Coverage for pygeodesy/booleans.py: 94%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''I{Boolean} operations on I{composite} polygons and I{clip}s. 

5 

6Classes L{BooleanFHP} and L{BooleanGH} are I{composites} and 

7provide I{boolean} operations C{intersection}, C{difference}, 

8C{reverse-difference}, C{sum} and C{union}. 

9 

10@note: A I{clip} is defined as a single, usually closed polygon, 

11 a I{composite} is a collection of one or more I{clip}s. 

12 

13@see: U{Forster-Hormann-Popa<https://www.ScienceDirect.com/science/ 

14 article/pii/S259014861930007X>} and U{Greiner-Hormann 

15 <http://www.Inf.USI.CH/hormann/papers/Greiner.1998.ECO.pdf>}. 

16''' 

17# make sure int/int division yields float quotient, see .basics 

18from __future__ import division as _; del _ # PYCHOK semicolon 

19 

20from pygeodesy.basics import isodd, issubclassof, map2, _xscalar 

21from pygeodesy.constants import EPS, EPS2, INT0, _0_0, _0_5, _1_0 

22from pygeodesy.errors import ClipError, _IsnotError, _TypeError, \ 

23 _ValueError, _xattr, _xkwds_get, _xkwds_pop2 

24from pygeodesy.fmath import favg, hypot, hypot2 

25# from pygeodesy.fsums import fsum1 # _MODS 

26from pygeodesy.interns import NN, _BANG_, _clip_, _clipid_, _COMMASPACE_, \ 

27 _composite_, _DOT_, _e_, _ELLIPSIS_, _few_, \ 

28 _height_, _lat_, _LatLon_, _lon_, _not_, \ 

29 _points_, _SPACE_, _too_, _X_, _x_, \ 

30 _B_, _d_, _R_ # PYCHOK used! 

31from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS 

32from pygeodesy.latlonBase import LatLonBase, \ 

33 LatLon2Tuple, Property_RO, property_RO 

34from pygeodesy.named import _name__, _Named, _NotImplemented, \ 

35 Fmt, pairs, unstr 

36# from pygeodesy.namedTuples import LatLon2Tupe # from .latlonBase 

37# from pygeodesy.points import boundsOf # _MODS 

38# from pygeodesy.props import Property_RO, property_RO # from .latlonBase 

39# from pygeodesy.streprs import Fmt, pairs, unstr # from .named 

40from pygeodesy.units import Height, HeightX 

41from pygeodesy.utily import fabs, _unrollon, _Wrap 

42 

43# from math import fabs # from .utily 

44 

45__all__ = _ALL_LAZY.booleans 

46__version__ = '24.06.06' 

47 

48_0_EPS = EPS # near-zero, positive 

49_EPS_0 = -EPS # near-zero, negative 

50_1_EPS = _1_0 + EPS # near-one, over 

51_EPS_1 = _1_0 - EPS # near-one, under 

52_10EPS = EPS * 10 # see ._2Abs, ._10eps 

53 

54_alpha_ = 'alpha' 

55_boolean_ = 'boolean' 

56_case_ = 'case' 

57_corners_ = 'corners' 

58_duplicate_ = 'duplicate' 

59_open_ = 'open' 

60 

61 

62def _Enum(txt, enum): # PYCHOK unused 

63 return txt # NN(txt, _TILDE_, enum) 

64 

65 

66class _L(object): # Intersection labels 

67 CROSSING = _Enum(_X_, 1) # C++ enum 

68 CROSSING_D = _Enum(_X_ + _d_, 8) 

69 CROSSINGs = (CROSSING, CROSSING_D) 

70 BOUNCING = _Enum(_B_, 2) 

71 BOUNCING_D = _Enum(_B_ + _d_, 9) 

72 BOUNCINGs = (BOUNCING, BOUNCING_D) + CROSSINGs 

73 LEFT_ON = _Enum('Lo', 3) 

74 ON_ON = _Enum('oo', 5) 

75 ON_LEFT = _Enum('oL', 6) 

76 ON_RIGHT = _Enum('oR', 7) 

77 RIGHT_ON = _Enum('Ro', 4) 

78 RIGHT_LEFT_ON = (RIGHT_ON, LEFT_ON) 

79 # Entry/Exit flags 

80 ENTRY = _Enum(_e_, 1) 

81 EXIT = _Enum(_x_, 0) 

82 Toggle = {ENTRY: EXIT, 

83 EXIT: ENTRY, 

84 None: None} 

85 

86_L = _L() # PYCHOK singleton 

87 

88 

89class _RP(object): # RelativePositions 

90 IS_Pm = _Enum('Pm', 2) # C++ enum 

91 IS_Pp = _Enum('Pp', 3) 

92 LEFT = _Enum('L', 0) 

93 RIGHT = _Enum(_R_, 1) 

94 

95_RP = _RP() # PYCHOK singleton 

96 

97_RP2L = {(_RP.LEFT, _RP.RIGHT): _L.CROSSING, 

98 (_RP.RIGHT, _RP.LEFT): _L.CROSSING, 

99 (_RP.LEFT, _RP.LEFT): _L.BOUNCING, 

100 (_RP.RIGHT, _RP.RIGHT): _L.BOUNCING, 

101 # overlapping cases 

102 (_RP.RIGHT, _RP.IS_Pp): _L.LEFT_ON, 

103 (_RP.IS_Pp, _RP.RIGHT): _L.LEFT_ON, 

104 (_RP.LEFT, _RP.IS_Pp): _L.RIGHT_ON, 

105 (_RP.IS_Pp, _RP.LEFT): _L.RIGHT_ON, 

106 (_RP.IS_Pm, _RP.IS_Pp): _L.ON_ON, 

107 (_RP.IS_Pp, _RP.IS_Pm): _L.ON_ON, 

108 (_RP.IS_Pm, _RP.RIGHT): _L.ON_LEFT, 

109 (_RP.RIGHT, _RP.IS_Pm): _L.ON_LEFT, 

110 (_RP.LEFT, _RP.IS_Pm): _L.ON_RIGHT, 

111 (_RP.IS_Pm, _RP.LEFT): _L.ON_RIGHT} 

112 

113 

114class _LatLonBool(_Named): 

115 '''(INTERNAL) Base class for L{LatLonFHP} and L{LatLonGH}. 

116 ''' 

117 _alpha = None # point AND intersection else length 

118 _checked = False # checked in phase 3 iff intersection 

119 _clipid = INT0 # (polygonal) clip identifier, number 

120 _dupof = None # original of a duplicate 

121# _e_x_str = NN # shut up PyChecker 

122 _height = Height(0) # interpolated height, usually meter 

123 _linked = None # link to neighbor iff intersection 

124 _next = None # link to the next vertex 

125 _prev = None # link to the previous vertex 

126 

127 def __init__(self, lat_ll, lon=None, height=0, clipid=INT0, wrap=False, **name): 

128 '''New C{LatLon[FHP|GH]} from separate C{lat}, C{lon}, C{height} and C{clipid} 

129 scalars or from a previous C{LatLon[FHP|GH]}, C{Clip[FHP|GH]4Tuple} or some 

130 other C{LatLon} instance. 

131 

132 @arg lat_ll: Latitude (C{scalar}) or a lat-/longitude (C{LatLon[FHP|GH]}, 

133 C{Clip[FHP|GH]4Tuple} or some other C{LatLon}). 

134 @kwarg lon: Longitude (C{scalar}), iff B{C{lat_ll}} is scalar, ignored 

135 otherwise. 

136 @kwarg height: Height (C{scalar}), conventionally C{meter}. 

137 @kwarg clipid: Clip identifier (C{int}). 

138 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{lat}} and B{C{lon}} (C{bool}). 

139 @kwarg name: Optional C{B{name}=NN} (C{str}). 

140 ''' 

141 h, name = _xkwds_pop2(name, h=height) if name else (height, name) 

142 

143 if lon is None: 

144 y, x = lat_ll.lat, lat_ll.lon 

145 h = _xattr(lat_ll, height=h) 

146 c = _xattr(lat_ll, clipid=clipid) 

147 else: 

148 y, x, c = lat_ll, lon, clipid 

149 self.y, self.x = _Wrap.latlon(y, x) if wrap else (y, x) 

150 # don't duplicate defaults 

151 if self._height != h: 

152 self._height = h 

153 if self._clipid != c: 

154 self._clipid = c 

155 if name: 

156 self.name = name 

157 

158 def __abs__(self): 

159 return max(fabs(self.x), fabs(self.y)) 

160 

161 def __eq__(self, other): 

162 return other is self or bool(_other(self, other) and 

163 other.x == self.x and 

164 other.y == self.y) 

165 

166 def __ne__(self, other): # required for Python 2 

167 return not self.__eq__(other) 

168 

169 def __repr__(self): 

170 '''String C{repr} of this lat-/longitude. 

171 ''' 

172 if self._prev or self._next: 

173 t = _ELLIPSIS_(self._prev, self._next) 

174 t = _SPACE_(self, Fmt.ANGLE(t)) 

175 else: 

176 t = str(self) 

177 return t 

178 

179 def __str__(self): 

180 '''String C{str} of this lat-/longitude. 

181 ''' 

182 t = (_lat_, self.lat), (_lon_, self.lon) 

183 if self._height: 

184 X = _X_ if self.isintersection else NN 

185 t += (_height_ + X, self._height), 

186 if self._clipid: 

187 t += (_clipid_, self._clipid), 

188 if self._alpha is not None: 

189 t += (_alpha_, self._alpha), 

190# if self._dupof: # recursion risk 

191# t += (_dupof_, self._dupof.name), 

192 t = pairs(t, prec=8, fmt=Fmt.g, ints=True) 

193 t = Fmt.PAREN(_COMMASPACE_.join(t)) 

194 if self._linked: 

195 k = _DOT_ if self._checked else _BANG_ 

196 t = NN(t, self._e_x_str(k)) # PYCHOK expected 

197 return NN(self.name, t) 

198 

199 def __sub__(self, other): 

200 _other(self, other) 

201 return self.__class__(self.y - other.y, # classof 

202 self.x - other.x) 

203 

204 def _2A(self, p2, p3): 

205 # I{Signed} area of a triangle, I{doubled}. 

206 x, y = self.x, self.y 

207 return (p2.x - x) * (p3.y - y) - \ 

208 (p3.x - x) * (p2.y - y) 

209 

210 def _2Abs(self, p2, p3, eps=_10EPS): 

211 # I{Unsigned} area of a triangle, I{doubled} 

212 # or 0 if below the given threshold C{eps}. 

213 a = fabs(self._2A(p2, p3)) 

214 return 0 if a < eps else a 

215 

216 @property_RO 

217 def clipid(self): 

218 '''Get the I{clipid} (C{int} or C{0}). 

219 ''' 

220 return self._clipid 

221 

222 def _equi(self, llb, eps): 

223 # Is this LLB I{equivalent} to B{C{llb}} within 

224 # the given I{non-negative} tolerance B{C{eps}}? 

225 return not (fabs(llb.lon - self.x) > eps or 

226 fabs(llb.lat - self.y) > eps) 

227 

228 @property_RO 

229 def height(self): 

230 '''Get the I{height} (C{Height} or C{int}). 

231 ''' 

232 h = self._height 

233 return HeightX(h) if self.isintersection else ( 

234 Height(h) if h else _LatLonBool._height) 

235 

236 def isequalTo(self, other, eps=None): 

237 '''Is this point equal to an B{C{other}} within a given, 

238 I{non-negative} tolerance, ignoring C{height}? 

239 

240 @arg other: The other point (C{LatLon}). 

241 @kwarg eps: Tolerance for equality (C{degrees} or C{None}). 

242 

243 @return: C{True} if equivalent, C{False} otherwise (C{bool}). 

244 

245 @raise TypeError: Invalid B{C{other}}. 

246 ''' 

247 try: 

248 return self._equi(other, _eps0(eps)) 

249 except (AttributeError, TypeError, ValueError): 

250 raise _IsnotError(_LatLon_, other=other) 

251 

252 @property_RO 

253 def isintersection(self): 

254 '''Is this an intersection? May be C{ispoint} too! 

255 ''' 

256 return bool(self._linked) 

257 

258 @property_RO 

259 def ispoint(self): 

260 '''Is this an I{original} point? May be C{isintersection} too! 

261 ''' 

262 return self._alpha is None 

263 

264 @property_RO 

265 def lat(self): 

266 '''Get the latitude (C{scalar}). 

267 ''' 

268 return self.y 

269 

270 @property_RO 

271 def latlon(self): 

272 '''Get the lat- and longitude (L{LatLon2Tuple}). 

273 ''' 

274 return LatLon2Tuple(self.y, self.x) 

275 

276 def _link(self, other): 

277 # Make this and an other point neighbors. 

278 # assert _other(self, other) 

279 self._linked = other 

280 other._linked = self 

281 

282 @property_RO 

283 def lon(self): 

284 '''Get the longitude (C{scalar}). 

285 ''' 

286 return self.x 

287 

288 def _toClas(self, Clas, clipid): 

289 # Return this vertex as a C{Clas} instance 

290 # (L{Clip[FHP|GH]4Tuple} or L{LatLon[FHP|GH]}). 

291 return Clas(self.lat, self.lon, self.height, clipid) 

292 

293 

294class LatLonFHP(_LatLonBool): 

295 '''A point or intersection in a L{BooleanFHP} clip or composite. 

296 ''' 

297 _en_ex = None 

298 _label = None 

299 _2split = None # or C{._Clip} 

300 _2xing = False 

301 

302 def __init__(self, lat_ll, lon=None, height=0, clipid=INT0, **wrap_name): 

303 '''New C{LatLonFHP} from separate C{lat}, C{lon}, C{h}eight and C{clipid} 

304 scalars, or from a previous L{LatLonFHP}, L{ClipFHP4Tuple} or some other 

305 C{LatLon} instance. 

306 

307 @arg lat_ll: Latitude (C{scalar}) or a lat-/longitude (L{LatLonFHP}, 

308 L{ClipFHP4Tuple} or some other C{LatLon}). 

309 

310 @see: L{Here<_LatLonBool.__init__>} for further details. 

311 ''' 

312 _LatLonBool.__init__(self, lat_ll, lon, height, clipid, **wrap_name) 

313 

314 def __add__(self, other): 

315 _other(self, other) 

316 return self.__class__(self.y + other.y, self.x + other.x) 

317 

318 def __mod__(self, other): # cross product 

319 _other(self, other) 

320 return self.x * other.y - self.y * other.x 

321 

322 def __mul__(self, other): # dot product 

323 _other(self, other) 

324 return self.x * other.x + self.y * other.y 

325 

326 def __rmul__(self, other): # scalar product 

327 _xscalar(other=other) 

328 return self.__class__(self.y * other, self.x * other) 

329 

330 def _e_x_str(self, t): # PYCHOK no cover 

331 if self._label: 

332 t = NN(self._label, t) 

333 if self._en_ex: 

334 t = NN(t, self._en_ex) 

335 return t 

336 

337 @property_RO 

338 def _isduplicate(self): 

339 # Is this point a I{duplicate} intersection? 

340 p = self._dupof 

341 return bool(p and self._linked 

342 and p is not self 

343 and p == self 

344# and p._alpha in (None, self._alpha) 

345 and self._alpha in (_0_0, p._alpha)) 

346 

347# @property_RO 

348# def _isduplicated(self): 

349# # Return the number of I{duplicates}? 

350# d, v = 0, self 

351# while v: 

352# if v._dupof is self: 

353# d += 1 

354# v = v._next 

355# if v is self: 

356# break 

357# return d 

358 

359 def isenclosedBy(self, *composites_points, **wrap): 

360 '''Is this point inside one or more composites or polygons based on 

361 the U{winding number<https://www.ScienceDirect.com/science/article/ 

362 pii/S0925772101000128>}? 

363 

364 @arg composites_points: Composites and/or iterables of points 

365 (L{ClipFHP4Tuple}, L{ClipGH4Tuple}, L{LatLonFHP}, 

366 L{LatLonGH} or any C{LatLon}). 

367 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True}, 

368 wrap or I{normalize} and unroll all C{points} (C{bool}). 

369 

370 @raise ValueError: Some C{points} invalid. 

371 

372 @see: U{Algorithm 6<https://www.ScienceDirect.com/science/ 

373 article/pii/S0925772101000128>}. 

374 ''' 

375 class _Pseudo(object): 

376 # Pseudo-_CompositeBase._clips tuple 

377 

378 @property_RO 

379 def _clips(self): 

380 for cp in _Cps(_CompositeFHP, composites_points, 

381 LatLonFHP.isenclosedBy): # PYCHOK yield 

382 for c in cp._clips: 

383 yield c 

384 

385 return self._isinside(_Pseudo(), **wrap) 

386 

387 def _isinside(self, composite, *excludes, **wrap): 

388 # Is this point inside a composite, excluding 

389 # certain C{_Clip}s? I{winding number}? 

390 x, y, i = self.x, self.y, False 

391 for c in composite._clips: 

392 if c not in excludes: 

393 w = 0 

394 for p1, p2 in c._edges2(**wrap): 

395 # edge [p1,p2] must straddle y 

396 if (p1.y < y) is not (p2.y < y): # or ^ 

397 r = p2.x > x 

398 s = p2.y > p1.y 

399 if p1.x < x: 

400 b = r and (s is (p1._2A(p2, self) > 0)) 

401 else: 

402 b = r or (s is (p1._2A(p2, self) > 0)) 

403 if b: 

404 w += 1 if s else -1 

405 if isodd(w): 

406 i = not i 

407 return i 

408 

409 @property_RO 

410 def _prev_next2(self): 

411 # Adjust 2-tuple (._prev, ._next) iff a I{duplicate} intersection 

412 p, n = self, self._next 

413 if self._isduplicate: 

414 p = self._dupof 

415 while p._isduplicate: 

416 p = p._dupof 

417 while n._isduplicate: 

418 n = n._next 

419 return p._prev, n 

420 

421# def _edge2(self): 

422# # Return the start and end point of the 

423# # edge containing I{intersection} C{v}. 

424# n = p = self 

425# while p.isintersection: 

426# p = p._prev 

427# if p is self: 

428# break 

429# while n.isintersection: 

430# n = n._next 

431# if n is self: 

432# break 

433# # assert p == self or not p._2Abs(self, n) 

434# return p, n 

435 

436 def _RPoracle(self, p1, p2, p3): 

437 # Relative Position oracle 

438 if p1._linked is self: # or p1._linked2(self): 

439 T = _RP.IS_Pm 

440 elif p3._linked is self: # or p3._linked2(self): 

441 T = _RP.IS_Pp 

442 elif p1._2A(p2, p3) > 0: # left turn 

443 T = _RP.LEFT if self._2A(p1, p2) > 0 and \ 

444 self._2A(p2, p3) > 0 else \ 

445 _RP.RIGHT # PYCHOK indent 

446 else: # right turn (or straight) 

447 T = _RP.RIGHT if self._2A(p1, p2) < 0 and \ 

448 self._2A(p2, p3) < 0 else \ 

449 _RP.LEFT # PYCHOK indent 

450 return T 

451 

452 

453class LatLonGH(_LatLonBool): 

454 '''A point or intersection in a L{BooleanGH} clip or composite. 

455 ''' 

456 _entry = None # entry or exit iff intersection 

457 

458 def __init__(self, lat_ll, lon=None, height=0, clipid=INT0, **wrap_name): 

459 '''New C{LatLonGH} from separate C{lat}, C{lon}, C{h}eight and C{clipid} 

460 scalars, or from a previous L{LatLonGH}, L{ClipGH4Tuple} or some other 

461 C{LatLon} instance. 

462 

463 @arg lat_ll: Latitude (C{scalar}) or a lat-/longitude (L{LatLonGH}, 

464 L{ClipGH4Tuple} or some other C{LatLon}). 

465 

466 @see: L{Here<_LatLonBool.__init__>} for further details. 

467 ''' 

468 _LatLonBool.__init__(self, lat_ll, lon, height, clipid, **wrap_name) 

469 

470 def _check(self): 

471 # Check-mark this vertex and its link. 

472 self._checked = True 

473 k = self._linked 

474 if k and not k._checked: 

475 k._checked = True 

476 

477 def _e_x_str(self, t): # PYCHOK no cover 

478 return t if self._entry is None else NN(t, 

479 (_e_ if self._entry else _x_)) 

480 

481 def isenclosedBy(self, *composites_points, **wrap): 

482 '''Is this point inside one or more composites or polygons based 

483 on the U{even-odd-rule<https://www.ScienceDirect.com/science/ 

484 article/pii/S0925772101000128>}? 

485 

486 @arg composites_points: Composites and/or iterables of points 

487 (L{ClipFHP4Tuple}, L{ClipGH4Tuple}, L{LatLonFHP}, 

488 L{LatLonGH} or any C{LatLon}). 

489 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True}, 

490 wrap or I{normalize} and unroll all C{points} (C{bool}). 

491 

492 @raise ValueError: Some B{C{points}} invalid. 

493 ''' 

494 class _Pseudo(object): 

495 # Pseudo-_CompositeBase._edges3 method 

496 

497 def _edges3(self, **kwds): 

498 for cp in _Cps(_CompositeGH, composites_points, 

499 LatLonGH.isenclosedBy): # PYCHOK yield 

500 for e in cp._edges3(**kwds): 

501 yield e 

502 

503 return self._isinside(_Pseudo(), **wrap) 

504 

505 def _isinside(self, composite, *bottom_top, **wrap): 

506 # Is this vertex inside the composite? I{even-odd rule}? 

507 

508 def _x(y, p1, p2): 

509 # return C{x} at given C{y} on edge [p1,p2] 

510 return (y - p1.y) / (p2.y - p1.y) * (p2.x - p1.x) 

511 

512 # The I{even-odd} rule counts the number of edges 

513 # intersecting a ray emitted from this point to 

514 # east-bound infinity. When I{odd} this point lies 

515 # inside, if I{even} outside. 

516 y, i = self.y, False 

517 if not (bottom_top and _outside(y, y, *bottom_top)): 

518 x = self.x 

519 for p1, p2, _ in composite._edges3(**wrap): 

520 if (p1.y < y) is not (p2.y < y): # or ^ 

521 r = p2.x > x 

522 if p1.x < x: 

523 b = r and (_x(y, p1, p2) > x) 

524 else: 

525 b = r or (_x(y, p1, p2) > x) 

526 if b: 

527 i = not i 

528 return i 

529 

530 

531class _Clip(_Named): 

532 '''(INTERNAL) A I{doubly-linked} list representing a I{closed} 

533 polygon of L{LatLonFHP} or L{LatLonGH} points, duplicates 

534 and intersections with other clips. 

535 ''' 

536 _composite = None 

537 _dups = 0 

538 _first = None 

539 _id = 0 

540 _identical = False 

541 _noInters = False 

542 _last = None 

543 _LL = None 

544 _len = 0 

545 _pushback = False 

546 

547 def __init__(self, composite, clipid=INT0): 

548 '''(INTERNAL) New C{_Clip}. 

549 ''' 

550 # assert isinstance(composite, _CompositeBase) 

551 if clipid in composite._clipids: 

552 raise ClipError(clipid=clipid, txt=_duplicate_) 

553 self._composite = composite 

554 self._id = clipid 

555 self._LL = composite._LL 

556 composite._clips = composite._clips + (self,) 

557 

558 def __contains__(self, point): # PYCHOK no cover 

559 '''Is the B{C{point}} in this clip? 

560 ''' 

561 for v in self: 

562 if v is point: # or ==? 

563 return True 

564 return False 

565 

566 def __eq__(self, other): 

567 '''Is this clip I{equivalent} to an B{C{other}} clip, 

568 do both have the same C{len}, the same points, in 

569 the same order, possibly rotated? 

570 ''' 

571 return self._equi(_other(self, other), 0) 

572 

573 def __ge__(self, other): 

574 '''See method C{__lt__}. 

575 ''' 

576 return not self.__lt__(other) 

577 

578 def __gt__(self, other): 

579 '''Is this clip C{"above"} an B{C{other}} clip, 

580 located or stretched farther North or East? 

581 ''' 

582 return self._bltr4 > _other(self, other)._bltr4 

583 

584 def __hash__(self): # PYCHOK no over 

585 return hash(self._bltr4) 

586 

587 def __iter__(self): 

588 '''Yield the points, duplicates and intersections. 

589 ''' 

590 v = f = self._first 

591 while v: 

592 yield v 

593 v = v._next 

594 if v is f: 

595 break 

596 

597 def __le__(self, other): 

598 '''See method C{__gt__}. 

599 ''' 

600 return not self.__gt__(other) 

601 

602 def __len__(self): 

603 '''Return the number of points, duplicates and 

604 intersections in this clip. 

605 ''' 

606 return self._len 

607 

608 def __lt__(self, other): 

609 '''Is this clip C{"below"} an B{C{other}} clip, 

610 located or stretched farther South or West? 

611 ''' 

612 return self._bltr4 < _other(self, other)._bltr4 

613 

614 def __ne__(self, other): # required for Python 2 

615 '''See method C{__eq__}. 

616 ''' 

617 return not self.__eq__(other) 

618 

619 _all = __iter__ 

620 

621 @property_RO 

622 def _all_ON_ON(self): 

623 # Check whether all vertices are ON_ON. 

624 L_ON_ON = _L.ON_ON 

625 return all(v._label is L_ON_ON for v in self) 

626 

627 def _append(self, y_v, *x_h_clipid): 

628 # Append a point given as C{y}, C{x}, C{h}eight and 

629 # C{clipid} args or as a C{LatLon[FHP|GH]}. 

630 self._last = v = self._LL(y_v, *x_h_clipid) if x_h_clipid else y_v 

631 self._len += 1 

632 # assert v._clipid == self._id 

633 

634 v._next = n = self._first 

635 if n is None: # set ._first 

636 self._first = p = n = v 

637 else: # insert before ._first 

638 v._prev = p = n._prev 

639 p._next = n._prev = v 

640 return v 

641 

642# def _appendedup(self, v, clipid=0): 

643# # Like C{._append}, but only append C{v} if not a 

644# # duplicate of the one previously append[edup]'ed. 

645# y, x, p = v.y, v.x, self._last 

646# if p is None or y != p.y or x != p.x or clipid != p._clipid: 

647# p = self._append(y, x, v._height, clipid) 

648# if v._linked: 

649# p._linked = True # to force errors 

650# return p 

651 

652 @Property_RO 

653 def _bltr4(self): 

654 # Get the bounds as 4-tuple C{(bottom, left, top, right)}. 

655 return map2(float, _MODS.points.boundsOf(self, wrap=False)) 

656 

657 def _bltr4eps(self, eps): 

658 # Get the ._bltr4 bounds tuple, slightly oversized. 

659 if eps > 0: # > EPS 

660 yb, xl, yt, xr = self._bltr4 

661 yb, yt = _low_high_eps2(yb, yt, eps) 

662 xl, xr = _low_high_eps2(xl, xr, eps) 

663 t = yb, xl, yt, xr 

664 else: 

665 t = self._bltr4 

666 return t 

667 

668 def _closed(self, raiser): # PYCHOK unused 

669 # End a clip, un-close it and check C{len}. 

670 p, f = self._last, self._first 

671 if f and f._prev is p and p is not f and \ 

672 p._next is f and p == f: # PYCHOK no cover 

673 # un-close the clip 

674 f._prev = p = p._prev 

675 p._next = f 

676 self._len -= 1 

677# elif f and raiser: 

678# raise self._OpenClipError(p, f) 

679 if len(self) < 3: 

680 raise self._Error(_too_(_few_)) 

681 

682 def _dup(self, q): 

683 # Duplicate a point (or intersection) as intersection. 

684 v = self._insert(q.y, q.x, q) 

685 v._alpha = q._alpha or _0_0 # _0_0 replaces None 

686 v._dupof = q._dupof or q 

687 # assert v._prev is q 

688 # assert q._next is v 

689 return v 

690 

691 def _edges2(self, wrap=False, **unused): 

692 # Yield each I{original} edge as a 2-tuple 

693 # (p1, p2), a pair of C{LatLon[FHP|GH])}s. 

694 p1 = p = f = self._first 

695 while p: 

696 p2 = p = p._next 

697 if p.ispoint: 

698 if wrap and p is not f: 

699 p2 = _unrollon(p1, p) 

700 yield p1, p2 

701 p1 = p2 

702 if p is f: 

703 break 

704 

705 def _equi(self, clip, eps): 

706 # Is this clip I{equivalent} to B{C{clip}} within 

707 # the given I{non-negative} tolerance B{C{eps}}? 

708 r, f = len(self), self._first 

709 if f and r == len(clip) and self._bltr4eps(eps) \ 

710 == clip._bltr4eps(eps): 

711 _equi = _LatLonBool._equi 

712 for v in clip: 

713 if _equi(f, v, eps): 

714 s, n = f, v 

715 for _ in range(r): 

716 s, n = s._next, n._next 

717 if not _equi(s, n, eps): 

718 break # next v 

719 else: # equivalent 

720 return True 

721 return False 

722 

723 def _Error(self, txt): # PYCHOK no cover 

724 # Build a C{ClipError} instance 

725 kwds = dict(len=len(self), txt=txt) 

726 if self._dups: 

727 kwds.update(dups=self._dups) 

728 cp = self._composite 

729 if self._id: 

730 try: 

731 i = cp._clips.index(self) 

732 if i != self._id: 

733 kwds[_clip_] = i 

734 except ValueError: 

735 pass 

736 kwds[_clipid_] = self._id 

737 return ClipError(cp._kind, cp.name, **kwds) 

738 

739 def _index(self, clips, eps): 

740 # see _CompositeBase._equi 

741 for i, c in enumerate(clips): 

742 if c._equi(self, eps): 

743 return i 

744 raise ValueError(NN) # like clips.index(self) 

745 

746 def _insert(self, y, x, start, *end_alpha): 

747 # insertVertex between points C{start} and 

748 # C{end}, ordered by C{alpha} iff given. 

749 v = self._LL(y, x, start._height, start._clipid) 

750 n = start._next 

751 if end_alpha: 

752 end, alpha = end_alpha 

753 v._alpha = alpha 

754 v._height = favg(v._height, end._height, f=alpha) 

755 # assert start is not end 

756 while n is not end and n._alpha < alpha: 

757 n = n._next 

758 v._next = n 

759 v._prev = p = n._prev 

760 p._next = n._prev = v 

761 self._len += 1 

762# _Clip._bltr4._update(self) 

763# _Clip._ishole._update(self) 

764 return v 

765 

766 def _intersection(self, unused, q, *p1_p2_alpha): 

767 # insert an intersection or make a point both 

768 if p1_p2_alpha: # intersection on edge 

769 v = self._insert(q.y, q.x, *p1_p2_alpha) 

770 else: # intersection at point 

771 v = q 

772 # assert not v._linked 

773 # assert v._alpha is None 

774 return v 

775 

776 def _intersections(self): 

777 # Yield all intersections, some may be points too. 

778 for v in self: 

779 if v.isintersection: 

780 yield v 

781 

782 @Property_RO 

783 def _ishole(self): # PYCHOK no cover 

784 # Is this clip a hole inside its composite? 

785 v = self._first 

786 return v._isinside(self._composite, self) if v else False 

787 

788 @property_RO 

789 def _nodups(self): 

790 # Yield all non-duplicates. 

791 for v in self: 

792 if not v._dupof: 

793 yield v 

794 

795 def _noXings(self, Union): 

796 # Are all intersections non-CROSSINGs, -BOUNCINGs? 

797 Xings = _L.BOUNCINGs if Union else _L.CROSSINGs 

798 return all(v._label not in Xings for v in self._intersections()) 

799 

800 def _OpenClipError(self, s, e): # PYCHOK no cover 

801 # Return a C{CloseError} instance 

802 t = NN(s, _ELLIPSIS_(_COMMASPACE_, e)) 

803 return self._Error(_SPACE_(_open_, t)) 

804 

805 def _point2(self, insert): 

806 # getNonIntersectionPoint and -Vertex 

807 if not (insert and self._noInters): 

808 for p in self._points(may_be=False): # not p._isduplicated? 

809 return p, None 

810 for n in self._intersections(): 

811 p, _ = n._prev_next2 

812 k = p._linked 

813 if k: 

814 if n._linked not in k._prev_next2: 

815 # create a pseudo-point 

816 k = _0_5 * (p + n) 

817 if insert: 

818 k = self._insert(k.y, k.x, n._prev) 

819 r = k # to remove later 

820 else: # no ._prev, ._next 

821 k._clipid = n._clipid 

822 r = None 

823 return k, r 

824 return None, None 

825 

826 def _points(self, may_be=True): 

827 # Yield all points I{in original order}, which may be intersections too. 

828 for v in self: 

829 if v.ispoint and (may_be or not v.isintersection): 

830 yield v 

831 

832 def _remove2(self, v): 

833 # Remove vertex C{v}. 

834 # assert not v._isduplicated 

835 if len(self) > 1: 

836 p = v._prev 

837 p._next = n = v._next 

838 n._prev = p 

839 if self._first is v: 

840 self._first = n 

841 if self._last is v: 

842 self._last = p 

843 self._len -= 1 

844 else: 

845 n = self._last = \ 

846 p = self._first = None 

847 self._len = 0 

848 return p, n 

849 

850 def _update_all(self): # PYCHOK no cover 

851 # Zap the I{cached} properties. 

852 _Clip._bltr4._update( self) 

853 _Clip._ishole._update(self) 

854 return self # for _special_identicals 

855 

856 def _Xings(self): 

857 # Yield all I{un-checked} CROSSING intersections. 

858 CROSSING = _L.CROSSING 

859 for v in self._intersections(): 

860 if v._label is CROSSING and not v._checked: 

861 yield v 

862 

863 

864class _CompositeBase(_Named): 

865 '''(INTERNAL) Base class for L{BooleanFHP} and L{BooleanGH} 

866 (C{_CompositeFHP} and C{_CompositeGH}). 

867 ''' 

868 _clips = () # tuple of C{_Clips} 

869 _eps = EPS # null edges 

870 _kind = _corners_ 

871 _LL = _LatLonBool # shut up PyChecker 

872 _raiser = False 

873 _xtend = False 

874 

875 def __init__(self, lls, kind=NN, eps=EPS, **name): 

876 '''(INTERNAL) See L{BooleanFHP} and L{BooleanGH}. 

877 ''' 

878 n = _name__(name, _or_nameof=lls) 

879 if n: 

880 self.name = n 

881 if kind: 

882 self._kind = kind 

883 if self._eps < eps: 

884 self._eps = eps 

885 

886 c = _Clip(self) 

887 lp = None 

888 for ll in lls: 

889 ll = self._LL(ll) 

890 if lp is None: 

891 c._id = ll._clipid # keep clipid 

892 lp = c._append(ll) 

893 elif ll._clipid != lp._clipid: # new clip 

894 c._closed(self.raiser) 

895 c = _Clip(self, ll._clipid) 

896 lp = c._append(ll) 

897 elif abs(ll - lp) > eps: # PYCHOK lp 

898 lp = c._append(ll) 

899 else: 

900 c._dups += 1 

901 c._closed(self.raiser) 

902 

903 def __contains__(self, point): # PYCHOK no cover 

904 '''Is the B{C{point}} in one of the clips? 

905 ''' 

906 for c in self._clips: 

907 if point in c: 

908 return True 

909 return False 

910 

911 def __eq__(self, other): 

912 '''Is this I{composite} equivalent to an B{C{other}}, i.e. 

913 do both contain I{equivalent} clips in the same or in a 

914 different order? Two clips are considered I{equivalent} 

915 if both have the same points etc. in the same order, 

916 possibly rotated. 

917 ''' 

918 return self._equi(_other(self, other), 0) 

919 

920 def __iter__(self): 

921 '''Yield all points, duplicates and intersections. 

922 ''' 

923 for c in self._clips: 

924 for v in c: 

925 yield v 

926 

927 def __ne__(self, other): # required for Python 2 

928 '''See method C{__eq__}. 

929 ''' 

930 return not self.__eq__(other) 

931 

932 def __len__(self): 

933 '''Return the I{total} number of points. 

934 ''' 

935 return sum(map(len, self._clips)) if self._clips else 0 

936 

937 def __repr__(self): 

938 '''String C{repr} of this composite. 

939 ''' 

940 c = len(self._clips) 

941 c = Fmt.SQUARE(c) if c > 1 else NN 

942 n = Fmt.SQUARE(len(self)) 

943 t = Fmt.PAREN(self) # XXX not unstr 

944 return NN(self.__class__.__name__, c, n, t) 

945 

946 def __str__(self): 

947 '''String C{str} of this composite. 

948 ''' 

949 return _COMMASPACE_.join(map(str, self)) 

950 

951 @property_RO 

952 def _bottom_top_eps2(self): 

953 # Get the bottom and top C{y} bounds, oversized. 

954 return _min_max_eps2(min(v.y for v in self), 

955 max(v.y for v in self)) 

956 

957 def _class(self, corners, kwds, **dflts): 

958 # Return a new instance 

959 _g = kwds.get 

960 kwds = dict((n, _g(n, v)) for n, v in dflts.items()) 

961 return self.__class__(corners or (), **kwds) 

962 

963 @property_RO 

964 def _clipids(self): # PYCHOK no cover 

965 for c in self._clips: 

966 yield c._id 

967 

968 def clipids(self): 

969 '''Return a tuple with all C{clipid}s, I{ordered}. 

970 ''' 

971 return tuple(self._clipids) 

972 

973# def _clipidups(self, other): 

974# # Number common C{clipid}s between this and an C{other} composite 

975# return len(set(self._clipids).intersection(set(other._clipids))) 

976 

977 def _edges3(self, **raiser_wrap): 

978 # Yield each I{original} edge as a 3-tuple 

979 # C{(LatLon[FHP|GH], LatLon[FHP|GH], _Clip)}. 

980 for c in self._clips: 

981 for p1, p2 in c._edges2(**raiser_wrap): 

982 yield p1, p2, c 

983 

984 def _encloses(self, lat, lon, **wrap): 

985 # see function .points.isenclosedBy 

986 return self._LL(lat, lon).isenclosedBy(self, **wrap) 

987 

988 @property 

989 def eps(self): 

990 '''Get the null edges tolerance (C{degrees}, usually). 

991 ''' 

992 return self._eps 

993 

994 @eps.setter # PYCHOK setter! 

995 def eps(self, eps): 

996 '''Set the null edges tolerance (C{degrees}, usually). 

997 ''' 

998 self._eps = eps 

999 

1000 def _10eps(self, **eps_): 

1001 # Get eps for _LatLonBool._2Abs 

1002 e = _xkwds_get(eps_, eps=self._eps) 

1003 if e != EPS: 

1004 e *= _10EPS / EPS 

1005 else: 

1006 e = _10EPS 

1007 return e 

1008 

1009 def _equi(self, other, eps): 

1010 # Is this composite I{equivalent} to an B{C{other}} within 

1011 # the given, I{non-negative} tolerance B{C{eps}}? 

1012 cs, co = self._clips, other._clips 

1013 if cs and len(cs) == len(co): 

1014 if eps > 0: 

1015 _index = _Clip._index 

1016 else: 

1017 def _index(c, cs, unused): 

1018 return cs.index(c) 

1019 try: 

1020 cs = list(sorted(cs)) 

1021 for c in sorted(co): 

1022 cs.pop(_index(c, cs, eps)) 

1023 except ValueError: # from ._index 

1024 pass 

1025 return False if cs else True 

1026 else: # both null? 

1027 return False if cs or co else True 

1028 

1029 def _intersections(self): 

1030 # Yield all intersections. 

1031 for c in self._clips: 

1032 for v in c._intersections(): 

1033 yield v 

1034 

1035 def isequalTo(self, other, eps=None): 

1036 '''Is this boolean/composite equal to an B{C{other}} within 

1037 a given, I{non-negative} tolerance? 

1038 

1039 @arg other: The other boolean/composite (C{Boolean[FHP|GB]}). 

1040 @kwarg eps: Tolerance for equality (C{degrees} or C{None}). 

1041 

1042 @return: C{True} if equivalent, C{False} otherwise (C{bool}). 

1043 

1044 @raise TypeError: Invalid B{C{other}}. 

1045 

1046 @see: Method C{__eq__}. 

1047 ''' 

1048 if isinstance(other, _CompositeBase): 

1049 return self._equi(other, _eps0(eps)) 

1050 raise _IsnotError(_boolean_, _composite_, other=other) 

1051 

1052 def _kwds(self, op, **more): 

1053 # Get all keyword arguments as C{dict}. 

1054 kwds = dict(raiser=self.raiser, eps=self.eps, 

1055 name=self.name or op.__name__) 

1056 kwds.update(more) 

1057 return kwds 

1058 

1059 @property_RO 

1060 def _left_right_eps2(self): 

1061 # Get the left and right C{x} bounds, oversized. 

1062 return _min_max_eps2(min(v.x for v in self), 

1063 max(v.x for v in self)) 

1064 

1065 def _points(self, may_be=True): # PYCHOK no cover 

1066 # Yield all I{original} points, which may be intersections too. 

1067 for c in self._clips: 

1068 for v in c._points(may_be=may_be): 

1069 yield v 

1070 

1071 @property 

1072 def raiser(self): 

1073 '''Get the option to throw L{ClipError} exceptions (C{bool}). 

1074 ''' 

1075 return self._raiser 

1076 

1077 @raiser.setter # PYCHOK setter! 

1078 def raiser(self, throw): 

1079 '''Set the option to throw L{ClipError} exceptions (C{bool}). 

1080 ''' 

1081 self._raiser = bool(throw) 

1082 

1083 def _results(self, _presults, Clas, closed=False, inull=False, **eps): 

1084 # Yield the dedup'd results, as L{ClipFHP4Tuple}s 

1085 C = self._LL if Clas is None else Clas 

1086 e = self._10eps(**eps) 

1087 for clipid, ns in enumerate(_presults): 

1088 f = p = v = None 

1089 for n in ns: 

1090 if f is None: 

1091 yield n._toClas(C, clipid) 

1092 f = p = n 

1093 elif v is None: 

1094 v = n # got f, p, v 

1095 elif inull or p._2Abs(v, n, eps=e): 

1096 yield v._toClas(C, clipid) 

1097 p, v = v, n 

1098 else: # null, colinear, ... skipped 

1099 v = n 

1100 if v and (inull or p._2Abs(v, f, eps=e)): 

1101 yield v._toClas(C, clipid) 

1102 p = v 

1103 if f and p != f and closed: # close clip 

1104 yield f._toClas(C, clipid) 

1105 

1106 def _sum(self, other, op): 

1107 # Combine this and an C{other} composite 

1108 LL = self._LL 

1109 sp = self.copy(name=self.name or op.__name__) 

1110 sp._clips, sid = (), INT0 # new clips 

1111 for cp in (self, other): 

1112 for c in cp._clips: 

1113 _ap = _Clip(sp, sid)._append 

1114 for v in c._nodups: 

1115 _ap(LL(v.y, v.x, v.height, sid)) 

1116 sid += 1 

1117 return sp 

1118 

1119 def _sum1(self, _a_p, *args, **kwds): # in .karney, .points 

1120 # Sum the area or perimeter of all clips 

1121 return _MODS.fsums.fsum1((_a_p(c, *args, **kwds) for c in self._clips), floats=True) 

1122 

1123 def _sum2(self, LL, _a_p, *args, **kwds): # in .sphericalNvector, -Trigonometry 

1124 # Sum the area or perimeter of all clips 

1125 

1126 def _lls(clip): # convert clip to LLs 

1127 _LL = LL 

1128 for v in clip: 

1129 yield _LL(v.lat, v.lon) # datum=Sphere 

1130 

1131 return _MODS.fsums.fsum1((_a_p(_lls(c), *args, **kwds) for c in self._clips), floats=True) 

1132 

1133 def toLatLon(self, LatLon=None, closed=False, **LatLon_kwds): 

1134 '''Yield all (non-duplicate) points and intersections 

1135 as an instance of B{C{LatLon}}. 

1136 

1137 @kwarg LatLon: Class to use (C{LatLon}) or if C{None}, 

1138 L{LatLonFHP} or L{LatLonGH}. 

1139 @kwarg closed: If C{True}, close each clip (C{bool}). 

1140 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} 

1141 keyword arguments, ignore if 

1142 C{B{LatLon} is None}. 

1143 

1144 @raise TypeError: Invalid B{C{LatLon}}. 

1145 

1146 @note: For intersections, C{height} is an instance 

1147 of L{HeightX}, otherwise of L{Height}. 

1148 ''' 

1149 if LatLon is None: 

1150 LL, kwds = self._LL, {} 

1151 elif issubclassof(LatLon, _LatLonBool, LatLonBase): 

1152 LL, kwds = LatLon, LatLon_kwds 

1153 else: 

1154 raise _TypeError(LatLon=LatLon) 

1155 

1156 for c in self._clips: 

1157 lf, cid = None, c._id 

1158 for v in c._nodups: 

1159 ll = LL(v.y, v.x, **kwds) 

1160 ll._height = v.height 

1161 if ll._clipid != cid: 

1162 ll._clipid = cid 

1163 yield ll 

1164 if lf is None: 

1165 lf = ll 

1166 if closed and lf: 

1167 yield lf 

1168 

1169 

1170class _CompositeFHP(_CompositeBase): 

1171 '''(INTERNAL) A list of clips representing a I{composite} 

1172 of L{LatLonFHP} points, duplicates and intersections 

1173 with an other I{composite}. 

1174 ''' 

1175 _LL = LatLonFHP 

1176 _Union = False 

1177 

1178 def __init__(self, lls, raiser=False, **name_kind_eps): 

1179 # New L{_CompositeFHP}. 

1180 if raiser: 

1181 self._raiser = True 

1182 _CompositeBase.__init__(self, lls, **name_kind_eps) 

1183 

1184 def _classify(self): 

1185 # 2) Classify intersection chains. 

1186 L = _L 

1187 for v in self._intersections(): 

1188 n, b = v, v._label 

1189 if b in L.RIGHT_LEFT_ON: # next chain 

1190 while True: 

1191 n._label = None # n.__dict__.pop('_label') 

1192 n = n._next 

1193 if n is v or n._label is not L.ON_ON: # n._label and ... 

1194 break 

1195 a = L.LEFT_ON if n._label is L.ON_LEFT else L.RIGHT_ON 

1196 v._label = n._label = L.BOUNCING_D if a is b else L.CROSSING_D 

1197 

1198 # 3) Copy labels 

1199 for v in self._intersections(): 

1200 v._linked._label = v._label 

1201 

1202 def _clip(self, corners, Union=False, Clas=None, 

1203 **closed_inull_raiser_eps): 

1204 # Clip this composite with another one, C{corners}, 

1205 # using Foster-Hormann-Popa's algorithm. 

1206 P = self 

1207 Q = self._class(corners, closed_inull_raiser_eps, 

1208 eps=P._eps, raiser=False) 

1209 if Union: 

1210 P._Union = Q._Union = True 

1211 

1212 bt = Q._bottom_top_eps2 

1213 lr = Q._left_right_eps2 

1214 # compute and insert intersections 

1215 for p1, p2, Pc in P._edges3(**closed_inull_raiser_eps): 

1216 if not (_outside(p1.x, p2.x, *lr) or 

1217 _outside(p1.y, p2.y, *bt)): 

1218 e = _EdgeFHP(p1, p2) 

1219 if e._dp2 > EPS2: # non-null edge 

1220 for q1, q2, Qc in Q._edges3(**closed_inull_raiser_eps): 

1221 for T, p, q in e._intersect3(q1, q2): 

1222 p = Pc._intersection(T, *p) 

1223 q = Qc._intersection(T, *q) 

1224 # assert not p._linked 

1225 # assert not q._linked 

1226 p._link(q) 

1227 

1228 # label and classify intersections 

1229 P._labelize() 

1230 P._classify() 

1231 

1232 # check for special cases 

1233 P._special_cases(Q) 

1234 Q._special_cases(P) 

1235 # handle identicals 

1236 P._special_identicals(Q) 

1237 

1238 # set Entry/Exit flags 

1239 P._set_entry_exits(Q) 

1240 Q._set_entry_exits(P) 

1241 

1242 # handle splits and crossings 

1243 P._splits_xings(Q) 

1244 

1245 # yield the results 

1246 return P._results(P._presults(Q), Clas, **closed_inull_raiser_eps) 

1247 

1248 @property_RO 

1249 def _identicals(self): 

1250 # Yield all clips marked C{._identical}. 

1251 for c in self._clips: 

1252 if c._identical: 

1253 yield c 

1254 

1255 def _labelize(self): 

1256 # 1) Intersections classification 

1257 for p in self._intersections(): 

1258 q = p._linked 

1259 # determine local configuration at this intersection 

1260 # and positions of Q- and Q+ relative to (P-, I, P+) 

1261 p1, p3 = p._prev_next2 

1262 q1, q3 = q._prev_next2 

1263 t = (q1._RPoracle(p1, p, p3), 

1264 q3._RPoracle(p1, p, p3)) 

1265 # check intersecting and overlapping cases 

1266 p._label = _RP2L.get(t, None) 

1267 

1268 def _presults(self, other): 

1269 # Yield the result clips, each as a generator 

1270 # of the L{_LatLonFHP}s in that clip 

1271 for cp in (self, other): 

1272 for c in cp._clips: 

1273 if c._pushback: 

1274 yield c._all() 

1275 for c in self._clips: 

1276 for X in c._Xings(): 

1277 yield self._resultX(X) 

1278 

1279 def _resultX(self, X): 

1280 # Yield the results from CROSSING C{X}. 

1281 L, U, v = _L, self._Union, X 

1282 while v: 

1283 v._checked = True 

1284 r = v # in P or Q 

1285 s = L.Toggle[v._en_ex] 

1286 e = (s is L.EXIT) ^ U 

1287 while True: 

1288 v = v._next if e else v._prev 

1289 yield v 

1290 v._checked = True 

1291 if v._en_ex is s or v is X: 

1292 break 

1293 if v is r: # full circle 

1294 raise ClipError(full_circle=v, clipid=v._clipid) 

1295 if v is not X: 

1296 v = v._linked 

1297 if v is X: 

1298 break 

1299 

1300 def _set_entry_exits(self, other): # MCCABE 14 

1301 # 4) Set entry/exit flags 

1302 L, U = _L, self._Union 

1303 for c in self._clips: 

1304 n, k = c._point2(True) 

1305 if n: 

1306 f = n 

1307 s = L.EXIT if n._isinside(other) else L.ENTRY 

1308 t = L.EXIT # first_chain_vertex = True 

1309 while True: 

1310 if n.isintersection: 

1311 b = n._label 

1312 if b is L.CROSSING: 

1313 n._en_ex = s 

1314 s = L.Toggle[s] 

1315 elif b is L.BOUNCING and ((s is L.EXIT) ^ U): 

1316 n._2split = c # see ._splits_xings 

1317 elif b is L.CROSSING_D: 

1318 n._en_ex = s 

1319 if (s is t) ^ U: 

1320 n._label = L.CROSSING 

1321 t = L.Toggle[t] 

1322 if t is L.EXIT: # first_chain_vertex == True 

1323 s = L.Toggle[s] 

1324 elif b is L.BOUNCING_D: 

1325 n._en_ex = s 

1326 if (s is t) ^ U: 

1327 n._2xing = True # see ._splits_xings 

1328 s = L.Toggle[s] 

1329 t = L.Toggle[t] 

1330 n = n._next # _, n = n._prev_next2 

1331 if n is f: 

1332 break # PYCHOK attr? 

1333 if k: 

1334 c._remove2(k) 

1335 

1336 def _special_cases(self, other): 

1337 # 3.5) Check special cases 

1338 U = self._Union 

1339 for c in self._clips: 

1340 if c._noXings(U): 

1341 c._noInters = True 

1342 if c._all_ON_ON: 

1343 c._identical = True 

1344 else: 

1345 p, _ = c._point2(False) 

1346 if p and (p._isinside(other) ^ U): 

1347 c._pushback = True 

1348 

1349 def _special_identicals(self, other): 

1350 # 3.5) Handle identicals 

1351 _u = _Clip._update_all 

1352 cds = dict((c._id, _u(c)) for c in other._identicals) 

1353 # assert len(cds) == len(other._identicals) 

1354 if cds: # PYCHOK no cover 

1355 for c in self._identicals: 

1356 c._update_all() 

1357 for v in c._intersections(): 

1358 d = cds.get(v._linked._clipid, None) 

1359 if d and d._ishole is c._ishole: 

1360 c._pushback = True 

1361 break # next c 

1362 

1363 @property_RO 

1364 def _2splits(self): 

1365 # Yield all intersections marked C{._2split} 

1366 for p in self._intersections(): 

1367 if p._2split: 

1368 # assert isinstance(p._2split, _Clip) 

1369 yield p 

1370 

1371 def _splits_xings(self, other): # MCCABE 15 

1372 # 5) Handle split pairs and 6) crossing candidates 

1373 

1374 def _2A_dup2(p, P): # PYCHOK unused 

1375 p1, p2 = p._prev_next2 

1376 ap = p1._2A(p, p2) 

1377 Pc = p._2split 

1378 # assert Pc in P._clips 

1379 # assert p in Pc 

1380 return ap, Pc._dup(p) 

1381 

1382 def _links2(ps, qs): # PYCHOK P unused? 

1383 # Yield each link as a 2-tuple(p, q) 

1384 id_qs = set(map(id, qs)) 

1385 if id_qs: 

1386 for p in ps: 

1387 q = p._linked 

1388 if q and id(q) in id_qs: 

1389 yield p, q 

1390 

1391 L = _L 

1392 E = L.ENTRY if self._Union else L.EXIT 

1393 X = L.Toggle[E] 

1394 for p, q in _links2(self._2splits, other._2splits): 

1395 ap, pp = _2A_dup2(p, self) 

1396 aq, qq = _2A_dup2(q, other) 

1397 if (ap * aq) > 0: # PYCHOK no cover 

1398 p._link(qq) # overwrites ... 

1399 q._link(pp) # ... p-q link 

1400 else: 

1401 pp._link(qq) 

1402 p._en_ex = q._en_ex = E 

1403 pp._en_ex = qq._en_ex = X 

1404 p._label = pp._label = \ 

1405 q._label = qq._label = L.CROSSING 

1406 

1407 for p, q in _links2(self._2xings, other._2xings): 

1408 p._label = q._label = L.CROSSING 

1409 

1410 @property_RO 

1411 def _2xings(self): 

1412 # Yield all intersections marked C{._2xing} 

1413 for p in self._intersections(): 

1414 if p._2xing: 

1415 yield p 

1416 

1417 

1418class _CompositeGH(_CompositeBase): 

1419 '''(INTERNAL) A list of clips representing a I{composite} 

1420 of L{LatLonGH} points, duplicates and intersections 

1421 with an other I{composite}. 

1422 ''' 

1423 _LL = LatLonGH 

1424 _xtend = False 

1425 

1426 def __init__(self, lls, raiser=False, xtend=False, **name_kind_eps): 

1427 # New L{_CompositeGH}. 

1428 if xtend: 

1429 self._xtend = True 

1430 elif raiser: 

1431 self._raiser = True 

1432 _CompositeBase.__init__(self, lls, **name_kind_eps) 

1433 

1434 def _clip(self, corners, s_entry, c_entry, Clas=None, 

1435 **closed_inull_raiser_xtend_eps): 

1436 # Clip this polygon with another one, C{corners}. 

1437 

1438 # Core of Greiner/Hormann's algorithm, enhanced U{Correia's 

1439 # <https://GitHub.com/helderco/univ-polyclip>} implementation*** 

1440 # and extended to optionally handle so-called "degenerate cases" 

1441 S = self 

1442 C = self._class(corners, closed_inull_raiser_xtend_eps, 

1443 raiser=False, xtend=False) 

1444 bt = C._bottom_top_eps2 

1445 lr = C._left_right_eps2 

1446 # 1. find intersections 

1447 for s1, s2, Sc in S._edges3(**closed_inull_raiser_xtend_eps): 

1448 if not (_outside(s1.x, s2.x, *lr) or 

1449 _outside(s1.y, s2.y, *bt)): 

1450 e = _EdgeGH(s1, s2, **closed_inull_raiser_xtend_eps) 

1451 if e._hypot2 > EPS2: # non-null edge 

1452 for c1, c2, Cc in C._edges3(**closed_inull_raiser_xtend_eps): 

1453 for y, x, sa, ca in e._intersect4(c1, c2): 

1454 s = Sc._insert(y, x, s1, s2, sa) 

1455 c = Cc._insert(y, x, c1, c2, ca) 

1456 s._link(c) 

1457 

1458 # 2. identify entry/exit intersections 

1459 if S._first: 

1460 s_entry ^= S._first._isinside(C, *bt) 

1461 for v in S._intersections(): 

1462 v._entry = s_entry = not s_entry 

1463 

1464 if C._first: 

1465 c_entry ^= C._first._isinside(S) 

1466 for v in C._intersections(): 

1467 v._entry = c_entry = not c_entry 

1468 

1469 # 3. yield the result(s) 

1470 return S._results(S._presults(), Clas, **closed_inull_raiser_xtend_eps) 

1471 

1472 @property_RO 

1473 def _first(self): 

1474 # Get the very first vertex of the first clip 

1475 for v in self: 

1476 return v 

1477 return None # PYCHOK no cover 

1478 

1479 def _kwds(self, op, **more): 

1480 # Get the kwds C{dict}. 

1481 return _CompositeBase._kwds(self, op, xtend=self.xtend, **more) 

1482 

1483 def _presults(self): 

1484 # Yield the unchecked intersection(s). 

1485 for c in self._clips: 

1486 for v in c._intersections(): 

1487 if not v._checked: 

1488 yield self._resultU(v) 

1489 

1490 def _resultU(self, v): 

1491 # Yield the result from an un-checked intersection. 

1492 while v and not v._checked: 

1493 v._check() 

1494 yield v 

1495 r = v 

1496 e = v._entry 

1497 while True: 

1498 v = v._next if e else v._prev 

1499 yield v 

1500 if v._linked: 

1501 break 

1502 if v is r: 

1503 raise ClipError(full_circle=v, clipid=v._clipid) 

1504 v = v._linked # switch 

1505 

1506 @property 

1507 def xtend(self): 

1508 '''Get the option to handle I{degenerate cases} (C{bool}). 

1509 ''' 

1510 return self._xtend 

1511 

1512 @xtend.setter # PYCHOK setter! 

1513 def xtend(self, xtend): 

1514 '''Set the option to handle I{degenerate cases} (C{bool}). 

1515 ''' 

1516 self._xtend = bool(xtend) 

1517 

1518 

1519class _EdgeFHP(object): 

1520 # An edge between two L{LatLonFHP} points. 

1521 

1522 X_INTERSECT = _Enum('Xi', 1) # C++ enum 

1523 X_OVERLAP = _Enum('Xo', 5) 

1524 P_INTERSECT = _Enum('Pi', 3) 

1525 P_OVERLAP = _Enum('Po', 7) 

1526 Ps = (P_INTERSECT, P_OVERLAP, X_OVERLAP) 

1527 Q_INTERSECT = _Enum('Qi', 2) 

1528 Q_OVERLAP = _Enum('Qo', 6) 

1529 Qs = (Q_INTERSECT, Q_OVERLAP, X_OVERLAP) 

1530 V_INTERSECT = _Enum('Vi', 4) 

1531 V_OVERLAP = _Enum('Vo', 8) 

1532 Vs = (V_INTERSECT, V_OVERLAP) 

1533 

1534 def __init__(self, p1, p2, **unused): 

1535 # New edge between points C{p1} and C{p2}, each a L{LatLonFHP}. 

1536 self._p1_p2 = p1, p2 

1537 self._dp = dp = p2 - p1 

1538 self._dp2 = dp * dp # dot product, hypot2 

1539 

1540 self._lr, \ 

1541 self._bt = _left_right_bottom_top_eps2(p1, p2) 

1542 

1543 def _intersect3(self, q1, q2): 

1544 # Yield intersection(s) Type or C{None} 

1545 if not (_outside(q1.x, q2.x, *self._lr) or 

1546 _outside(q1.y, q2.y, *self._bt)): 

1547 dq = q2 - q1 

1548 dq2 = dq * dq # dot product, hypot2 

1549 if dq2 > EPS2: # like ._clip 

1550 T, E = None, _EdgeFHP # self.__class__ 

1551 p1, p2 = self._p1_p2 

1552 ap1 = p1._2A(q1, q2) 

1553 ap2_1 = p2._2A(q1, q2) - ap1 

1554 if fabs(ap2_1) > _0_EPS: # non-parallel edges 

1555 aq1 = q1._2A(p1, p2) 

1556 aq2_1 = q2._2A(p1, p2) - aq1 

1557 if fabs(aq2_1) > _0_EPS: 

1558 # compute and classify alpha and beta 

1559 a, a_0, a_0_1, _ = _alpha4(-ap1 / ap2_1) 

1560 b, b_0, b_0_1, _ = _alpha4(-aq1 / aq2_1) 

1561 # distinguish intersection types 

1562 T = E.X_INTERSECT if a_0_1 and b_0_1 else ( 

1563 E.P_INTERSECT if a_0_1 and b_0 else ( 

1564 E.Q_INTERSECT if a_0 and b_0_1 else ( 

1565 E.V_INTERSECT if a_0 and b_0 else None))) 

1566 

1567 elif fabs(ap1) < _0_EPS: # parallel or colinear edges 

1568 dp = self._dp 

1569 d1 = q1 - p1 

1570 # compute and classify alpha and beta 

1571 a, a_0, a_0_1, _a_0_1 = _alpha4((d1 * dp) / self._dp2) 

1572 b, b_0, b_0_1, _b_0_1 = _alpha4((d1 * dq) / (-dq2)) 

1573 # distinguish overlap type 

1574 T = E.X_OVERLAP if a_0_1 and b_0_1 else ( 

1575 E.P_OVERLAP if a_0_1 and _b_0_1 else ( 

1576 E.Q_OVERLAP if _a_0_1 and b_0_1 else ( 

1577 E.V_OVERLAP if a_0 and b_0 else None))) 

1578 

1579 if T: 

1580 if T is E.X_INTERSECT: 

1581 v = p1 + a * self._dp 

1582 yield T, (v, p1, p2, a), (v, q1, q2, b) 

1583 elif T in E.Vs: 

1584 yield T, (p1,), (q1,) 

1585 else: 

1586 if T in E.Qs: 

1587 yield T, (p1,), (p1, q1, q2, b) 

1588 if T in E.Ps: 

1589 yield T, (q1, p1, p2, a), (q1,) 

1590 

1591 

1592class _EdgeGH(object): 

1593 # An edge between two L{LatLonGH} points. 

1594 

1595 _raiser = False 

1596 _xtend = False 

1597 

1598 def __init__(self, s1, s2, raiser=False, xtend=False, **unused): 

1599 # New edge between points C{s1} and C{s2}, each a L{LatLonGH}. 

1600 self._s1, self._s2 = s1, s2 

1601 self._x_sx_y_sy = (s1.x, s2.x - s1.x, 

1602 s1.y, s2.y - s1.y) 

1603 self._lr, \ 

1604 self._bt = _left_right_bottom_top_eps2(s1, s2) 

1605 

1606 if xtend: 

1607 self._xtend = True 

1608 elif raiser: 

1609 self._raiser = True 

1610 

1611 def _alpha2(self, x, y, dx, dy): 

1612 # Return C{(alpha)}, see .points.nearestOn5 

1613 a = (y * dy + x * dx) / self._hypot2 

1614 d = (y * dx - x * dy) / self._hypot0 

1615 return a, fabs(d) 

1616 

1617 def _Error(self, n, *args, **kwds): # PYCHOK no cover 

1618 t = unstr(_EdgeGH.__name__, self._s1, self._s2) 

1619 t = _DOT_(t, _EdgeGH._intersect4.__name__) 

1620 t = unstr(t, *args, **kwds) 

1621 return ClipError(_case_, n, txt=t) 

1622 

1623 @Property_RO 

1624 def _hypot0(self): 

1625 _, sx, _, sy = self._x_sx_y_sy 

1626 return hypot(sx, sy) * _0_EPS 

1627 

1628 @Property_RO 

1629 def _hypot2(self): 

1630 _, sx, _, sy = self._x_sx_y_sy 

1631 return hypot2(sx, sy) 

1632 

1633 def _intersect4(self, c1, c2, parallel=True): # MCCABE 14 

1634 # Yield the intersection(s) of this and another edge. 

1635 

1636 # @return: None, 1 or 2 intersections, each a 4-Tuple 

1637 # (y, x, s_alpha, c_alpha) with intersection 

1638 # coordinates x and y and both alphas. 

1639 

1640 # @raise ClipError: Intersection unhandled. 

1641 

1642 # @see: U{Intersection point of two line segments 

1643 # <http://PaulBourke.net/geometry/pointlineplane/>}. 

1644 c1_x, c1_y = c1.x, c1.y 

1645 if not (_outside(c1_x, c2.x, *self._lr) or 

1646 _outside(c1_y, c2.y, *self._bt)): 

1647 x, sx, \ 

1648 y, sy = self._x_sx_y_sy 

1649 

1650 cx = c2.x - c1_x 

1651 cy = c2.y - c1_y 

1652 d = cy * sx - cx * sy 

1653 

1654 if fabs(d) > _0_EPS: # non-parallel edges 

1655 dx = x - c1_x 

1656 dy = y - c1_y 

1657 ca = (sx * dy - sy * dx) / d 

1658 if _0_EPS < ca < _EPS_1 or (self._xtend and 

1659 _EPS_0 < ca < _1_EPS): 

1660 sa = (cx * dy - cy * dx) / d 

1661 if _0_EPS < sa < _EPS_1 or (self._xtend and 

1662 _EPS_0 < sa < _1_EPS): 

1663 yield (y + sa * sy), (x + sa * sx), sa, ca 

1664 

1665 # unhandled, "degenerate" cases 1, 2 or 3 

1666 elif self._raiser and not (sa < _EPS_0 or sa > _1_EPS): # PYCHOK no cover 

1667 raise self._Error(1, c1, c2, sa=sa) # intersection at s1 or s2 

1668 

1669 elif self._raiser and not (ca < _EPS_0 or ca > _1_EPS): # PYCHOK no cover 

1670 # intersection at c1 or c2 or at c1 or c2 and s1 or s2 

1671 sa = (cx * dy - cy * dx) / d 

1672 e = 2 if sa < _EPS_0 or sa > _1_EPS else 3 

1673 raise self._Error(e, c1, c2, ca=ca) 

1674 

1675 elif parallel and (sx or sy) and (cx or cy): # PYCHOK no cover 

1676 # non-null, parallel or colinear edges 

1677 sa1, d1 = self._alpha2(c1_x - x, c1_y - y, sx, sy) 

1678 sa2, d2 = self._alpha2(c2.x - x, c2.y - y, sx, sy) 

1679 if max(d1, d2) < _0_EPS: 

1680 if self._xtend and not _outside(sa1, sa2, _EPS_0, _1_EPS): 

1681 if sa1 > sa2: # anti-parallel 

1682 sa1, sa2 = sa2, sa1 

1683 ca1, ca2 = _1_0, _0_0 

1684 else: # parallel 

1685 ca1, ca2 = _0_0, _1_0 

1686 ca = fabs((sx / cx) if cx else (sy / cy)) 

1687 # = hypot(sx, sy) / hypot(cx, cy) 

1688 if sa1 < 0: # s1 is between c1 and c2 

1689 ca *= ca1 + sa1 

1690 yield y, x, ca1, _alpha1(ca) 

1691 else: # c1 is between s1 and s2 

1692 yield (y + sa1 * sy), (x + sa1 * sx), sa1, ca1 

1693 if sa2 > 1: # s2 is between c1 and c2 

1694 ca *= sa2 - _1_0 

1695 yield (y + sy), (x + sx), ca2, _alpha1(ca2 - ca) 

1696 else: # c2 is between s1 and s2 

1697 yield (y + sa2 * sy), (x + sa2 * sx), sa2, ca2 

1698 elif self._raiser and not _outside(sa1, sa2, _0_0, _1_EPS): 

1699 raise self._Error(4, c1, c2, d1=d1, d2=d2) 

1700 

1701 

1702class _BooleanBase(object): 

1703 # Shared C{Boolean[FHP|GH]} methods. 

1704 

1705 def __add__(self, other): 

1706 '''Sum: C{this + other} clips. 

1707 ''' 

1708 return self._sum(_other(self, other), self.__add__) # PYCHOK OK 

1709 

1710 def __and__(self, other): 

1711 '''Intersection: C{this & other}. 

1712 ''' 

1713 return self._boolean(other, False, False, self.__and__) # PYCHOK OK 

1714 

1715 def __iadd__(self, other): 

1716 '''In-place sum: C{this += other} clips. 

1717 ''' 

1718 return self._inplace(self.__add__(other)) 

1719 

1720 def __iand__(self, other): 

1721 '''In-place intersection: C{this &= other}. 

1722 ''' 

1723 return self._inplace(self.__and__(other)) 

1724 

1725 def __ior__(self, other): 

1726 '''In-place union: C{this |= other}. 

1727 ''' 

1728 return self._inplace(self.__or__(other)) 

1729 

1730 def __or__(self, other): 

1731 '''Union: C{this | other}. 

1732 ''' 

1733 return self._boolean(other, True, True, self.__or__) # PYCHOK OK 

1734 

1735 def __radd__(self, other): 

1736 '''Reverse sum: C{other + this} clips. 

1737 ''' 

1738 return _other(self, other)._sum(self, self.__radd__) 

1739 

1740 def __rand__(self, other): 

1741 '''Reverse intersection: C{other & this} 

1742 ''' 

1743 return _other(self, other).__and__(self) 

1744 

1745 def __ror__(self, other): 

1746 '''Reverse union: C{other | this} 

1747 ''' 

1748 return _other(self, other).__or__(self) 

1749 

1750 def _boolean4(self, other, op): 

1751 # Set up a new C{Boolean[FHP|GH]}. 

1752 C = self.__class__ 

1753 kwds = C._kwds(self, op) 

1754 a = C(self, **kwds) 

1755 b = _other(self, other) 

1756 return a, b, C, kwds 

1757 

1758 def _inplace(self, r): 

1759 # Replace this with a L{Boolean*} result. 

1760 self._clips, r._clips = r._clips, None 

1761# if self._raiser != r._raiser: 

1762# self._raiser = r._raiser 

1763# if self._xtend != r._xtend: 

1764# self._xtend = r._xtend 

1765# if self._eps != r._eps: 

1766# self._eps = r._eps 

1767 return self 

1768 

1769 

1770class BooleanFHP(_CompositeFHP, _BooleanBase): 

1771 '''I{Composite} class providing I{boolean} operations between two 

1772 I{composites} using U{Forster-Hormann-Popa<https://www.ScienceDirect.com/ 

1773 science/article/pii/S259014861930007X>}'s C++ implementation, transcoded 

1774 to pure Python. 

1775 

1776 The supported operations between (composite) polygon A and B are: 

1777 

1778 - C = A & B or A &= B, intersection of A and B 

1779 

1780 - C = A + B or A += B, sum of A and B clips 

1781 

1782 - C = A | B or A |= B, union of A and B 

1783 

1784 - A == B or A != B, equivalent A and B clips 

1785 

1786 - A.isequalTo(B, eps), equivalent within tolerance 

1787 

1788 @see: Methods C{__eq__} and C{isequalTo}, function L{clipFHP4} 

1789 and class L{BooleanGH}. 

1790 ''' 

1791 _kind = _boolean_ 

1792 

1793 def __init__(self, lls, raiser=False, eps=EPS, **name): 

1794 '''New L{BooleanFHP} operand for I{boolean} operation. 

1795 

1796 @arg lls: The polygon points and clips (iterable of L{LatLonFHP}s, 

1797 L{ClipFHP4Tuple}s or other C{LatLon}s). 

1798 @kwarg raiser: If C{True}, throw L{ClipError} exceptions (C{bool}). 

1799 @kwarg esp: Tolerance for eliminating null edges (C{degrees}, same 

1800 units as the B{C{lls}} coordinates). 

1801 @kwarg name: Optional C{B{name}=NN} (C{str}). 

1802 ''' 

1803 _CompositeFHP.__init__(self, lls, raiser=raiser, eps=eps, **name) 

1804 

1805 def __isub__(self, other): 

1806 '''Not implemented.''' 

1807 return _NotImplemented(self, other) 

1808 

1809 def __rsub__(self, other): 

1810 '''Not implemented.''' 

1811 return _NotImplemented(self, other) 

1812 

1813 def __sub__(self, other): 

1814 '''Not implemented.''' 

1815 return _NotImplemented(self, other) 

1816 

1817 def _boolean(self, other, Union, unused, op): 

1818 # One C{BooleanFHP} operation. 

1819 p, q, C, kwds = self._boolean4(other, op) 

1820 r = p._clip(q, Union=Union, **kwds) 

1821 return C(r, **kwds) 

1822 

1823 

1824class BooleanGH(_CompositeGH, _BooleanBase): 

1825 '''I{Composite} class providing I{boolean} operations between two 

1826 I{composites} using the U{Greiner-Hormann<http://www.Inf.USI.CH/ 

1827 hormann/papers/Greiner.1998.ECO.pdf>} algorithm and U{Correia 

1828 <https://GitHub.com/helderco/univ-polyclip>}'s implementation, 

1829 modified and extended. 

1830 

1831 The supported operations between (composite) polygon A and B are: 

1832 

1833 - C = A - B or A -= B, difference A less B 

1834 

1835 - C = B - A or B -= A, difference B less B 

1836 

1837 - C = A & B or A &= B, intersection of A and B 

1838 

1839 - C = A + B or A += B, sum of A and B clips 

1840 

1841 - C = A | B or A |= B, union of A and B 

1842 

1843 - A == B or A != B, equivalent A and B clips 

1844 

1845 - A.isequalTo(B, eps), equivalent within tolerance 

1846 

1847 @note: To handle I{degenerate cases} like C{point-edge} and 

1848 C{point-point} intersections, use class L{BooleanFHP}. 

1849 

1850 @see: Methods C{__eq__} and C{isequalTo}, function L{clipGH4} 

1851 and class L{BooleanFHP}. 

1852 ''' 

1853 _kind = _boolean_ 

1854 

1855 def __init__(self, lls, raiser=True, xtend=False, eps=EPS, **name): 

1856 '''New L{BooleanFHP} operand for I{boolean} operation. 

1857 

1858 @arg lls: The polygon points and clips (iterable of L{LatLonGH}s, 

1859 L{ClipGH4Tuple}s or other C{LatLon}s). 

1860 @kwarg raiser: If C{True}, throw L{ClipError} exceptions (C{bool}). 

1861 @kwarg xtend: If C{True}, extend edges of I{degenerate cases}, an 

1862 attempt to handle the latter (C{bool}). 

1863 @kwarg esp: Tolerance for eliminating null edges (C{degrees}, same 

1864 units as the B{C{lls}} coordinates). 

1865 @kwarg name: Optional C{B{name}=NN} (C{str}). 

1866 ''' 

1867 _CompositeGH.__init__(self, lls, raiser=raiser, xtend=xtend, eps=eps, **name) 

1868 

1869 def _boolean(self, other, s_entry, c_entry, op): 

1870 # One C{BooleanGH} operation. 

1871 s, c, C, kwds = self._boolean4(other, op) 

1872 r = s._clip(c, s_entry, c_entry, **kwds) 

1873 return C(r, **kwds) 

1874 

1875 def __isub__(self, other): 

1876 '''In-place difference: C{this -= other}. 

1877 ''' 

1878 return self._inplace(self.__sub__(other)) 

1879 

1880 def __rsub__(self, other): 

1881 ''' Reverse difference: C{other - this} 

1882 ''' 

1883 return _other(self, other).__sub__(self) 

1884 

1885 def __sub__(self, other): 

1886 '''Difference: C{this - other}. 

1887 ''' 

1888 return self._boolean(other, True, False, self.__sub__) 

1889 

1890 

1891def _alpha1(alpha): 

1892 # Return C{alpha} in C{[0..1]} range 

1893 if _EPS_0 < alpha < _1_EPS: 

1894 return max(_0_0, min(alpha, _1_0)) 

1895 t = _not_(Fmt.SQUARE(_ELLIPSIS_(0, 1))) 

1896 raise ClipError(_alpha_, alpha, txt=t) 

1897 

1898 

1899def _alpha4(a): 

1900 # Return 4-tuple (alpha, -EPS < alpha < EPS, 

1901 # 0 < alpha < 1, 

1902 # not 0 < alpha < 1) 

1903 return (a, False, True, False) if _0_EPS < a < _EPS_1 else ( 

1904 (a, False, False, True) if _0_EPS < fabs(a) else 

1905 (a, True, False, False)) 

1906 

1907 

1908def _Cps(Cp, composites_points, where): 

1909 # Yield composites and points as a C{Cp} composite. 

1910 try: 

1911 kwds = dict(kind=_points_, name__=where) 

1912 for cp in composites_points: 

1913 yield cp if isBoolean(cp) else Cp(cp, **kwds) 

1914 except (AttributeError, ClipError, TypeError, ValueError) as x: 

1915 raise _ValueError(points=cp, cause=x) 

1916 

1917 

1918def _eps0(eps): 

1919 # Adjust C{eps} or C{None}. 

1920 return eps if eps and eps > EPS else 0 

1921 

1922 

1923def isBoolean(obj): 

1924 '''Check for C{Boolean} composites. 

1925 

1926 @arg obj: The object (any C{type}). 

1927 

1928 @return: C{True} if B{C{obj}} is L{BooleanFHP}, L{BooleanGH} 

1929 or some other composite, C{False} otherwise. 

1930 ''' 

1931 return isinstance(obj, _CompositeBase) 

1932 

1933 

1934def _left_right_bottom_top_eps2(p1, p2): 

1935 '''(INTERNAL) Return 2-tuple C{(left, right), (bottom, top)}, oversized. 

1936 ''' 

1937 return (_min_max_eps2(p1.x, p2.x), 

1938 _min_max_eps2(p1.y, p2.y)) 

1939 

1940 

1941def _low_high_eps2(lo, hi, eps): 

1942 '''(INTERNAL) Return 2-tuple C{(lo, hi)}, oversized. 

1943 ''' 

1944 lo *= (_1_0 + eps) if lo < 0 else (_1_0 - eps) 

1945 hi *= (_1_0 - eps) if hi < 0 else (_1_0 + eps) 

1946 return (lo or -eps), (hi or eps) 

1947 

1948 

1949def _min_max_eps2(*xs): 

1950 '''(INTERNAL) Return 2-tuple C{(min, max)}, oversized. 

1951 ''' 

1952 lo, hi = min(xs), max(xs) 

1953 lo *= _1_EPS if lo < 0 else _EPS_1 

1954 hi *= _EPS_1 if hi < 0 else _1_EPS 

1955 return (lo or _EPS_0), (hi or _0_EPS) 

1956 

1957 

1958def _other(this, other): 

1959 '''(INTERNAL) Check for compatible C{type}s. 

1960 ''' 

1961 C = this.__class__ 

1962 if isinstance(other, C): 

1963 return other 

1964 raise _IsnotError(C.__name__, other=other) 

1965 

1966 

1967def _outside(x1, x2, lo, hi): 

1968 '''(INTERNAL) Is C{(x1, x2)} outside C{(lo, hi)}? 

1969 ''' 

1970 return max(x1, x2) < lo or min(x1, x2) > hi 

1971 

1972 

1973__all__ += _ALL_DOCS(_BooleanBase, _Clip, 

1974 _CompositeBase, _CompositeFHP, _CompositeGH, 

1975 _LatLonBool) 

1976 

1977# **) MIT License 

1978# 

1979# Copyright (C) 2018-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1980# 

1981# Permission is hereby granted, free of charge, to any person obtaining a 

1982# copy of this software and associated documentation files (the "Software"), 

1983# to deal in the Software without restriction, including without limitation 

1984# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1985# and/or sell copies of the Software, and to permit persons to whom the 

1986# Software is furnished to do so, subject to the following conditions: 

1987# 

1988# The above copyright notice and this permission notice shall be included 

1989# in all copies or substantial portions of the Software. 

1990# 

1991# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1992# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1993# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1994# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1995# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1996# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1997# OTHER DEALINGS IN THE SOFTWARE. 

1998 

1999# ***) GNU GPL 3 

2000# 

2001# Copyright (C) 2011-2012 Helder Correia <Helder.MC@Gmail.com> 

2002# 

2003# This program is free software: you can redistribute it and/or 

2004# modify it under the terms of the GNU General Public License as 

2005# published by the Free Software Foundation, either version 3 of 

2006# the License, or any later version. 

2007# 

2008# This program is distributed in the hope that it will be useful, 

2009# but WITHOUT ANY WARRANTY; without even the implied warranty of 

2010# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 

2011# GNU General Public License for more details. 

2012# 

2013# You should have received a copy of the GNU General Public License 

2014# along with this program. If not, see <http://www.GNU.org/licenses/>. 

2015# 

2016# You should have received the README file along with this program. 

2017# If not, see <https://GitHub.com/helderco/univ-polyclip>.