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|---|---|---|---|
| 1 | /** | ||
| 2 | * \file | ||
| 3 | * \brief Elliptical arc curve | ||
| 4 | * | ||
| 5 | *//* | ||
| 6 | * Authors: | ||
| 7 | * MenTaLguY <mental@rydia.net> | ||
| 8 | * Marco Cecchetti <mrcekets at gmail.com> | ||
| 9 | * Krzysztof Kosiński <tweenk.pl@gmail.com> | ||
| 10 | * | ||
| 11 | * Copyright 2007-2009 Authors | ||
| 12 | * | ||
| 13 | * This library is free software; you can redistribute it and/or | ||
| 14 | * modify it either under the terms of the GNU Lesser General Public | ||
| 15 | * License version 2.1 as published by the Free Software Foundation | ||
| 16 | * (the "LGPL") or, at your option, under the terms of the Mozilla | ||
| 17 | * Public License Version 1.1 (the "MPL"). If you do not alter this | ||
| 18 | * notice, a recipient may use your version of this file under either | ||
| 19 | * the MPL or the LGPL. | ||
| 20 | * | ||
| 21 | * You should have received a copy of the LGPL along with this library | ||
| 22 | * in the file COPYING-LGPL-2.1; if not, write to the Free Software | ||
| 23 | * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA | ||
| 24 | * You should have received a copy of the MPL along with this library | ||
| 25 | * in the file COPYING-MPL-1.1 | ||
| 26 | * | ||
| 27 | * The contents of this file are subject to the Mozilla Public License | ||
| 28 | * Version 1.1 (the "License"); you may not use this file except in | ||
| 29 | * compliance with the License. You may obtain a copy of the License at | ||
| 30 | * http://www.mozilla.org/MPL/ | ||
| 31 | * | ||
| 32 | * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY | ||
| 33 | * OF ANY KIND, either express or implied. See the LGPL or the MPL for | ||
| 34 | * the specific language governing rights and limitations. | ||
| 35 | */ | ||
| 36 | |||
| 37 | #ifndef LIB2GEOM_SEEN_ELLIPTICAL_ARC_H | ||
| 38 | #define LIB2GEOM_SEEN_ELLIPTICAL_ARC_H | ||
| 39 | |||
| 40 | #include <algorithm> | ||
| 41 | #include <2geom/affine.h> | ||
| 42 | #include <2geom/angle.h> | ||
| 43 | #include <2geom/bezier-curve.h> | ||
| 44 | #include <2geom/curve.h> | ||
| 45 | #include <2geom/ellipse.h> | ||
| 46 | #include <2geom/sbasis-curve.h> // for non-native methods | ||
| 47 | #include <2geom/utils.h> | ||
| 48 | |||
| 49 | namespace Geom | ||
| 50 | { | ||
| 51 | |||
| 52 | class EllipticalArc : public Curve | ||
| 53 | { | ||
| 54 | public: | ||
| 55 | /** @brief Creates an arc with all variables set to zero. */ | ||
| 56 | ✗ | EllipticalArc() | |
| 57 | ✗ | : _initial_point(0,0) | |
| 58 | ✗ | , _final_point(0,0) | |
| 59 | ✗ | , _large_arc(false) | |
| 60 | ✗ | {} | |
| 61 | /** @brief Create a new elliptical arc. | ||
| 62 | * @param ip Initial point of the arc | ||
| 63 | * @param r Rays of the ellipse as a point | ||
| 64 | * @param rot Angle of rotation of the X axis of the ellipse in radians | ||
| 65 | * @param large If true, the large arc is chosen (always >= 180 degrees), otherwise | ||
| 66 | * the smaller arc is chosen | ||
| 67 | * @param sweep If true, the clockwise arc is chosen, otherwise the counter-clockwise | ||
| 68 | * arc is chosen | ||
| 69 | * @param fp Final point of the arc */ | ||
| 70 | ✗ | EllipticalArc( Point const &ip, Point const &r, | |
| 71 | Coord rot_angle, bool large_arc, bool sweep, | ||
| 72 | Point const &fp | ||
| 73 | ) | ||
| 74 | ✗ | : _initial_point(ip) | |
| 75 | ✗ | , _final_point(fp) | |
| 76 | ✗ | , _ellipse(0, 0, r[X], r[Y], rot_angle) | |
| 77 | ✗ | , _angles(0, 0, sweep) | |
| 78 | ✗ | , _large_arc(large_arc) | |
| 79 | { | ||
| 80 | ✗ | _updateCenterAndAngles(); | |
| 81 | ✗ | } | |
| 82 | |||
| 83 | /// Create a new elliptical arc, giving the ellipse's rays as separate coordinates. | ||
| 84 | 7 | EllipticalArc( Point const &ip, Coord rx, Coord ry, | |
| 85 | Coord rot_angle, bool large_arc, bool sweep, | ||
| 86 | Point const &fp | ||
| 87 | ) | ||
| 88 | 14 | : _initial_point(ip) | |
| 89 | 7 | , _final_point(fp) | |
| 90 | 7 | , _ellipse(0, 0, rx, ry, rot_angle) | |
| 91 |
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7 | , _angles(0, 0, sweep) |
| 92 |
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7 | , _large_arc(large_arc) |
| 93 | { | ||
| 94 |
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7 | _updateCenterAndAngles(); |
| 95 | 7 | } | |
| 96 | |||
| 97 | /// @name Retrieve basic information | ||
| 98 | /// @{ | ||
| 99 | |||
| 100 | /** @brief Get a coordinate of the elliptical arc's center. | ||
| 101 | * @param d The dimension to retrieve | ||
| 102 | * @return The selected coordinate of the center */ | ||
| 103 | 108 | Coord center(Dim2 d) const { return _ellipse.center(d); } | |
| 104 | |||
| 105 | /** @brief Get the arc's center | ||
| 106 | * @return The arc's center, situated on the intersection of the ellipse's rays */ | ||
| 107 | 87 | Point center() const { return _ellipse.center(); } | |
| 108 | |||
| 109 | /** @brief Get one of the ellipse's rays | ||
| 110 | * @param d Dimension to retrieve | ||
| 111 | * @return The selected ray of the ellipse */ | ||
| 112 | 456155 | Coord ray(Dim2 d) const { return _ellipse.ray(d); } | |
| 113 | |||
| 114 | /** @brief Get both rays as a point | ||
| 115 | * @return Point with X equal to the X ray and Y to Y ray */ | ||
| 116 | 10413 | Point rays() const { return _ellipse.rays(); } | |
| 117 | |||
| 118 | /** @brief Get the defining ellipse's rotation | ||
| 119 | * @return Angle between the +X ray of the ellipse and the +X axis */ | ||
| 120 | 20521 | Angle rotationAngle() const { | |
| 121 | 20521 | return _ellipse.rotationAngle(); | |
| 122 | } | ||
| 123 | |||
| 124 | /** @brief Whether the arc is larger than half an ellipse. | ||
| 125 | * @return True if the arc is larger than \f$\pi\f$, false otherwise */ | ||
| 126 | 565 | bool largeArc() const { return _large_arc; } | |
| 127 | |||
| 128 | /** @brief Whether the arc turns clockwise | ||
| 129 | * @return True if the arc makes a clockwise turn when going from initial to final | ||
| 130 | * point, false otherwise */ | ||
| 131 | 30122 | bool sweep() const { return _angles.sweep(); } | |
| 132 | |||
| 133 | 9917 | Angle initialAngle() const { return _angles.initialAngle(); } | |
| 134 | 9871 | Angle finalAngle() const { return _angles.finalAngle(); } | |
| 135 | /// @} | ||
| 136 | |||
| 137 | /// @name Modify parameters | ||
| 138 | /// @{ | ||
| 139 | |||
| 140 | /// Change all of the arc's parameters. | ||
| 141 | void set( Point const &ip, double rx, double ry, | ||
| 142 | double rot_angle, bool large_arc, bool sweep, | ||
| 143 | Point const &fp | ||
| 144 | ) | ||
| 145 | { | ||
| 146 | _initial_point = ip; | ||
| 147 | _final_point = fp; | ||
| 148 | _ellipse.setRays(rx, ry); | ||
| 149 | _ellipse.setRotationAngle(rot_angle); | ||
| 150 | _angles.setSweep(sweep); | ||
| 151 | _large_arc = large_arc; | ||
| 152 | _updateCenterAndAngles(); | ||
| 153 | } | ||
| 154 | |||
| 155 | /// Change all of the arc's parameters. | ||
| 156 | void set( Point const &ip, Point const &r, | ||
| 157 | Angle rot_angle, bool large_arc, bool sweep, | ||
| 158 | Point const &fp | ||
| 159 | ) | ||
| 160 | { | ||
| 161 | _initial_point = ip; | ||
| 162 | _final_point = fp; | ||
| 163 | _ellipse.setRays(r); | ||
| 164 | _ellipse.setRotationAngle(rot_angle); | ||
| 165 | _angles.setSweep(sweep); | ||
| 166 | _large_arc = large_arc; | ||
| 167 | _updateCenterAndAngles(); | ||
| 168 | } | ||
| 169 | |||
| 170 | /** @brief Change the initial and final point in one operation. | ||
| 171 | * This method exists because modifying any of the endpoints causes rather costly | ||
| 172 | * recalculations of the center and extreme angles. | ||
| 173 | * @param ip New initial point | ||
| 174 | * @param fp New final point */ | ||
| 175 | void setEndpoints(Point const &ip, Point const &fp) { | ||
| 176 | _initial_point = ip; | ||
| 177 | _final_point = fp; | ||
| 178 | _updateCenterAndAngles(); | ||
| 179 | } | ||
| 180 | /// @} | ||
| 181 | |||
| 182 | /// @name Evaluate the arc as a function | ||
| 183 | /// @{ | ||
| 184 | /** Check whether the arc contains the given angle | ||
| 185 | * @param t The angle to check | ||
| 186 | * @return True if the arc contains the angle, false otherwise */ | ||
| 187 | bool containsAngle(Angle angle) const { return _angles.contains(angle); } | ||
| 188 | |||
| 189 | /** @brief Evaluate the arc at the specified angular coordinate | ||
| 190 | * @param t Angle | ||
| 191 | * @return Point corresponding to the given angle */ | ||
| 192 | Point pointAtAngle(Coord t) const; | ||
| 193 | |||
| 194 | /** @brief Evaluate one of the arc's coordinates at the specified angle | ||
| 195 | * @param t Angle | ||
| 196 | * @param d The dimension to retrieve | ||
| 197 | * @return Selected coordinate of the arc at the specified angle */ | ||
| 198 | Coord valueAtAngle(Coord t, Dim2 d) const; | ||
| 199 | |||
| 200 | /// Compute the curve time value corresponding to the given angular value. | ||
| 201 | 20178 | Coord timeAtAngle(Angle a) const { return _angles.timeAtAngle(a); } | |
| 202 | |||
| 203 | /// Compute the angular domain value corresponding to the given time value. | ||
| 204 | 20615 | Angle angleAt(Coord t) const { return _angles.angleAt(t); } | |
| 205 | |||
| 206 | /** @brief Compute the amount by which the angle parameter changes going from start to end. | ||
| 207 | * This has range \f$(-2\pi, 2\pi)\f$ and thus cannot be represented as instance | ||
| 208 | * of the class Angle. Add this to the initial angle to obtain the final angle. */ | ||
| 209 | 23 | Coord sweepAngle() const { return _angles.sweepAngle(); } | |
| 210 | |||
| 211 | /** @brief Get the elliptical angle spanned by the arc. | ||
| 212 | * This is basically the absolute value of sweepAngle(). */ | ||
| 213 | 23 | Coord angularExtent() const { return _angles.extent(); } | |
| 214 | |||
| 215 | /// Get the angular interval of the arc. | ||
| 216 | 9 | AngleInterval angularInterval() const { return _angles; } | |
| 217 | |||
| 218 | /// Evaluate the arc in the curve domain, i.e. \f$[0, 1]\f$. | ||
| 219 | Point pointAt(Coord t) const override; | ||
| 220 | |||
| 221 | /// Evaluate a single coordinate on the arc in the curve domain. | ||
| 222 | Coord valueAt(Coord t, Dim2 d) const override; | ||
| 223 | |||
| 224 | /** @brief Compute a transform that maps the unit circle to the arc's ellipse. | ||
| 225 | * Each ellipse can be interpreted as a translated, scaled and rotate unit circle. | ||
| 226 | * This function returns the transform that maps the unit circle to the arc's ellipse. | ||
| 227 | * @return Transform from unit circle to the arc's ellipse */ | ||
| 228 | 42468 | Affine unitCircleTransform() const { | |
| 229 | 42468 | Affine result = _ellipse.unitCircleTransform(); | |
| 230 | 42468 | return result; | |
| 231 | } | ||
| 232 | |||
| 233 | /** @brief Compute a transform that maps the arc's ellipse to the unit circle. */ | ||
| 234 | Affine inverseUnitCircleTransform() const { | ||
| 235 | Affine result = _ellipse.inverseUnitCircleTransform(); | ||
| 236 | return result; | ||
| 237 | } | ||
| 238 | /// @} | ||
| 239 | |||
| 240 | /// @name Deal with degenerate ellipses. | ||
| 241 | /// @{ | ||
| 242 | /** @brief Check whether both rays are nonzero. | ||
| 243 | * If they are not, the arc is represented as a line segment instead. */ | ||
| 244 | 248380 | bool isChord() const { | |
| 245 |
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248380 | return ray(X) == 0 || ray(Y) == 0; |
| 246 | } | ||
| 247 | |||
| 248 | /** @brief Get the line segment connecting the arc's endpoints. | ||
| 249 | * @return A linear segment with initial and final point corresponding to those of the arc. */ | ||
| 250 | 80000 | LineSegment chord() const { return LineSegment(_initial_point, _final_point); } | |
| 251 | /// @} | ||
| 252 | |||
| 253 | // implementation of overloads goes here | ||
| 254 | 6386 | Point initialPoint() const override { return _initial_point; } | |
| 255 | 6327 | Point finalPoint() const override { return _final_point; } | |
| 256 | 303 | Curve* duplicate() const override { return new EllipticalArc(*this); } | |
| 257 | ✗ | void setInitial(Point const &p) override { | |
| 258 | ✗ | _initial_point = p; | |
| 259 | ✗ | _updateCenterAndAngles(); | |
| 260 | ✗ | } | |
| 261 | 30 | void setFinal(Point const &p) override { | |
| 262 | 30 | _final_point = p; | |
| 263 | 30 | _updateCenterAndAngles(); | |
| 264 | 30 | } | |
| 265 | 106 | bool isDegenerate() const override { | |
| 266 | 106 | return _initial_point == _final_point; | |
| 267 | } | ||
| 268 | 90138 | bool isLineSegment() const override { return isChord(); } | |
| 269 | 40038 | Rect boundsFast() const override { | |
| 270 | 40038 | return boundsExact(); | |
| 271 | } | ||
| 272 | Rect boundsExact() const override; | ||
| 273 | void expandToTransformed(Rect &bbox, Affine const &transform) const override; | ||
| 274 | // TODO: native implementation of the following methods | ||
| 275 | ✗ | OptRect boundsLocal(OptInterval const &i, unsigned int deg) const override { | |
| 276 | ✗ | return SBasisCurve(toSBasis()).boundsLocal(i, deg); | |
| 277 | } | ||
| 278 | std::vector<double> roots(double v, Dim2 d) const override; | ||
| 279 | #ifdef HAVE_GSL | ||
| 280 | std::vector<double> allNearestTimes( Point const& p, double from = 0, double to = 1 ) const override; | ||
| 281 | 37 | double nearestTime( Point const& p, double from = 0, double to = 1 ) const override { | |
| 282 |
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37 | if ( are_near(ray(X), ray(Y)) && are_near(center(), p) ) { |
| 283 | ✗ | return from; | |
| 284 | } | ||
| 285 |
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37 | return allNearestTimes(p, from, to).front(); |
| 286 | } | ||
| 287 | #endif | ||
| 288 | std::vector<CurveIntersection> intersect(Curve const &other, Coord eps=EPSILON) const override; | ||
| 289 | ✗ | int degreesOfFreedom() const override { return 7; } | |
| 290 | Curve *derivative() const override; | ||
| 291 | |||
| 292 | using Curve::operator*=; | ||
| 293 | void operator*=(Translate const &tr) override; | ||
| 294 | void operator*=(Scale const &s) override; | ||
| 295 | void operator*=(Rotate const &r) override; | ||
| 296 | void operator*=(Zoom const &z) override; | ||
| 297 | void operator*=(Affine const &m) override; | ||
| 298 | |||
| 299 | std::vector<Point> pointAndDerivatives(Coord t, unsigned int n) const override; | ||
| 300 | D2<SBasis> toSBasis() const override; | ||
| 301 | Curve *portion(double f, double t) const override; | ||
| 302 | Curve *reverse() const override; | ||
| 303 | bool isNear(Curve const &other, Coord precision) const override; | ||
| 304 | void feed(PathSink &sink, bool moveto_initial) const override; | ||
| 305 | int winding(Point const &p) const override; | ||
| 306 | |||
| 307 | protected: | ||
| 308 | bool _equalTo(Curve const &c) const override; | ||
| 309 | |||
| 310 | private: | ||
| 311 | void _updateCenterAndAngles(); | ||
| 312 | std::vector<ShapeIntersection> _filterIntersections(std::vector<ShapeIntersection> &&xs, bool is_first) const; | ||
| 313 | bool _validateIntersection(ShapeIntersection &xing, bool is_first) const; | ||
| 314 | std::vector<ShapeIntersection> _intersectSameEllipse(EllipticalArc const *other) const; | ||
| 315 | |||
| 316 | Point _initial_point, _final_point; | ||
| 317 | Ellipse _ellipse; | ||
| 318 | AngleInterval _angles; | ||
| 319 | bool _large_arc; | ||
| 320 | }; // end class EllipticalArc | ||
| 321 | |||
| 322 | |||
| 323 | // implemented in elliptical-arc-from-sbasis.cpp | ||
| 324 | /** @brief Fit an elliptical arc to an SBasis fragment. | ||
| 325 | * @relates EllipticalArc */ | ||
| 326 | bool arc_from_sbasis(EllipticalArc &ea, D2<SBasis> const &in, | ||
| 327 | double tolerance = EPSILON, unsigned num_samples = 20); | ||
| 328 | |||
| 329 | /** @brief Debug output for elliptical arcs. | ||
| 330 | * @relates EllipticalArc */ | ||
| 331 | std::ostream &operator<<(std::ostream &out, EllipticalArc const &ea); | ||
| 332 | |||
| 333 | } // end namespace Geom | ||
| 334 | |||
| 335 | #endif // LIB2GEOM_SEEN_ELLIPTICAL_ARC_H | ||
| 336 | |||
| 337 | /* | ||
| 338 | Local Variables: | ||
| 339 | mode:c++ | ||
| 340 | c-file-style:"stroustrup" | ||
| 341 | c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +)) | ||
| 342 | indent-tabs-mode:nil | ||
| 343 | fill-column:99 | ||
| 344 | End: | ||
| 345 | */ | ||
| 346 | // vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 : | ||
| 347 |