| Line | Branch | Exec | Source |
|---|---|---|---|
| 1 | /** | ||
| 2 | * \file | ||
| 3 | * \brief Various trigoniometric helper functions | ||
| 4 | *//* | ||
| 5 | * Authors: | ||
| 6 | * Johan Engelen <goejendaagh@zonnet.nl> | ||
| 7 | * Marco Cecchetti <mrcekets at gmail.com> | ||
| 8 | * Krzysztof Kosiński <tweenk.pl@gmail.com> | ||
| 9 | * | ||
| 10 | * Copyright (C) 2007-2010 Authors | ||
| 11 | * | ||
| 12 | * This library is free software; you can redistribute it and/or | ||
| 13 | * modify it either under the terms of the GNU Lesser General Public | ||
| 14 | * License version 2.1 as published by the Free Software Foundation | ||
| 15 | * (the "LGPL") or, at your option, under the terms of the Mozilla | ||
| 16 | * Public License Version 1.1 (the "MPL"). If you do not alter this | ||
| 17 | * notice, a recipient may use your version of this file under either | ||
| 18 | * the MPL or the LGPL. | ||
| 19 | * | ||
| 20 | * You should have received a copy of the LGPL along with this library | ||
| 21 | * in the file COPYING-LGPL-2.1; if not, write to the Free Software | ||
| 22 | * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA | ||
| 23 | * You should have received a copy of the MPL along with this library | ||
| 24 | * in the file COPYING-MPL-1.1 | ||
| 25 | * | ||
| 26 | * The contents of this file are subject to the Mozilla Public License | ||
| 27 | * Version 1.1 (the "License"); you may not use this file except in | ||
| 28 | * compliance with the License. You may obtain a copy of the License at | ||
| 29 | * http://www.mozilla.org/MPL/ | ||
| 30 | * | ||
| 31 | * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY | ||
| 32 | * OF ANY KIND, either express or implied. See the LGPL or the MPL for | ||
| 33 | * the specific language governing rights and limitations. | ||
| 34 | * | ||
| 35 | */ | ||
| 36 | |||
| 37 | #ifndef LIB2GEOM_SEEN_ANGLE_H | ||
| 38 | #define LIB2GEOM_SEEN_ANGLE_H | ||
| 39 | |||
| 40 | #include <cmath> | ||
| 41 | #include <boost/operators.hpp> | ||
| 42 | #include <2geom/exception.h> | ||
| 43 | #include <2geom/coord.h> | ||
| 44 | #include <2geom/point.h> | ||
| 45 | |||
| 46 | namespace Geom { | ||
| 47 | |||
| 48 | #ifndef M_PI | ||
| 49 | # define M_PI 3.14159265358979323846 | ||
| 50 | #endif | ||
| 51 | #ifndef M_1_2PI | ||
| 52 | # define M_1_2PI 0.159154943091895335768883763373 | ||
| 53 | #endif | ||
| 54 | |||
| 55 | /** @brief Wrapper for angular values. | ||
| 56 | * | ||
| 57 | * This class is a convenience wrapper that implements the behavior generally expected of angles, | ||
| 58 | * like addition modulo \f$2\pi\f$. The value returned from the default conversion | ||
| 59 | * to <tt>double</tt> is in the range \f$[-\pi, \pi)\f$ - the convention used by C's | ||
| 60 | * math library. | ||
| 61 | * | ||
| 62 | * This class holds only a single floating point value, so passing it by value will generally | ||
| 63 | * be faster than passing it by const reference. | ||
| 64 | * | ||
| 65 | * @ingroup Primitives | ||
| 66 | */ | ||
| 67 | class Angle | ||
| 68 | : boost::additive< Angle | ||
| 69 | , boost::additive< Angle, Coord | ||
| 70 | , boost::equality_comparable< Angle | ||
| 71 | , boost::equality_comparable< Angle, Coord | ||
| 72 | > > > > | ||
| 73 | { | ||
| 74 | public: | ||
| 75 | 6 | Angle() : _angle(0) {} | |
| 76 | 10299 | Angle(Coord v) : _angle(v) { _normalize(); } // this can be called implicitly | |
| 77 | 84885 | explicit Angle(Point const &p) : _angle(atan2(p)) { _normalize(); } | |
| 78 | Angle(Point const &a, Point const &b) : _angle(angle_between(a, b)) { _normalize(); } | ||
| 79 | 110393 | operator Coord() const { return radians(); } | |
| 80 | 115532 | Angle &operator+=(Angle o) { | |
| 81 | 115532 | _angle += o._angle; | |
| 82 | 115532 | _normalize(); | |
| 83 | 115532 | return *this; | |
| 84 | } | ||
| 85 | 112002 | Angle &operator-=(Angle o) { | |
| 86 | 112002 | _angle -= o._angle; | |
| 87 | 112002 | _normalize(); | |
| 88 | 112002 | return *this; | |
| 89 | } | ||
| 90 | 115532 | Angle &operator+=(Coord a) { | |
| 91 |
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115532 | *this += Angle(a); |
| 92 | 115532 | return *this; | |
| 93 | } | ||
| 94 | 10652 | Angle &operator-=(Coord a) { | |
| 95 |
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10652 | *this -= Angle(a); |
| 96 | 10652 | return *this; | |
| 97 | } | ||
| 98 | 53564 | bool operator==(Angle o) const { | |
| 99 | 53564 | return _angle == o._angle; | |
| 100 | } | ||
| 101 | bool operator==(Coord c) const { | ||
| 102 | return _angle == Angle(c)._angle; | ||
| 103 | } | ||
| 104 | |||
| 105 | /** @brief Get the angle as radians. | ||
| 106 | * @return Number in range \f$[-\pi, \pi)\f$. */ | ||
| 107 | 110439 | Coord radians() const { | |
| 108 |
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110439 | return _angle >= M_PI ? _angle - 2*M_PI : _angle; |
| 109 | } | ||
| 110 | /** @brief Get the angle as positive radians. | ||
| 111 | * @return Number in range \f$[0, 2\pi)\f$. */ | ||
| 112 | 972340 | Coord radians0() const { | |
| 113 | 972340 | return _angle; | |
| 114 | } | ||
| 115 | /** @brief Get the angle as degrees in math convention. | ||
| 116 | * @return Number in range [-180, 180) obtained by scaling the result of radians() | ||
| 117 | * by \f$180/\pi\f$. */ | ||
| 118 | Coord degrees() const { return radians() * (180.0 / M_PI); } | ||
| 119 | /** @brief Get the angle as degrees in clock convention. | ||
| 120 | * This method converts the angle to the "clock convention": angles start from the +Y axis | ||
| 121 | * and grow clockwise. This means that 0 corresponds to \f$\pi/2\f$ radians, | ||
| 122 | * 90 to 0 radians, 180 to \f$-\pi/2\f$ radians, and 270 to \f$\pi\f$ radians. | ||
| 123 | * @return A number in the range [0, 360). | ||
| 124 | */ | ||
| 125 | Coord degreesClock() const { | ||
| 126 | Coord ret = 90.0 - _angle * (180.0 / M_PI); | ||
| 127 | if (ret < 0) ret += 360; | ||
| 128 | return ret; | ||
| 129 | } | ||
| 130 | /** @brief Create an angle from its measure in radians. */ | ||
| 131 | static Angle from_radians(Coord d) { | ||
| 132 | Angle a(d); | ||
| 133 | return a; | ||
| 134 | } | ||
| 135 | /** @brief Create an angle from its measure in degrees. */ | ||
| 136 | static Angle from_degrees(Coord d) { | ||
| 137 | Angle a(d * (M_PI / 180.0)); | ||
| 138 | return a; | ||
| 139 | } | ||
| 140 | /** @brief Create an angle from its measure in degrees in clock convention. | ||
| 141 | * @see Angle::degreesClock() */ | ||
| 142 | static Angle from_degrees_clock(Coord d) { | ||
| 143 | // first make sure d is in [0, 360) | ||
| 144 | d = std::fmod(d, 360.0); | ||
| 145 | if (d < 0) d += 360.0; | ||
| 146 | Coord rad = M_PI/2 - d * (M_PI / 180.0); | ||
| 147 | if (rad < 0) rad += 2*M_PI; | ||
| 148 | Angle a; | ||
| 149 | a._angle = rad; | ||
| 150 | return a; | ||
| 151 | } | ||
| 152 | private: | ||
| 153 | |||
| 154 | 10299 | void _normalize() { | |
| 155 | 10299 | _angle = std::fmod(_angle, 2*M_PI); | |
| 156 |
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10299 | if (_angle < 0) _angle += 2*M_PI; |
| 157 | //_angle -= floor(_angle * (1.0/(2*M_PI))) * 2*M_PI; | ||
| 158 | 10299 | } | |
| 159 | Coord _angle; // this is always in [0, 2pi) | ||
| 160 | friend class AngleInterval; | ||
| 161 | }; | ||
| 162 | |||
| 163 | 76 | inline Angle distance(Angle const &a, Angle const &b) { | |
| 164 | // the distance cannot be larger than M_PI. | ||
| 165 | 76 | Coord ac = a.radians0(); | |
| 166 | 76 | Coord bc = b.radians0(); | |
| 167 | 76 | Coord d = fabs(ac - bc); | |
| 168 |
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76 | return Angle(d > M_PI ? 2*M_PI - d : d); |
| 169 | } | ||
| 170 | |||
| 171 | /** @brief Directed angular interval. | ||
| 172 | * | ||
| 173 | * Wrapper for directed angles with defined start and end values. Useful e.g. for representing | ||
| 174 | * the portion of an ellipse in an elliptical arc. Both extreme angles are contained | ||
| 175 | * in the interval (it is a closed interval). Angular intervals can also be interptered | ||
| 176 | * as functions \f$f: [0, 1] \to [-\pi, \pi)\f$, which return the start angle for 0, | ||
| 177 | * the end angle for 1, and interpolate linearly for other values. Note that such functions | ||
| 178 | * are not continuous if the interval crosses the angle \f$\pi\f$. | ||
| 179 | * | ||
| 180 | * This class can represent all directed angular intervals, including empty ones. | ||
| 181 | * However, not all possible intervals can be created with the constructors. | ||
| 182 | * For full control, use the setInitial(), setFinal() and setAngles() methods. | ||
| 183 | * | ||
| 184 | * @ingroup Primitives | ||
| 185 | */ | ||
| 186 | class AngleInterval | ||
| 187 | : boost::equality_comparable< AngleInterval > | ||
| 188 | { | ||
| 189 | public: | ||
| 190 | 2 | AngleInterval() {} | |
| 191 | /** @brief Create an angular interval from two angles and direction. | ||
| 192 | * If the initial and final angle are the same, a degenerate interval | ||
| 193 | * (containing only one angle) will be created. | ||
| 194 | * @param s Starting angle | ||
| 195 | * @param e Ending angle | ||
| 196 | * @param cw Which direction the interval goes. True means that it goes | ||
| 197 | * in the direction of increasing angles, while false means in the direction | ||
| 198 | * of decreasing angles. */ | ||
| 199 | 19726 | AngleInterval(Angle s, Angle e, bool cw = false) | |
| 200 | 19726 | : _start_angle(s), _end_angle(e), _sweep(cw), _full(false) | |
| 201 | 19726 | {} | |
| 202 | 7 | AngleInterval(double s, double e, bool cw = false) | |
| 203 | 7 | : _start_angle(s), _end_angle(e), _sweep(cw), _full(false) | |
| 204 | 7 | {} | |
| 205 | /** @brief Create an angular interval from three angles. | ||
| 206 | * If the inner angle is exactly equal to initial or final angle, | ||
| 207 | * the sweep flag will be set to true, i.e. the interval will go | ||
| 208 | * in the direction of increasing angles. | ||
| 209 | * | ||
| 210 | * If the initial and final angle are the same, but the inner angle | ||
| 211 | * is different, a full angle in the direction of increasing angles | ||
| 212 | * will be created. | ||
| 213 | * | ||
| 214 | * @param s Initial angle | ||
| 215 | * @param inner Angle contained in the interval | ||
| 216 | * @param e Final angle */ | ||
| 217 | AngleInterval(Angle s, Angle inner, Angle e) | ||
| 218 | : _start_angle(s) | ||
| 219 | , _end_angle(e) | ||
| 220 | , _sweep((inner-s).radians0() <= (e-s).radians0()) | ||
| 221 | , _full(s == e && s != inner) | ||
| 222 | { | ||
| 223 | if (_full) { | ||
| 224 | _sweep = true; | ||
| 225 | } | ||
| 226 | } | ||
| 227 | |||
| 228 | /// Get the start angle. | ||
| 229 | 9943 | Angle initialAngle() const { return _start_angle; } | |
| 230 | /// Get the end angle. | ||
| 231 | 9897 | Angle finalAngle() const { return _end_angle; } | |
| 232 | /// Check whether the interval goes in the direction of increasing angles. | ||
| 233 | 30122 | bool sweep() const { return _sweep; } | |
| 234 | /// Check whether the interval contains only a single angle. | ||
| 235 | bool isDegenerate() const { | ||
| 236 | return _start_angle == _end_angle && !_full; | ||
| 237 | } | ||
| 238 | /// Check whether the interval contains all angles. | ||
| 239 | 53531 | bool isFull() const { | |
| 240 |
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53531 | return _start_angle == _end_angle && _full; |
| 241 | } | ||
| 242 | |||
| 243 | /** @brief Set the initial angle. | ||
| 244 | * @param a Angle to set | ||
| 245 | * @param prefer_full Whether to set a full angular interval when | ||
| 246 | * the initial angle is set to the final angle */ | ||
| 247 | 11592 | void setInitial(Angle a, bool prefer_full = false) { | |
| 248 | 11592 | _start_angle = a; | |
| 249 |
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11592 | _full = prefer_full && a == _end_angle; |
| 250 | 11592 | } | |
| 251 | |||
| 252 | /** @brief Set the final angle. | ||
| 253 | * @param a Angle to set | ||
| 254 | * @param prefer_full Whether to set a full angular interval when | ||
| 255 | * the initial angle is set to the final angle */ | ||
| 256 | 11592 | void setFinal(Angle a, bool prefer_full = false) { | |
| 257 | 11592 | _end_angle = a; | |
| 258 |
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11592 | _full = prefer_full && a == _start_angle; |
| 259 | 11592 | } | |
| 260 | /** @brief Set both angles at once. | ||
| 261 | * The direction (sweep flag) is left unchanged. | ||
| 262 | * @param s Initial angle | ||
| 263 | * @param e Final angle | ||
| 264 | * @param prefer_full Whether to set a full interval when the passed | ||
| 265 | * initial and final angle are the same */ | ||
| 266 | 48 | void setAngles(Angle s, Angle e, bool prefer_full = false) { | |
| 267 | 48 | _start_angle = s; | |
| 268 | 48 | _end_angle = e; | |
| 269 |
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48 | _full = prefer_full && s == e; |
| 270 | 48 | } | |
| 271 | /// Set whether the interval goes in the direction of increasing angles. | ||
| 272 | 7 | void setSweep(bool s) { _sweep = s; } | |
| 273 | |||
| 274 | /// Reverse the direction of the interval while keeping contained values the same. | ||
| 275 | 40016 | void reverse() { | |
| 276 | using std::swap; | ||
| 277 | 40016 | swap(_start_angle, _end_angle); | |
| 278 | 40016 | _sweep = !_sweep; | |
| 279 | 40016 | } | |
| 280 | /// Get a new interval with reversed direction. | ||
| 281 | AngleInterval reversed() const { | ||
| 282 | AngleInterval result(*this); | ||
| 283 | result.reverse(); | ||
| 284 | return result; | ||
| 285 | } | ||
| 286 | |||
| 287 | /// Get an angle corresponding to the specified time value. | ||
| 288 | 20615 | Angle angleAt(Coord t) const { | |
| 289 |
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20615 | Coord span = extent(); |
| 290 |
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20615 | Angle ret = _start_angle.radians0() + span * (_sweep ? t : -t); |
| 291 | 20615 | return ret; | |
| 292 | } | ||
| 293 | Angle operator()(Coord t) const { return angleAt(t); } | ||
| 294 | |||
| 295 | /** @brief Compute a time value that would evaluate to the given angle. | ||
| 296 | * If the start and end angle are exactly the same, NaN will be returned. | ||
| 297 | * Negative values will be returned for angles between the initial angle | ||
| 298 | * and the angle exactly opposite the midpoint of the interval. */ | ||
| 299 | 20178 | Coord timeAtAngle(Angle a) const { | |
| 300 |
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20178 | if (_full) { |
| 301 | ✗ | Angle ta = _sweep ? a - _start_angle : _start_angle - a; | |
| 302 | ✗ | return ta.radians0() / (2*M_PI); | |
| 303 | } | ||
| 304 | 20178 | Coord ex = extent(); | |
| 305 | 20178 | Coord outex = 2*M_PI - ex; | |
| 306 |
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20178 | if (_sweep) { |
| 307 |
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10043 | Angle midout = _start_angle - outex / 2; |
| 308 |
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10043 | Angle acmp = a - midout, scmp = _start_angle - midout; |
| 309 |
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10043 | if (acmp.radians0() >= scmp.radians0()) { |
| 310 |
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6160 | return (a - _start_angle).radians0() / ex; |
| 311 | } else { | ||
| 312 |
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3883 | return -(_start_angle - a).radians0() / ex; |
| 313 | } | ||
| 314 | } else { | ||
| 315 |
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10135 | Angle midout = _start_angle + outex / 2; |
| 316 |
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10135 | Angle acmp = a - midout, scmp = _start_angle - midout; |
| 317 |
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10135 | if (acmp.radians0() <= scmp.radians0()) { |
| 318 |
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8961 | return (_start_angle - a).radians0() / ex; |
| 319 | } else { | ||
| 320 |
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1174 | return -(a - _start_angle).radians0() / ex; |
| 321 | } | ||
| 322 | } | ||
| 323 | } | ||
| 324 | |||
| 325 | /// Check whether the interval includes the given angle. | ||
| 326 | 209258 | bool contains(Angle a) const { | |
| 327 |
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209258 | if (_full) return true; |
| 328 | 209258 | Coord s = _start_angle.radians0(); | |
| 329 | 209258 | Coord e = _end_angle.radians0(); | |
| 330 | 209258 | Coord x = a.radians0(); | |
| 331 |
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209258 | if (_sweep) { |
| 332 |
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202762 | if (s < e) return x >= s && x <= e; |
| 333 |
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47768 | return x >= s || x <= e; |
| 334 | } else { | ||
| 335 |
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6496 | if (s > e) return x <= s && x >= e; |
| 336 |
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462 | return x <= s || x >= e; |
| 337 | } | ||
| 338 | } | ||
| 339 | /** @brief Extent of the angle interval. | ||
| 340 | * Equivalent to the absolute value of the sweep angle. | ||
| 341 | * @return Extent in range \f$[0, 2\pi)\f$. */ | ||
| 342 | 40816 | Coord extent() const { | |
| 343 |
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40816 | if (_full) return 2*M_PI; |
| 344 | 40816 | return _sweep | |
| 345 |
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102151 | ? (_end_angle - _start_angle).radians0() |
| 346 |
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81632 | : (_start_angle - _end_angle).radians0(); |
| 347 | } | ||
| 348 | /** @brief Get the sweep angle of the interval. | ||
| 349 | * This is the value you need to add to the initial angle to get the final angle. | ||
| 350 | * It is positive when sweep is true. Denoted as \f$\Delta\theta\f$ in the SVG | ||
| 351 | * elliptical arc implementation notes. */ | ||
| 352 | 23 | Coord sweepAngle() const { | |
| 353 |
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23 | if (_full) return _sweep ? 2*M_PI : -2*M_PI; |
| 354 | 23 | Coord sa = _end_angle.radians0() - _start_angle.radians0(); | |
| 355 |
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23 | if (_sweep && sa < 0) sa += 2*M_PI; |
| 356 |
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23 | if (!_sweep && sa > 0) sa -= 2*M_PI; |
| 357 | 23 | return sa; | |
| 358 | } | ||
| 359 | |||
| 360 | /// Check another interval for equality. | ||
| 361 | bool operator==(AngleInterval const &other) const { | ||
| 362 | if (_start_angle != other._start_angle) return false; | ||
| 363 | if (_end_angle != other._end_angle) return false; | ||
| 364 | if (_sweep != other._sweep) return false; | ||
| 365 | if (_full != other._full) return false; | ||
| 366 | return true; | ||
| 367 | } | ||
| 368 | |||
| 369 | static AngleInterval create_full(Angle start, bool sweep = true) { | ||
| 370 | AngleInterval result; | ||
| 371 | result._start_angle = result._end_angle = start; | ||
| 372 | result._sweep = sweep; | ||
| 373 | result._full = true; | ||
| 374 | return result; | ||
| 375 | } | ||
| 376 | |||
| 377 | private: | ||
| 378 | Angle _start_angle; | ||
| 379 | Angle _end_angle; | ||
| 380 | bool _sweep; | ||
| 381 | bool _full; | ||
| 382 | }; | ||
| 383 | |||
| 384 | /** @brief Given an angle in degrees, return radians | ||
| 385 | * @relates Angle */ | ||
| 386 | 188 | inline constexpr Coord rad_from_deg(Coord deg) { return deg / 180.0 * M_PI;} | |
| 387 | /** @brief Given an angle in radians, return degrees | ||
| 388 | * @relates Angle */ | ||
| 389 | 12 | inline constexpr Coord deg_from_rad(Coord rad) { return rad / M_PI * 180.0;} | |
| 390 | |||
| 391 | } // namespace Geom | ||
| 392 | |||
| 393 | namespace std { | ||
| 394 | template <> class iterator_traits<Geom::Angle> {}; | ||
| 395 | } | ||
| 396 | |||
| 397 | #endif // LIB2GEOM_SEEN_ANGLE_H | ||
| 398 | |||
| 399 | /* | ||
| 400 | Local Variables: | ||
| 401 | mode:c++ | ||
| 402 | c-file-style:"stroustrup" | ||
| 403 | c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +)) | ||
| 404 | indent-tabs-mode:nil | ||
| 405 | fill-column:99 | ||
| 406 | End: | ||
| 407 | */ | ||
| 408 | // vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 : | ||
| 409 |