GCC Code Coverage Report

Directory: ./
File: src/2geom/curve.cpp
Date: 2024-03-18 17:01:34
Exec Total Coverage
Lines: 77 99 77.8%
Functions: 6 11 54.5%
Branches: 72 138 52.2%
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1 /* Abstract curve type - implementation of default methods
2 *
3 * Authors:
4 * MenTaLguY <mental@rydia.net>
5 * Marco Cecchetti <mrcekets at gmail.com>
6 * Krzysztof Kosiński <tweenk.pl@gmail.com>
7 * Rafał Siejakowski <rs@rs-math.net>
8 *
9 * Copyright 2007-2009 Authors
10 *
11 * This library is free software; you can redistribute it and/or
12 * modify it either under the terms of the GNU Lesser General Public
13 * License version 2.1 as published by the Free Software Foundation
14 * (the "LGPL") or, at your option, under the terms of the Mozilla
15 * Public License Version 1.1 (the "MPL"). If you do not alter this
16 * notice, a recipient may use your version of this file under either
17 * the MPL or the LGPL.
18 *
19 * You should have received a copy of the LGPL along with this library
20 * in the file COPYING-LGPL-2.1; if not, write to the Free Software
21 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
22 * You should have received a copy of the MPL along with this library
23 * in the file COPYING-MPL-1.1
24 *
25 * The contents of this file are subject to the Mozilla Public License
26 * Version 1.1 (the "License"); you may not use this file except in
27 * compliance with the License. You may obtain a copy of the License at
28 * http://www.mozilla.org/MPL/
29 *
30 * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
31 * OF ANY KIND, either express or implied. See the LGPL or the MPL for
32 * the specific language governing rights and limitations.
33 */
34
35 #include <2geom/curve.h>
36 #include <2geom/exception.h>
37 #include <2geom/nearest-time.h>
38 #include <2geom/sbasis-geometric.h>
39 #include <2geom/sbasis-to-bezier.h>
40 #include <2geom/ord.h>
41 #include <2geom/path-sink.h>
42
43 namespace Geom
44 {
45
46 ✗ Coord Curve::nearestTime(Point const& p, Coord a, Coord b) const
47 {
48 ✗ return nearest_time(p, toSBasis(), a, b);
49 }
50
51 ✗ std::vector<Coord> Curve::allNearestTimes(Point const& p, Coord from, Coord to) const
52 {
53 ✗ return all_nearest_times(p, toSBasis(), from, to);
54 }
55
56 ✗ Coord Curve::length(Coord tolerance) const
57 {
58 ✗ return ::Geom::length(toSBasis(), tolerance);
59 }
60
61 4 int Curve::winding(Point const &p) const
62 {
63 try {
64
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 4 std::vector<Coord> ts = roots(p[Y], Y);
65
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 4 if(ts.empty()) return 0;
66
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 4 std::sort(ts.begin(), ts.end());
67
68 // skip endpoint roots when they are local maxima on the Y axis
69 // this follows the convention used in other winding routines,
70 // i.e. that the bottommost coordinate is not part of the shape
71
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 4 bool ignore_0 = unitTangentAt(0)[Y] <= 0;
72
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 4 bool ignore_1 = unitTangentAt(1)[Y] >= 0;
73
74 4 int wind = 0;
75
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 12 for (double t : ts) {
76 //std::cout << t << std::endl;
77
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 8 if ((t == 0 && ignore_0) || (t == 1 && ignore_1)) continue;
78
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 8 if (valueAt(t, X) > p[X]) { // root is ray intersection
79
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 4 Point tangent = unitTangentAt(t);
80
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 4 if (tangent[Y] > 0) {
81 // at the point of intersection, curve goes in +Y direction,
82 // so it winds in the direction of positive angles
83 ✗ ++wind;
84
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 4 } else if (tangent[Y] < 0) {
85 ✗ --wind;
86 }
87 }
88 }
89 4 return wind;
90
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 4 } catch (InfiniteSolutions const &e) {
91 // this means we encountered a line segment exactly coincident with the point
92 // skip, since this will be taken care of by endpoint roots in other segments
93 ✗ return 0;
94 ✗ }
95 }
96
97 ✗ std::vector<CurveIntersection> Curve::intersect(Curve const &/*other*/, Coord /*eps*/) const
98 {
99 // TODO: approximate as Bezier
100 ✗ THROW_NOTIMPLEMENTED();
101 }
102
103 68 std::vector<CurveIntersection> Curve::intersectSelf(Coord eps) const
104 {
105 /// Represents a sub-arc of the curve.
106 struct Subcurve
107 {
108 std::unique_ptr<Curve> curve;
109 Interval parameter_range;
110
111 65 Subcurve(Curve *piece, Coord from, Coord to)
112 65 : curve{piece}
113
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 65 , parameter_range{from, to}
114 65 {}
115 };
116
117 /// A closure to split the curve into portions at the prescribed split points.
118 68 auto const split_into_subcurves = [this] (std::vector<Coord> const &splits) {
119 32 std::vector<Subcurve> result;
120
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 32 result.reserve(splits.size() + 1);
121 32 Coord previous = 0;
122
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 80 for (Coord split : splits) {
123 // Use global EPSILON since we're operating on normalized curve times.
124
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 48 if (split < EPSILON || split > 1.0 - EPSILON) {
125 15 continue;
126 }
127
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 33 result.emplace_back(portion(previous, split), previous, split);
128 33 previous = split;
129 }
130
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 32 result.emplace_back(portion(previous, 1.0), previous, 1.0);
131 64 return result;
132 ✗ };
133
134 /// A closure to find pairwise intersections between the passed subcurves.
135 68 auto const pairwise_intersect = [=](std::vector<Subcurve> const &subcurves) {
136 32 std::vector<CurveIntersection> result;
137
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 97 for (unsigned i = 0; i < subcurves.size(); i++) {
138
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 107 for (unsigned j = i + 1; j < subcurves.size(); j++) {
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 42 auto const xings = subcurves[i].curve->intersect(*subcurves[j].curve, eps);
140
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 82 for (auto const &xing : xings) {
141 // To avoid duplicate intersections, skip values at exactly 1.
142
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 40 if (xing.first == 1. || xing.second == 1.) {
143 23 continue;
144 }
145
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 17 Coord const ti = subcurves[i].parameter_range.valueAt(xing.first);
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 17 Coord const tj = subcurves[j].parameter_range.valueAt(xing.second);
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 17 result.emplace_back(ti, tj, xing.point());
148 }
149 42 }
150 }
151
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 32 std::sort(result.begin(), result.end());
152 32 return result;
153 ✗ };
154
155 // Monotonic segments cannot have self-intersections. Thus, we can split
156 // the curve at critical points of the X or Y coordinate and intersect
157 // the portions. However, there's the risk that a juncture between two
158 // adjacent portions is mistaken for an intersection due to numerical errors.
159 // Hence, we run the algorithm for both the X and Y coordinates and only
160 // keep the intersections that show up in both intersection lists.
161
162 // Find the critical points of both coordinates.
163
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 68 std::unique_ptr<Curve> deriv{derivative()};
164
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 68 auto const crits_x = deriv->roots(0, X);
165
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 68 auto const crits_y = deriv->roots(0, Y);
166
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 68 if (crits_x.empty() || crits_y.empty()) {
167 52 return {};
168 }
169
170 // Split into pieces in two ways and find self-intersections.
171
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 16 auto const pieces_x = split_into_subcurves(crits_x);
172
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 16 auto const pieces_y = split_into_subcurves(crits_y);
173
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 16 auto const crossings_from_x = pairwise_intersect(pieces_x);
174
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 16 auto const crossings_from_y = pairwise_intersect(pieces_y);
175
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 16 if (crossings_from_x.empty() || crossings_from_y.empty()) {
176 12 return {};
177 }
178
179 // Filter the results, only keeping self-intersections found by both approaches.
180 4 std::vector<CurveIntersection> result;
181 4 unsigned index_y = 0;
182
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 8 for (auto &&candidate_x : crossings_from_x) {
183 // Find a crossing corresponding to this one in the y-method collection.
184
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 4 while (index_y != crossings_from_y.size()) {
185 4 auto const gap = crossings_from_y[index_y].first - candidate_x.first;
186
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 4 if (std::abs(gap) < EPSILON) {
187 // We found the matching intersection!
188
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 2 result.emplace_back(candidate_x);
189 2 index_y++;
190 2 break;
191
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 2 } else if (gap < 0.0) {
192 ✗ index_y++;
193 } else {
194 2 break;
195 }
196 }
197 }
198 4 return result;
199 68 }
200
201 173 Point Curve::unitTangentAt(Coord t, unsigned n) const
202 {
203
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 173 std::vector<Point> derivs = pointAndDerivatives(t, n);
204
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 177 for (unsigned deriv_n = 1; deriv_n < derivs.size(); deriv_n++) {
205 176 Coord length = derivs[deriv_n].length();
206
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 176 if ( ! are_near(length, 0) ) {
207 // length of derivative is non-zero, so return unit vector
208 172 return derivs[deriv_n] / length;
209 }
210 }
211 1 return Point (0,0);
212 173 };
213
214 ✗ void Curve::feed(PathSink &sink, bool moveto_initial) const
215 {
216 ✗ std::vector<Point> pts;
217 ✗ sbasis_to_bezier(pts, toSBasis(), 2); //TODO: use something better!
218 ✗ if (moveto_initial) {
219 ✗ sink.moveTo(initialPoint());
220 }
221 ✗ sink.curveTo(pts[0], pts[1], pts[2]);
222 ✗ }
223
224 } // namespace Geom
225
226 /*
227 Local Variables:
228 mode:c++
229 c-file-style:"stroustrup"
230 c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
231 indent-tabs-mode:nil
232 fill-column:99
233 End:
234 */
235 // vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :
236