z1.label2 == z2.label2) {t1=z1.label2.t; t2=z2.label2.t; return z1.label2.id;}
// if we get here, it's not possible to identify the segment
// => the edge is going to be handled as line segment
return 0;
}
/** This function expects 3 colinear points p1, p2, and q, where q lies between p1 and p2,
* i.e. q divides the line \f$ \overline{p_1 p_2} \f$ somewhere. The function returns
* the corresponding division ratio. */
static double division_ratio (const IntPoint &p1, const IntPoint &p2, const IntPoint &q) {
if (p1 == p2 || q == p1)
return 0;
if (q == p2)
return 1;
if (p1.X == p2.X)
return double(q.Y-p1.Y)/(p2.Y-p1.Y);
return double(q.X-p1.X)/(p2.X-p1.X);
}
/** Returns the label of point q that lies on the line between points p1 and p2. */
inline ZLabel division_label (const IntPoint &p1, const IntPoint &p2, const IntPoint &q) {
double t1, t2;
double s=0;
int32_t id = segment_id(p1, p2, t1, t2);
if (id > 0)
s = t1+(t2-t1)*division_ratio(p1, p2, q);
return ZLabel(id, s);
}
/** This method is called if the clipper library finds an intersection between two polygon edges.
* It populates the z coordinate of the intersection point with the idexes of the two edges.
* @param[in] e1bot first endpoint of edge 1
* @param[in] e1top second endpoint of edge 1
* @param[in] e2bot first endpoint of edge 2
* @param[in] e2top second endpoint of edge 2
* @param[in] ip intersection point of edge 1 and 2 */
void PathClipper::callback (IntPoint &e1bot, IntPoint &e1top, IntPoint &e2bot, IntPoint &e2top, IntPoint &ip) {
ZLabel label1 = division_label(e1bot, e1top, ip);
ZLabel label2 = division_label(e2bot, e2top, ip);
ip.Z = ZType(label1, label2);
}
/** Iterates along the polygon edges until the endpoint of the current
* path segment is found and returns its vector index afterwards.
* @param[in] polygon the polygon to be processed
* @param[in] start index of the vertex where the iteration starts
* @param[out] label if not 0, retrieves the label of the endpoint
* @param[in] startLabel if true, the found endpoint is treated as start point and
* parameter 'label' gets the corresponding value */
static size_t find_segment_endpoint (const Polygon &polygon, size_t start, ZLabel *label=0, bool startLabel=false) {
if (polygon.empty())
return 0;
const size_t num_points = polygon.size();
int i = start%num_points;
double t1=0, t2=0; // time parameters of start and endpoint of current edge
int32_t id1 = segment_id(polygon[i], polygon[(i+1)%num_points], t1, t2);
int32_t id2 = id1;
double t = t2; // time parameter of resulting endpoint
for (size_t j=1; id1 == id2 && j < num_points; j++) {
t = t2;
i = (i+1)%num_points;
if (id1 == 0)
break;
id2 = segment_id(polygon[i], polygon[(i+1)%num_points], t1, t2);
}
if (label) {
*label = ZLabel(id1, id1 < 0 ? 0 : t);
if (startLabel && id1 != 0)
*label = polygon[i].Z.otherLabel(*label);
}
return i;
}
/** Reconstructs a curved path from the set of polygons.
* @param[in] polygons set of polygons to reconstruct
* @param[out] path the reconstructed curved path */
void PathClipper::reconstruct (const Polygons &polygons, CurvedPath &path) {
for (const Polygon &polygon : polygons)
reconstruct(polygon, path);
}
/** Reconstructs a curved path from a single polygon.
* @param[in] polygon polygon to reconstruct
* @param[out] path the reconstructed curved path */
void PathClipper::reconstruct (const Polygon &polygon, CurvedPath &path) {
size_t num_points = polygon.size();
if (num_points < 2)
return;
ZLabel label1, label2; // labels of the current segment's start and endpoint
int index1 = find_segment_endpoint(polygon, 0, &label1, true);
int index2 = find_segment_endpoint(polygon, index1, &label2);
int diff = (num_points+index2-index1)%num_points;
path.moveto(to_DPair(polygon[index1]));
for (size_t count = diff; count <= num_points; count += diff) {
if (diff == 1 || label1.id <= 0) // line segment?
path.lineto(to_DPair(polygon[index2]));
else { // Bézier curve segment
Bezier bezier(_curves[label1.id-1], label1.t, label2.t);
if (label1.t > label2.t)
bezier.reverse();
path.cubicto(bezier.point(1), bezier.point(2), bezier.point(3));
}
if (label1.id == 0)
find_segment_endpoint(polygon, index2, &label1, true);
else
label1 = polygon[index2].Z.otherLabel(label2);
index1 = index2;
index2 = find_segment_endpoint(polygon, index1, &label2);
diff = (num_points+index2-index1)%num_points;
}
path.closepath();
}
inline PolyFillType polyFillType (CurvedPath::WindingRule wr) {
return (wr == CurvedPath::WindingRule::NON_ZERO) ? pftNonZero : pftEvenOdd;
}
/** Computes the intersection of to curved paths.
* @param[in] p1 first curved path
* @param[in] p2 second curved path
* @param[out] result intersection of p1 and p2 */
void PathClipper::intersect (const CurvedPath &p1, const CurvedPath &p2, CurvedPath &result) {
if (p1.size() < 2 || p2.size() < 2)
return;
Clipper clipper;
Polygons polygons;
flatten(p1, polygons);
clipper.AddPaths(polygons, ptSubject, true);
polygons.clear();
flatten(p2, polygons);
clipper.AddPaths(polygons, ptClip, true);
clipper.ZFillFunction(callback);
Polygons flattenedPath;
clipper.Execute(ctIntersection, flattenedPath, polyFillType(p1.windingRule()), polyFillType(p2.windingRule()));
reconstruct(flattenedPath, result);
}
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