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, _xisscalar 

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 

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 Fmt, _Named, _NotImplemented, pairs, unstr 

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

36# from pygeodesy.points import boundsOf # _MODS 

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

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

39from pygeodesy.units import Height, HeightX 

40from pygeodesy.utily import fabs, _unrollon, _Wrap 

41 

42# from math import fabs # from .utily 

43 

44__all__ = _ALL_LAZY.booleans 

45__version__ = '24.02.06' 

46 

47_0_EPS = EPS # near-zero, positive 

48_EPS_0 = -EPS # near-zero, negative 

49_1_EPS = _1_0 + EPS # near-one, over 

50_EPS_1 = _1_0 - EPS # near-one, under 

51_10EPS = EPS * 10 # see ._2Abs, ._10eps 

52 

53_alpha_ = 'alpha' 

54_boolean_ = 'boolean' 

55_case_ = 'case' 

56_corners_ = 'corners' 

57_duplicate_ = 'duplicate' 

58_open_ = 'open' 

59 

60 

61def _Enum(txt, enum): # PYCHOK unused 

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

63 

64 

65class _L(object): # Intersection labels 

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

67 CROSSING_D = _Enum(_X_ + _d_, 8) 

68 CROSSINGs = (CROSSING, CROSSING_D) 

69 BOUNCING = _Enum(_B_, 2) 

70 BOUNCING_D = _Enum(_B_ + _d_, 9) 

71 BOUNCINGs = (BOUNCING, BOUNCING_D) + CROSSINGs 

72 LEFT_ON = _Enum('Lo', 3) 

73 ON_ON = _Enum('oo', 5) 

74 ON_LEFT = _Enum('oL', 6) 

75 ON_RIGHT = _Enum('oR', 7) 

76 RIGHT_ON = _Enum('Ro', 4) 

77 RIGHT_LEFT_ON = (RIGHT_ON, LEFT_ON) 

78 # Entry/Exit flags 

79 ENTRY = _Enum(_e_, 1) 

80 EXIT = _Enum(_x_, 0) 

81 Toggle = {ENTRY: EXIT, 

82 EXIT: ENTRY, 

83 None: None} 

84 

85_L = _L() # PYCHOK singleton 

86 

87 

88class _RP(object): # RelativePositions 

89 IS_Pm = _Enum('Pm', 2) # C++ enum 

90 IS_Pp = _Enum('Pp', 3) 

91 LEFT = _Enum('L', 0) 

92 RIGHT = _Enum(_R_, 1) 

93 

94_RP = _RP() # PYCHOK singleton 

95 

96_RP2L = {(_RP.LEFT, _RP.RIGHT): _L.CROSSING, 

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

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

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

100 # overlapping cases 

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

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

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

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

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

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

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

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

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

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

111 

112 

113class _LatLonBool(_Named): 

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

115 ''' 

116 _alpha = None # point AND intersection else length 

117 _checked = False # checked in phase 3 iff intersection 

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

119 _dupof = None # original of a duplicate 

120# _e_x_str = NN # shut up PyChecker 

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

122 _linked = None # link to neighbor iff intersection 

123 _next = None # link to the next vertex 

124 _prev = None # link to the previous vertex 

125 

126 def __init__(self, lat_ll, lon=None, height=0, clipid=INT0, 

127 wrap=False, name=NN): 

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

129 and C{clipid} scalars or from a previous C{LatLon[FHP|GH]}, 

130 a C{Clip[FHP|GH]4Tuple} or some other C{LatLon} instance. 

131 

132 @arg lat_ll: Latitude (C{scalar}) or a lat/longitude 

133 (C{LatLon[FHP|GH]}, aC{Clip[FHP|GH]4Tuple} 

134 or some other C{LatLon}). 

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

136 scalar, ignored otherwise. 

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

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

139 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{lat}} 

140 and B{C{lon}} (C{bool}). 

141 @kwarg name: Optional name (C{str}). 

142 ''' 

143 if lon is None: 

144 y, x = lat_ll.lat, lat_ll.lon 

145 h = _xattr(lat_ll, height=height) 

146 c = _xattr(lat_ll, clipid=clipid) 

147 else: 

148 y, x = lat_ll, lon 

149 h, c = height, clipid 

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

151 # don't duplicate defaults 

152 if self._height != h: 

153 self._height = h 

154 if self._clipid != c: 

155 self._clipid = c 

156 if name: 

157 self.name = name 

158 

159 def __abs__(self): 

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

161 

162 def __eq__(self, other): 

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

164 other.x == self.x and 

165 other.y == self.y) 

166 

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

168 return not self.__eq__(other) 

169 

170 def __repr__(self): 

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

172 ''' 

173 if self._prev or self._next: 

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

175 t = _SPACE_(self, Fmt.ANGLE(t)) 

176 else: 

177 t = str(self) 

178 return t 

179 

180 def __str__(self): 

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

182 ''' 

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

184 if self._height: 

185 X = _X_ if self.isintersection else NN 

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

187 if self._clipid: 

188 t += (_clipid_, self._clipid), 

189 if self._alpha is not None: 

190 t += (_alpha_, self._alpha), 

191# if self._dupof: # recursion risk 

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

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

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

195 if self._linked: 

196 k = _DOT_ if self._checked else _BANG_ 

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

198 return NN(self.name, t) 

199 

200 def __sub__(self, other): 

201 _other(self, other) 

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

203 self.x - other.x) 

204 

205 def _2A(self, p2, p3): 

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

207 x, y = self.x, self.y 

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

209 (p3.x - x) * (p2.y - y) 

210 

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

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

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

214 a = fabs(self._2A(p2, p3)) 

215 return 0 if a < eps else a 

216 

217 @property_RO 

218 def clipid(self): 

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

220 ''' 

221 return self._clipid 

222 

223 def _equi(self, llb, eps): 

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

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

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

227 fabs(llb.lat - self.y) > eps) 

228 

229 @property_RO 

230 def height(self): 

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

232 ''' 

233 h = self._height 

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

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

236 

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

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

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

240 

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

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

243 

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

245 

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

247 ''' 

248 try: 

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

250 except (AttributeError, TypeError, ValueError): 

251 raise _IsnotError(_LatLon_, other=other) 

252 

253 @property_RO 

254 def isintersection(self): 

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

256 ''' 

257 return bool(self._linked) 

258 

259 @property_RO 

260 def ispoint(self): 

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

262 ''' 

263 return self._alpha is None 

264 

265 @property_RO 

266 def lat(self): 

267 '''Get the latitude (C{scalar}). 

268 ''' 

269 return self.y 

270 

271 @property_RO 

272 def latlon(self): 

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

274 ''' 

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

276 

277 def _link(self, other): 

278 # Make this and an other point neighbors. 

279 # assert _other(self, other) 

280 self._linked = other 

281 other._linked = self 

282 

283 @property_RO 

284 def lon(self): 

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

286 ''' 

287 return self.x 

288 

289 def _toClas(self, Clas, clipid): 

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

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

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

293 

294 

295class LatLonFHP(_LatLonBool): 

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

297 ''' 

298 _en_ex = None 

299 _label = None 

300 _2split = None # or C{._Clip} 

301 _2xing = False 

302 

303 def __init__(self, lat_ll, *lon_h_clipid, **wrap_name): 

304 '''New C{LatLonFHP} from separate C{lat}, C{lon}, C{h}eight 

305 and C{clipid} scalars, or from a previous L{LatLonFHP}, 

306 a L{ClipFHP4Tuple} or some other C{LatLon} instance. 

307 

308 @arg lat_ll: Latitude (C{scalar}) or a lat/longitude 

309 (L{LatLonFHP}, C{LatLon} or L{ClipFHP4Tuple}). 

310 @arg lon_h_clipid: Longitude (C{scalar}), C{h}eight and 

311 C{clipid} iff B{C{lat_ll}} is scalar, 

312 ignored otherwise. 

313 @kwarg wrap_name: Keyword arguments C{B{wrap}=False} and 

314 C{B{name}=NN}. If C{B{wrap} is True}, wrap 

315 or I{normalize} the lat- and longitude 

316 (C{bool}). Optional B{C{name}} (C{str}). 

317 ''' 

318 _LatLonBool.__init__(self, lat_ll, *lon_h_clipid, **wrap_name) 

319 

320 def __add__(self, other): 

321 _other(self, other) 

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

323 

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

325 _other(self, other) 

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

327 

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

329 _other(self, other) 

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

331 

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

333 _xisscalar(other=other) 

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

335 

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

337 if self._label: 

338 t = NN(self._label, t) 

339 if self._en_ex: 

340 t = NN(t, self._en_ex) 

341 return t 

342 

343 @property_RO 

344 def _isduplicate(self): 

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

346 p = self._dupof 

347 return bool(p and self._linked 

348 and p is not self 

349 and p == self 

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

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

352 

353# @property_RO 

354# def _isduplicated(self): 

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

356# d, v = 0, self 

357# while v: 

358# if v._dupof is self: 

359# d += 1 

360# v = v._next 

361# if v is self: 

362# break 

363# return d 

364 

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

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

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

368 article/pii/S0925772101000128>}? 

369 

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

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

372 L{LatLonGH} or any C{LatLon}). 

373 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

374 C{points} (C{bool}). 

375 

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

377 

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

379 article/pii/S0925772101000128>}. 

380 ''' 

381 class _Pseudo(object): 

382 # Pseudo-_CompositeBase._clips tuple 

383 

384 @property_RO 

385 def _clips(self): 

386 for cp in _Cps(_CompositeFHP, composites_points, 

387 LatLonFHP.isenclosedBy): # PYCHOK yield 

388 for c in cp._clips: 

389 yield c 

390 

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

392 

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

394 # Is this point inside a composite, excluding 

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

396 x, y, i = self.x, self.y, False 

397 for c in composite._clips: 

398 if c not in excludes: 

399 w = 0 

400 for p1, p2 in c._edges2(**wrap): 

401 # edge [p1,p2] must straddle y 

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

403 r = p2.x > x 

404 s = p2.y > p1.y 

405 if p1.x < x: 

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

407 else: 

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

409 if b: 

410 w += 1 if s else -1 

411 if isodd(w): 

412 i = not i 

413 return i 

414 

415 @property_RO 

416 def _prev_next2(self): 

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

418 p, n = self, self._next 

419 if self._isduplicate: 

420 p = self._dupof 

421 while p._isduplicate: 

422 p = p._dupof 

423 while n._isduplicate: 

424 n = n._next 

425 return p._prev, n 

426 

427# def _edge2(self): 

428# # Return the start and end point of the 

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

430# n = p = self 

431# while p.isintersection: 

432# p = p._prev 

433# if p is self: 

434# break 

435# while n.isintersection: 

436# n = n._next 

437# if n is self: 

438# break 

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

440# return p, n 

441 

442 def _RPoracle(self, p1, p2, p3): 

443 # Relative Position oracle 

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

445 T = _RP.IS_Pm 

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

447 T = _RP.IS_Pp 

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

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

450 self._2A(p2, p3) > 0 else \ 

451 _RP.RIGHT # PYCHOK indent 

452 else: # right turn (or straight) 

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

454 self._2A(p2, p3) < 0 else \ 

455 _RP.LEFT # PYCHOK indent 

456 return T 

457 

458 

459class LatLonGH(_LatLonBool): 

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

461 ''' 

462 _entry = None # entry or exit iff intersection 

463 

464 def __init__(self, lat_ll, *lon_h_clipid, **wrap_name): 

465 '''New C{LatLonGH} from separate C{lat}, C{lon}, C{h}eight 

466 and C{clipid} scalars, or from a previous L{LatLonGH}, 

467 L{ClipGH4Tuple} or some other C{LatLon} instance. 

468 

469 @arg lat_ll: Latitude (C{scalar}) or a lat/longitude 

470 (L{LatLonGH}, C{LatLon} or L{ClipGH4Tuple}). 

471 @arg lon_h_clipid: Longitude (C{scalar}), C{h}eight and 

472 C{clipid} iff B{C{lat_ll}} is scalar, 

473 ignored otherwise. 

474 @kwarg wrap_name: Keyword arguments C{B{wrap}=False} and 

475 C{B{name}=NN}. If C{B{wrap} is True}, wrap 

476 or I{normalize} the lat- and longitude 

477 (C{bool}). Optional B{C{name}} (C{str}). 

478 ''' 

479 _LatLonBool.__init__(self, lat_ll, *lon_h_clipid, **wrap_name) 

480 

481 def _check(self): 

482 # Check-mark this vertex and its link. 

483 self._checked = True 

484 k = self._linked 

485 if k and not k._checked: 

486 k._checked = True 

487 

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

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

490 (_e_ if self._entry else _x_)) 

491 

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

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

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

495 article/pii/S0925772101000128>}? 

496 

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

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

499 L{LatLonGH} or any C{LatLon}). 

500 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

501 C{points} (C{bool}). 

502 

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

504 ''' 

505 class _Pseudo(object): 

506 # Pseudo-_CompositeBase._edges3 method 

507 

508 def _edges3(self, **kwds): 

509 for cp in _Cps(_CompositeGH, composites_points, 

510 LatLonGH.isenclosedBy): # PYCHOK yield 

511 for e in cp._edges3(**kwds): 

512 yield e 

513 

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

515 

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

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

518 

519 def _x(y, p1, p2): 

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

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

522 

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

524 # intersecting a ray emitted from this point to 

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

526 # inside, if I{even} outside. 

527 y, i = self.y, False 

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

529 x = self.x 

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

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

532 r = p2.x > x 

533 if p1.x < x: 

534 b = r and (_x(y, p1, p2) > x) 

535 else: 

536 b = r or (_x(y, p1, p2) > x) 

537 if b: 

538 i = not i 

539 return i 

540 

541 

542class _Clip(_Named): 

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

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

545 and intersections with other clips. 

546 ''' 

547 _composite = None 

548 _dups = 0 

549 _first = None 

550 _id = 0 

551 _identical = False 

552 _noInters = False 

553 _last = None 

554 _LL = None 

555 _len = 0 

556 _pushback = False 

557 

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

559 '''(INTERNAL) New C{_Clip}. 

560 ''' 

561 # assert isinstance(composite, _CompositeBase) 

562 if clipid in composite._clipids: 

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

564 self._composite = composite 

565 self._id = clipid 

566 self._LL = composite._LL 

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

568 

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

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

571 ''' 

572 for v in self: 

573 if v is point: # or ==? 

574 return True 

575 return False 

576 

577 def __eq__(self, other): 

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

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

580 the same order, possibly rotated? 

581 ''' 

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

583 

584 def __ge__(self, other): 

585 '''See method C{__lt__}. 

586 ''' 

587 return not self.__lt__(other) 

588 

589 def __gt__(self, other): 

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

591 located or stretched farther North or East? 

592 ''' 

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

594 

595 def __hash__(self): # PYCHOK no over 

596 return hash(self._bltr4) 

597 

598 def __iter__(self): 

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

600 ''' 

601 v = f = self._first 

602 while v: 

603 yield v 

604 v = v._next 

605 if v is f: 

606 break 

607 

608 def __le__(self, other): 

609 '''See method C{__gt__}. 

610 ''' 

611 return not self.__gt__(other) 

612 

613 def __len__(self): 

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

615 intersections in this clip. 

616 ''' 

617 return self._len 

618 

619 def __lt__(self, other): 

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

621 located or stretched farther South or West? 

622 ''' 

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

624 

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

626 '''See method C{__eq__}. 

627 ''' 

628 return not self.__eq__(other) 

629 

630 _all = __iter__ 

631 

632 @property_RO 

633 def _all_ON_ON(self): 

634 # Check whether all vertices are ON_ON. 

635 L_ON_ON = _L.ON_ON 

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

637 

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

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

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

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

642 self._len += 1 

643 # assert v._clipid == self._id 

644 

645 v._next = n = self._first 

646 if n is None: # set ._first 

647 self._first = p = n = v 

648 else: # insert before ._first 

649 v._prev = p = n._prev 

650 p._next = n._prev = v 

651 return v 

652 

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

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

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

656# y, x, p = v.y, v.x, self._last 

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

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

659# if v._linked: 

660# p._linked = True # to force errors 

661# return p 

662 

663 @Property_RO 

664 def _bltr4(self): 

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

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

667 

668 def _bltr4eps(self, eps): 

669 # Get the ._bltr4 bounds tuple, oversized. 

670 if eps > 0: # > EPS 

671 yb, xl, yt, xr = self._bltr4 

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

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

674 t = yb, xl, yt, xr 

675 else: 

676 t = self._bltr4 

677 return t 

678 

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

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

681 p, f = self._last, self._first 

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

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

684 # un-close the clip 

685 f._prev = p = p._prev 

686 p._next = f 

687 self._len -= 1 

688# elif f and raiser: 

689# raise self._OpenClipError(p, f) 

690 if len(self) < 3: 

691 raise self._Error(_too_(_few_)) 

692 

693 def _dup(self, q): 

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

695 v = self._insert(q.y, q.x, q) 

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

697 v._dupof = q._dupof or q 

698 # assert v._prev is q 

699 # assert q._next is v 

700 return v 

701 

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

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

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

705 p1 = p = f = self._first 

706 while p: 

707 p2 = p = p._next 

708 if p.ispoint: 

709 if wrap and p is not f: 

710 p2 = _unrollon(p1, p) 

711 yield p1, p2 

712 p1 = p2 

713 if p is f: 

714 break 

715 

716 def _equi(self, clip, eps): 

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

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

719 r, f = len(self), self._first 

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

721 == clip._bltr4eps(eps): 

722 _equi = _LatLonBool._equi 

723 for v in clip: 

724 if _equi(f, v, eps): 

725 s, n = f, v 

726 for _ in range(r): 

727 s, n = s._next, n._next 

728 if not _equi(s, n, eps): 

729 break # next v 

730 else: # equivalent 

731 return True 

732 return False 

733 

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

735 # Build a C{ClipError} instance 

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

737 if self._dups: 

738 kwds.update(dups=self._dups) 

739 cp = self._composite 

740 if self._id: 

741 try: 

742 i = cp._clips.index(self) 

743 if i != self._id: 

744 kwds[_clip_] = i 

745 except ValueError: 

746 pass 

747 kwds[_clipid_] = self._id 

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

749 

750 def _index(self, clips, eps): 

751 # see _CompositeBase._equi 

752 for i, c in enumerate(clips): 

753 if c._equi(self, eps): 

754 return i 

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

756 

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

758 # insertVertex between points C{start} and 

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

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

761 n = start._next 

762 if end_alpha: 

763 end, alpha = end_alpha 

764 v._alpha = alpha 

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

766 # assert start is not end 

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

768 n = n._next 

769 v._next = n 

770 v._prev = p = n._prev 

771 p._next = n._prev = v 

772 self._len += 1 

773# _Clip._bltr4._update(self) 

774# _Clip._ishole._update(self) 

775 return v 

776 

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

778 # insert an intersection or make a point both 

779 if p1_p2_alpha: # intersection on edge 

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

781 else: # intersection at point 

782 v = q 

783 # assert not v._linked 

784 # assert v._alpha is None 

785 return v 

786 

787 def _intersections(self): 

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

789 for v in self: 

790 if v.isintersection: 

791 yield v 

792 

793 @Property_RO 

794 def _ishole(self): # PYCHOK no cover 

795 # Is this clip a hole inside its composite? 

796 v = self._first 

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

798 

799 @property_RO 

800 def _nodups(self): 

801 # Yield all non-duplicates. 

802 for v in self: 

803 if not v._dupof: 

804 yield v 

805 

806 def _noXings(self, Union): 

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

808 Ls = _L.BOUNCINGs if Union else _L.CROSSINGs 

809 return all(v._label not in Ls for v in self._intersections()) 

810 

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

812 # Return a C{CloseError} instance 

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

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

815 

816 def _point2(self, insert): 

817 # getNonIntersectionPoint and -Vertex 

818 if not (insert and self._noInters): 

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

820 return p, None 

821 for n in self._intersections(): 

822 p, _ = n._prev_next2 

823 k = p._linked 

824 if k: 

825 if n._linked not in k._prev_next2: 

826 # create a pseudo-point 

827 k = _0_5 * (p + n) 

828 if insert: 

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

830 r = k # to remove later 

831 else: # no ._prev, ._next 

832 k._clipid = n._clipid 

833 r = None 

834 return k, r 

835 return None, None 

836 

837 def _points(self, may_be=True): 

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

839 for v in self: 

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

841 yield v 

842 

843 def _remove2(self, v): 

844 # Remove vertex C{v}. 

845 # assert not v._isduplicated 

846 if len(self) > 1: 

847 p = v._prev 

848 p._next = n = v._next 

849 n._prev = p 

850 if self._first is v: 

851 self._first = n 

852 if self._last is v: 

853 self._last = p 

854 self._len -= 1 

855 else: 

856 n = self._last = \ 

857 p = self._first = None 

858 self._len = 0 

859 return p, n 

860 

861 def _update_all(self): # PYCHOK no cover 

862 # Zap the I{cached} properties. 

863 _Clip._bltr4._update( self) 

864 _Clip._ishole._update(self) 

865 return self # for _special_identicals 

866 

867 def _Xings(self): 

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

869 CROSSING = _L.CROSSING 

870 for v in self._intersections(): 

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

872 yield v 

873 

874 

875class _CompositeBase(_Named): 

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

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

878 ''' 

879 _clips = () # tuple of C{_Clips} 

880 _eps = EPS # null edges 

881 _kind = _corners_ 

882 _LL = _LatLonBool # shut up PyChecker 

883 _raiser = False 

884 _xtend = False 

885 

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

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

888 ''' 

889 n = name or _xattr(lls, name=NN) 

890 if n: 

891 self.name = n 

892 if kind: 

893 self._kind = kind 

894 if self._eps < eps: 

895 self._eps = eps 

896 

897 c = _Clip(self) 

898 lp = None 

899 for ll in lls: 

900 ll = self._LL(ll) 

901 if lp is None: 

902 c._id = ll._clipid # keep clipid 

903 lp = c._append(ll) 

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

905 c._closed(self.raiser) 

906 c = _Clip(self, ll._clipid) 

907 lp = c._append(ll) 

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

909 lp = c._append(ll) 

910 else: 

911 c._dups += 1 

912 c._closed(self.raiser) 

913 

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

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

916 ''' 

917 for c in self._clips: 

918 if point in c: 

919 return True 

920 return False 

921 

922 def __eq__(self, other): 

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

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

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

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

927 possibly rotated. 

928 ''' 

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

930 

931 def __iter__(self): 

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

933 ''' 

934 for c in self._clips: 

935 for v in c: 

936 yield v 

937 

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

939 '''See method C{__eq__}. 

940 ''' 

941 return not self.__eq__(other) 

942 

943 def __len__(self): 

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

945 ''' 

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

947 

948 def __repr__(self): 

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

950 ''' 

951 c = len(self._clips) 

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

953 n = Fmt.SQUARE(len(self)) 

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

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

956 

957 def __str__(self): 

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

959 ''' 

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

961 

962 @property_RO 

963 def _bottom_top_eps2(self): 

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

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

966 max(v.y for v in self)) 

967 

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

969 # Return a new instance 

970 _g = kwds.get 

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

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

973 

974 @property_RO 

975 def _clipids(self): # PYCHOK no cover 

976 for c in self._clips: 

977 yield c._id 

978 

979 def clipids(self): 

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

981 ''' 

982 return tuple(self._clipids) 

983 

984# def _clipidups(self, other): 

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

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

987 

988 def _edges3(self, **raiser_wrap): 

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

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

991 for c in self._clips: 

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

993 yield p1, p2, c 

994 

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

996 # see function .points.isenclosedBy 

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

998 

999 @property 

1000 def eps(self): 

1001 '''Get the null edges tolerance (C{degrees}, usually). 

1002 ''' 

1003 return self._eps 

1004 

1005 @eps.setter # PYCHOK setter! 

1006 def eps(self, eps): 

1007 '''Set the null edges tolerance (C{degrees}, usually). 

1008 ''' 

1009 self._eps = eps 

1010 

1011 def _10eps(self, **eps): 

1012 # Get eps for _LatLonBool._2Abs 

1013 e = _xkwds_get(eps, eps=self._eps) 

1014 if e != EPS: 

1015 e *= _10EPS / EPS 

1016 else: 

1017 e = _10EPS 

1018 return e 

1019 

1020 def _equi(self, other, eps): 

1021 # Is this composite I{equivalent} to an B{C{other}} within 

1022 # the given, I{non-negative} tolerance B{C{eps}}? 

1023 cs, co = self._clips, other._clips 

1024 if cs and len(cs) == len(co): 

1025 if eps > 0: 

1026 _index = _Clip._index 

1027 else: 

1028 def _index(c, cs, unused): 

1029 return cs.index(c) 

1030 try: 

1031 cs = list(sorted(cs)) 

1032 for c in sorted(co): 

1033 cs.pop(_index(c, cs, eps)) 

1034 except ValueError: # from ._index 

1035 pass 

1036 return False if cs else True 

1037 else: # both null? 

1038 return False if cs or co else True 

1039 

1040 def _intersections(self): 

1041 # Yield all intersections. 

1042 for c in self._clips: 

1043 for v in c._intersections(): 

1044 yield v 

1045 

1046 def isequalTo(self, other, eps=None): 

1047 '''Is this boolean/composite equal to an B{C{other}} within 

1048 a given, I{non-negative} tolerance? 

1049 

1050 @arg other: The other boolean/composite (C{Boolean[FHP|GB]}). 

1051 @kwarg eps: Tolerance for equality (C{degrees} or C{None}). 

1052 

1053 @return: C{True} if equivalent, C{False} otherwise (C{bool}). 

1054 

1055 @raise TypeError: Invalid B{C{other}}. 

1056 

1057 @see: Method C{__eq__}. 

1058 ''' 

1059 if isinstance(other, _CompositeBase): 

1060 return self._equi(other, _eps0(eps)) 

1061 raise _IsnotError(_boolean_, _composite_, other=other) 

1062 

1063 def _kwds(self, op, **more): 

1064 # Get all keyword arguments as C{dict}. 

1065 kwds = dict(raiser=self.raiser, eps=self.eps, 

1066 name=self.name or op.__name__) 

1067 kwds.update(more) 

1068 return kwds 

1069 

1070 @property_RO 

1071 def _left_right_eps2(self): 

1072 # Get the left and right C{x} bounds, oversized. 

1073 return _min_max_eps2(min(v.x for v in self), 

1074 max(v.x for v in self)) 

1075 

1076 def _points(self, may_be=True): # PYCHOK no cover 

1077 # Yield all I{original} points, which may be intersections too. 

1078 for c in self._clips: 

1079 for v in c._points(may_be=may_be): 

1080 yield v 

1081 

1082 @property 

1083 def raiser(self): 

1084 '''Get the option to throw L{ClipError} exceptions (C{bool}). 

1085 ''' 

1086 return self._raiser 

1087 

1088 @raiser.setter # PYCHOK setter! 

1089 def raiser(self, throw): 

1090 '''Set the option to throw L{ClipError} exceptions (C{bool}). 

1091 ''' 

1092 self._raiser = bool(throw) 

1093 

1094 def _results(self, _presults, Clas, closed=False, inull=False, **eps): 

1095 # Yield the dedup'd results, as L{ClipFHP4Tuple}s 

1096 C = self._LL if Clas is None else Clas 

1097 e = self._10eps(**eps) 

1098 for clipid, ns in enumerate(_presults): 

1099 f = p = v = None 

1100 for n in ns: 

1101 if f is None: 

1102 yield n._toClas(C, clipid) 

1103 f = p = n 

1104 elif v is None: 

1105 v = n # got f, p, v 

1106 elif inull or p._2Abs(v, n, eps=e): 

1107 yield v._toClas(C, clipid) 

1108 p, v = v, n 

1109 else: # null, colinear, ... skipped 

1110 v = n 

1111 if v and (inull or p._2Abs(v, f, eps=e)): 

1112 yield v._toClas(C, clipid) 

1113 p = v 

1114 if f and p != f and closed: # close clip 

1115 yield f._toClas(C, clipid) 

1116 

1117 def _sum(self, other, op): 

1118 # Combine this and an C{other} composite 

1119 LL = self._LL 

1120 sp = self.copy(name=self.name or op.__name__) 

1121 sp._clips, sid = (), INT0 # new clips 

1122 for cp in (self, other): 

1123 for c in cp._clips: 

1124 _ap = _Clip(sp, sid)._append 

1125 for v in c._nodups: 

1126 _ap(LL(v.y, v.x, v.height, sid)) 

1127 sid += 1 

1128 return sp 

1129 

1130 def _sum1(self, _a_p, *args, **kwds): # in .karney, .points 

1131 # Sum the area or perimeter of all clips 

1132 return _MODS.fsums.fsum1((_a_p(c, *args, **kwds) for c in self._clips), floats=True) 

1133 

1134 def _sum2(self, LL, _a_p, *args, **kwds): # in .sphericalNvector, -Trigonometry 

1135 # Sum the area or perimeter of all clips 

1136 

1137 def _lls(clip): # convert clip to LLs 

1138 _LL = LL 

1139 for v in clip: 

1140 yield _LL(v.lat, v.lon) # datum=Sphere 

1141 

1142 return _MODS.fsums.fsum1((_a_p(_lls(c), *args, **kwds) for c in self._clips), floats=True) 

1143 

1144 def toLatLon(self, LatLon=None, closed=False, **LatLon_kwds): 

1145 '''Yield all (non-duplicate) points and intersections 

1146 as an instance of B{C{LatLon}}. 

1147 

1148 @kwarg LatLon: Class to use (C{LatLon}) or if C{None}, 

1149 L{LatLonFHP} or L{LatLonGH}. 

1150 @kwarg closed: If C{True}, close each clip (C{bool}). 

1151 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} 

1152 keyword arguments, ignore if 

1153 C{B{LatLon} is None}. 

1154 

1155 @raise TypeError: Invalid B{C{LatLon}}. 

1156 

1157 @note: For intersections, C{height} is an instance 

1158 of L{HeightX}, otherwise of L{Height}. 

1159 ''' 

1160 if LatLon is None: 

1161 LL, kwds = self._LL, {} 

1162 elif issubclassof(LatLon, _LatLonBool, LatLonBase): 

1163 LL, kwds = LatLon, LatLon_kwds 

1164 else: 

1165 raise _TypeError(LatLon=LatLon) 

1166 

1167 for c in self._clips: 

1168 lf, cid = None, c._id 

1169 for v in c._nodups: 

1170 ll = LL(v.y, v.x, **kwds) 

1171 ll._height = v.height 

1172 if ll._clipid != cid: 

1173 ll._clipid = cid 

1174 yield ll 

1175 if lf is None: 

1176 lf = ll 

1177 if closed and lf: 

1178 yield lf 

1179 

1180 

1181class _CompositeFHP(_CompositeBase): 

1182 '''(INTERNAL) A list of clips representing a I{composite} 

1183 of L{LatLonFHP} points, duplicates and intersections 

1184 with an other I{composite}. 

1185 ''' 

1186 _LL = LatLonFHP 

1187 _Union = False 

1188 

1189 def __init__(self, lls, raiser=False, **name_kind_eps): 

1190 # New L{_CompositeFHP}. 

1191 if raiser: 

1192 self._raiser = True 

1193 _CompositeBase.__init__(self, lls, **name_kind_eps) 

1194 

1195 def _classify(self): 

1196 # 2) Classify intersection chains. 

1197 L = _L 

1198 for v in self._intersections(): 

1199 n, b = v, v._label 

1200 if b in L.RIGHT_LEFT_ON: # next chain 

1201 while True: 

1202 n._label = None # n.__dict__.pop('_label') 

1203 n = n._next 

1204 if n is v or n._label is not L.ON_ON: # n._label and ... 

1205 break 

1206 a = L.LEFT_ON if n._label is L.ON_LEFT else L.RIGHT_ON 

1207 v._label = n._label = L.BOUNCING_D if a is b else L.CROSSING_D 

1208 

1209 # 3) Copy labels 

1210 for v in self._intersections(): 

1211 v._linked._label = v._label 

1212 

1213 def _clip(self, corners, Union=False, Clas=None, 

1214 **closed_inull_raiser_eps): 

1215 # Clip this composite with another one, C{corners}, 

1216 # using Foster-Hormann-Popa's algorithm. 

1217 P = self 

1218 Q = self._class(corners, closed_inull_raiser_eps, 

1219 eps=P._eps, raiser=False) 

1220 if Union: 

1221 P._Union = Q._Union = True 

1222 

1223 bt = Q._bottom_top_eps2 

1224 lr = Q._left_right_eps2 

1225 # compute and insert intersections 

1226 for p1, p2, Pc in P._edges3(**closed_inull_raiser_eps): 

1227 if not (_outside(p1.x, p2.x, *lr) or 

1228 _outside(p1.y, p2.y, *bt)): 

1229 e = _EdgeFHP(p1, p2) 

1230 if e._dp2 > EPS2: # non-null edge 

1231 for q1, q2, Qc in Q._edges3(**closed_inull_raiser_eps): 

1232 for T, p, q in e._intersect3(q1, q2): 

1233 p = Pc._intersection(T, *p) 

1234 q = Qc._intersection(T, *q) 

1235 # assert not p._linked 

1236 # assert not q._linked 

1237 p._link(q) 

1238 

1239 # label and classify intersections 

1240 P._labelize() 

1241 P._classify() 

1242 

1243 # check for special cases 

1244 P._special_cases(Q) 

1245 Q._special_cases(P) 

1246 # handle identicals 

1247 P._special_identicals(Q) 

1248 

1249 # set Entry/Exit flags 

1250 P._set_entry_exits(Q) 

1251 Q._set_entry_exits(P) 

1252 

1253 # handle splits and crossings 

1254 P._splits_xings(Q) 

1255 

1256 # yield the results 

1257 return P._results(P._presults(Q), Clas, **closed_inull_raiser_eps) 

1258 

1259 @property_RO 

1260 def _identicals(self): 

1261 # Yield all clips marked C{._identical}. 

1262 for c in self._clips: 

1263 if c._identical: 

1264 yield c 

1265 

1266 def _labelize(self): 

1267 # 1) Intersections classification 

1268 for p in self._intersections(): 

1269 q = p._linked 

1270 # determine local configuration at this intersection 

1271 # and positions of Q- and Q+ relative to (P-, I, P+) 

1272 p1, p3 = p._prev_next2 

1273 q1, q3 = q._prev_next2 

1274 t = (q1._RPoracle(p1, p, p3), 

1275 q3._RPoracle(p1, p, p3)) 

1276 # check intersecting and overlapping cases 

1277 p._label = _RP2L.get(t, None) 

1278 

1279 def _presults(self, other): 

1280 # Yield the result clips, each as a generator 

1281 # of the L{_LatLonFHP}s in that clip 

1282 for cp in (self, other): 

1283 for c in cp._clips: 

1284 if c._pushback: 

1285 yield c._all() 

1286 for c in self._clips: 

1287 for X in c._Xings(): 

1288 yield self._resultX(X) 

1289 

1290 def _resultX(self, X): 

1291 # Yield the results from CROSSING C{X}. 

1292 L, U, v = _L, self._Union, X 

1293 while v: 

1294 v._checked = True 

1295 r = v # in P or Q 

1296 s = L.Toggle[v._en_ex] 

1297 e = (s is L.EXIT) ^ U 

1298 while True: 

1299 v = v._next if e else v._prev 

1300 yield v 

1301 v._checked = True 

1302 if v._en_ex is s or v is X: 

1303 break 

1304 if v is r: # full circle 

1305 raise ClipError(full_circle=v, clipid=v._clipid) 

1306 if v is not X: 

1307 v = v._linked 

1308 if v is X: 

1309 break 

1310 

1311 def _set_entry_exits(self, other): # MCCABE 14 

1312 # 4) Set entry/exit flags 

1313 L, U = _L, self._Union 

1314 for c in self._clips: 

1315 n, k = c._point2(True) 

1316 if n: 

1317 f = n 

1318 s = L.EXIT if n._isinside(other) else L.ENTRY 

1319 t = L.EXIT # first_chain_vertex = True 

1320 while True: 

1321 if n.isintersection: 

1322 b = n._label 

1323 if b is L.CROSSING: 

1324 n._en_ex = s 

1325 s = L.Toggle[s] 

1326 elif b is L.BOUNCING and ((s is L.EXIT) ^ U): 

1327 n._2split = c # see ._splits_xings 

1328 elif b is L.CROSSING_D: 

1329 n._en_ex = s 

1330 if (s is t) ^ U: 

1331 n._label = L.CROSSING 

1332 t = L.Toggle[t] 

1333 if t is L.EXIT: # first_chain_vertex == True 

1334 s = L.Toggle[s] 

1335 elif b is L.BOUNCING_D: 

1336 n._en_ex = s 

1337 if (s is t) ^ U: 

1338 n._2xing = True # see ._splits_xings 

1339 s = L.Toggle[s] 

1340 t = L.Toggle[t] 

1341 n = n._next # _, n = n._prev_next2 

1342 if n is f: 

1343 break # PYCHOK attr? 

1344 if k: 

1345 c._remove2(k) 

1346 

1347 def _special_cases(self, other): 

1348 # 3.5) Check special cases 

1349 U = self._Union 

1350 for c in self._clips: 

1351 if c._noXings(U): 

1352 c._noInters = True 

1353 if c._all_ON_ON: 

1354 c._identical = True 

1355 else: 

1356 p, _ = c._point2(False) 

1357 if p and (p._isinside(other) ^ U): 

1358 c._pushback = True 

1359 

1360 def _special_identicals(self, other): 

1361 # 3.5) Handle identicals 

1362 _u = _Clip._update_all 

1363 cds = dict((c._id, _u(c)) for c in other._identicals) 

1364 # assert len(cds) == len(other._identicals) 

1365 if cds: # PYCHOK no cover 

1366 for c in self._identicals: 

1367 c._update_all() 

1368 for v in c._intersections(): 

1369 d = cds.get(v._linked._clipid, None) 

1370 if d and d._ishole is c._ishole: 

1371 c._pushback = True 

1372 break # next c 

1373 

1374 @property_RO 

1375 def _2splits(self): 

1376 # Yield all intersections marked C{._2split} 

1377 for p in self._intersections(): 

1378 if p._2split: 

1379 # assert isinstance(p._2split, _Clip) 

1380 yield p 

1381 

1382 def _splits_xings(self, other): # MCCABE 15 

1383 # 5) Handle split pairs and 6) crossing candidates 

1384 

1385 def _2A_dup2(p, P): # PYCHOK unused 

1386 p1, p2 = p._prev_next2 

1387 ap = p1._2A(p, p2) 

1388 Pc = p._2split 

1389 # assert Pc in P._clips 

1390 # assert p in Pc 

1391 return ap, Pc._dup(p) 

1392 

1393 def _links2(ps, qs): # PYCHOK P unused? 

1394 # Yield each link as a 2-tuple(p, q) 

1395 id_qs = set(map(id, qs)) 

1396 if id_qs: 

1397 for p in ps: 

1398 q = p._linked 

1399 if q and id(q) in id_qs: 

1400 yield p, q 

1401 

1402 L = _L 

1403 E = L.ENTRY if self._Union else L.EXIT 

1404 X = L.Toggle[E] 

1405 for p, q in _links2(self._2splits, other._2splits): 

1406 ap, pp = _2A_dup2(p, self) 

1407 aq, qq = _2A_dup2(q, other) 

1408 if (ap * aq) > 0: # PYCHOK no cover 

1409 p._link(qq) # overwrites ... 

1410 q._link(pp) # ... p-q link 

1411 else: 

1412 pp._link(qq) 

1413 p._en_ex = q._en_ex = E 

1414 pp._en_ex = qq._en_ex = X 

1415 p._label = pp._label = \ 

1416 q._label = qq._label = L.CROSSING 

1417 

1418 for p, q in _links2(self._2xings, other._2xings): 

1419 p._label = q._label = L.CROSSING 

1420 

1421 @property_RO 

1422 def _2xings(self): 

1423 # Yield all intersections marked C{._2xing} 

1424 for p in self._intersections(): 

1425 if p._2xing: 

1426 yield p 

1427 

1428 

1429class _CompositeGH(_CompositeBase): 

1430 '''(INTERNAL) A list of clips representing a I{composite} 

1431 of L{LatLonGH} points, duplicates and intersections 

1432 with an other I{composite}. 

1433 ''' 

1434 _LL = LatLonGH 

1435 _xtend = False 

1436 

1437 def __init__(self, lls, raiser=False, xtend=False, **name_kind_eps): 

1438 # New L{_CompositeGH}. 

1439 if xtend: 

1440 self._xtend = True 

1441 elif raiser: 

1442 self._raiser = True 

1443 _CompositeBase.__init__(self, lls, **name_kind_eps) 

1444 

1445 def _clip(self, corners, s_entry, c_entry, Clas=None, 

1446 **closed_inull_raiser_xtend_eps): 

1447 # Clip this polygon with another one, C{corners}. 

1448 

1449 # Core of Greiner/Hormann's algorithm, enhanced U{Correia's 

1450 # <https://GitHub.com/helderco/univ-polyclip>} implementation*** 

1451 # and extended to optionally handle so-called "degenerate cases" 

1452 S = self 

1453 C = self._class(corners, closed_inull_raiser_xtend_eps, 

1454 raiser=False, xtend=False) 

1455 bt = C._bottom_top_eps2 

1456 lr = C._left_right_eps2 

1457 # 1. find intersections 

1458 for s1, s2, Sc in S._edges3(**closed_inull_raiser_xtend_eps): 

1459 if not (_outside(s1.x, s2.x, *lr) or 

1460 _outside(s1.y, s2.y, *bt)): 

1461 e = _EdgeGH(s1, s2, **closed_inull_raiser_xtend_eps) 

1462 if e._hypot2 > EPS2: # non-null edge 

1463 for c1, c2, Cc in C._edges3(**closed_inull_raiser_xtend_eps): 

1464 for y, x, sa, ca in e._intersect4(c1, c2): 

1465 s = Sc._insert(y, x, s1, s2, sa) 

1466 c = Cc._insert(y, x, c1, c2, ca) 

1467 s._link(c) 

1468 

1469 # 2. identify entry/exit intersections 

1470 if S._first: 

1471 s_entry ^= S._first._isinside(C, *bt) 

1472 for v in S._intersections(): 

1473 v._entry = s_entry = not s_entry 

1474 

1475 if C._first: 

1476 c_entry ^= C._first._isinside(S) 

1477 for v in C._intersections(): 

1478 v._entry = c_entry = not c_entry 

1479 

1480 # 3. yield the result(s) 

1481 return S._results(S._presults(), Clas, **closed_inull_raiser_xtend_eps) 

1482 

1483 @property_RO 

1484 def _first(self): 

1485 # Get the very first vertex of the first clip 

1486 for v in self: 

1487 return v 

1488 return None # PYCHOK no cover 

1489 

1490 def _kwds(self, op, **more): 

1491 # Get the kwds C{dict}. 

1492 return _CompositeBase._kwds(self, op, xtend=self.xtend, **more) 

1493 

1494 def _presults(self): 

1495 # Yield the unchecked intersection(s). 

1496 for c in self._clips: 

1497 for v in c._intersections(): 

1498 if not v._checked: 

1499 yield self._resultU(v) 

1500 

1501 def _resultU(self, v): 

1502 # Yield the result from an un-checked intersection. 

1503 while v and not v._checked: 

1504 v._check() 

1505 yield v 

1506 r = v 

1507 e = v._entry 

1508 while True: 

1509 v = v._next if e else v._prev 

1510 yield v 

1511 if v._linked: 

1512 break 

1513 if v is r: 

1514 raise ClipError(full_circle=v, clipid=v._clipid) 

1515 v = v._linked # switch 

1516 

1517 @property 

1518 def xtend(self): 

1519 '''Get the option to handle I{degenerate cases} (C{bool}). 

1520 ''' 

1521 return self._xtend 

1522 

1523 @xtend.setter # PYCHOK setter! 

1524 def xtend(self, xtend): 

1525 '''Set the option to handle I{degenerate cases} (C{bool}). 

1526 ''' 

1527 self._xtend = bool(xtend) 

1528 

1529 

1530class _EdgeFHP(object): 

1531 # An edge between two L{LatLonFHP} points. 

1532 

1533 X_INTERSECT = _Enum('Xi', 1) # C++ enum 

1534 X_OVERLAP = _Enum('Xo', 5) 

1535 P_INTERSECT = _Enum('Pi', 3) 

1536 P_OVERLAP = _Enum('Po', 7) 

1537 Ps = (P_INTERSECT, P_OVERLAP, X_OVERLAP) 

1538 Q_INTERSECT = _Enum('Qi', 2) 

1539 Q_OVERLAP = _Enum('Qo', 6) 

1540 Qs = (Q_INTERSECT, Q_OVERLAP, X_OVERLAP) 

1541 V_INTERSECT = _Enum('Vi', 4) 

1542 V_OVERLAP = _Enum('Vo', 8) 

1543 Vs = (V_INTERSECT, V_OVERLAP) 

1544 

1545 def __init__(self, p1, p2, **unused): 

1546 # New edge between points C{p1} and C{p2}, each a L{LatLonFHP}. 

1547 self._p1_p2 = p1, p2 

1548 self._dp = dp = p2 - p1 

1549 self._dp2 = dp * dp # dot product, hypot2 

1550 

1551 self._lr, \ 

1552 self._bt = _left_right_bottom_top_eps2(p1, p2) 

1553 

1554 def _intersect3(self, q1, q2): 

1555 # Yield intersection(s) Type or C{None} 

1556 if not (_outside(q1.x, q2.x, *self._lr) or 

1557 _outside(q1.y, q2.y, *self._bt)): 

1558 dq = q2 - q1 

1559 dq2 = dq * dq # dot product, hypot2 

1560 if dq2 > EPS2: # like ._clip 

1561 T, E = None, _EdgeFHP # self.__class__ 

1562 p1, p2 = self._p1_p2 

1563 ap1 = p1._2A(q1, q2) 

1564 ap2_1 = p2._2A(q1, q2) - ap1 

1565 if fabs(ap2_1) > _0_EPS: # non-parallel edges 

1566 aq1 = q1._2A(p1, p2) 

1567 aq2_1 = q2._2A(p1, p2) - aq1 

1568 if fabs(aq2_1) > _0_EPS: 

1569 # compute and classify alpha and beta 

1570 a, a_0, a_0_1, _ = _alpha4(-ap1 / ap2_1) 

1571 b, b_0, b_0_1, _ = _alpha4(-aq1 / aq2_1) 

1572 # distinguish intersection types 

1573 T = E.X_INTERSECT if a_0_1 and b_0_1 else ( 

1574 E.P_INTERSECT if a_0_1 and b_0 else ( 

1575 E.Q_INTERSECT if a_0 and b_0_1 else ( 

1576 E.V_INTERSECT if a_0 and b_0 else None))) 

1577 

1578 elif fabs(ap1) < _0_EPS: # parallel or colinear edges 

1579 dp = self._dp 

1580 d1 = q1 - p1 

1581 # compute and classify alpha and beta 

1582 a, a_0, a_0_1, _a_0_1 = _alpha4((d1 * dp) / self._dp2) 

1583 b, b_0, b_0_1, _b_0_1 = _alpha4((d1 * dq) / (-dq2)) 

1584 # distinguish overlap type 

1585 T = E.X_OVERLAP if a_0_1 and b_0_1 else ( 

1586 E.P_OVERLAP if a_0_1 and _b_0_1 else ( 

1587 E.Q_OVERLAP if _a_0_1 and b_0_1 else ( 

1588 E.V_OVERLAP if a_0 and b_0 else None))) 

1589 

1590 if T: 

1591 if T is E.X_INTERSECT: 

1592 v = p1 + a * self._dp 

1593 yield T, (v, p1, p2, a), (v, q1, q2, b) 

1594 elif T in E.Vs: 

1595 yield T, (p1,), (q1,) 

1596 else: 

1597 if T in E.Qs: 

1598 yield T, (p1,), (p1, q1, q2, b) 

1599 if T in E.Ps: 

1600 yield T, (q1, p1, p2, a), (q1,) 

1601 

1602 

1603class _EdgeGH(object): 

1604 # An edge between two L{LatLonGH} points. 

1605 

1606 _raiser = False 

1607 _xtend = False 

1608 

1609 def __init__(self, s1, s2, raiser=False, xtend=False, **unused): 

1610 # New edge between points C{s1} and C{s2}, each a L{LatLonGH}. 

1611 self._s1, self._s2 = s1, s2 

1612 self._x_sx_y_sy = (s1.x, s2.x - s1.x, 

1613 s1.y, s2.y - s1.y) 

1614 self._lr, \ 

1615 self._bt = _left_right_bottom_top_eps2(s1, s2) 

1616 

1617 if xtend: 

1618 self._xtend = True 

1619 elif raiser: 

1620 self._raiser = True 

1621 

1622 def _alpha2(self, x, y, dx, dy): 

1623 # Return C{(alpha)}, see .points.nearestOn5 

1624 a = (y * dy + x * dx) / self._hypot2 

1625 d = (y * dx - x * dy) / self._hypot0 

1626 return a, fabs(d) 

1627 

1628 def _Error(self, n, *args, **kwds): # PYCHOK no cover 

1629 t = unstr(_EdgeGH.__name__, self._s1, self._s2) 

1630 t = _DOT_(t, _EdgeGH._intersect4.__name__) 

1631 t = unstr(t, *args, **kwds) 

1632 return ClipError(_case_, n, txt=t) 

1633 

1634 @Property_RO 

1635 def _hypot0(self): 

1636 _, sx, _, sy = self._x_sx_y_sy 

1637 return hypot(sx, sy) * _0_EPS 

1638 

1639 @Property_RO 

1640 def _hypot2(self): 

1641 _, sx, _, sy = self._x_sx_y_sy 

1642 return hypot2(sx, sy) 

1643 

1644 def _intersect4(self, c1, c2, parallel=True): # MCCABE 14 

1645 # Yield the intersection(s) of this and another edge. 

1646 

1647 # @return: None, 1 or 2 intersections, each a 4-Tuple 

1648 # (y, x, s_alpha, c_alpha) with intersection 

1649 # coordinates x and y and both alphas. 

1650 

1651 # @raise ClipError: Intersection unhandled. 

1652 

1653 # @see: U{Intersection point of two line segments 

1654 # <http://PaulBourke.net/geometry/pointlineplane/>}. 

1655 c1_x, c1_y = c1.x, c1.y 

1656 if not (_outside(c1_x, c2.x, *self._lr) or 

1657 _outside(c1_y, c2.y, *self._bt)): 

1658 x, sx, \ 

1659 y, sy = self._x_sx_y_sy 

1660 

1661 cx = c2.x - c1_x 

1662 cy = c2.y - c1_y 

1663 d = cy * sx - cx * sy 

1664 

1665 if fabs(d) > _0_EPS: # non-parallel edges 

1666 dx = x - c1_x 

1667 dy = y - c1_y 

1668 ca = (sx * dy - sy * dx) / d 

1669 if _0_EPS < ca < _EPS_1 or (self._xtend and 

1670 _EPS_0 < ca < _1_EPS): 

1671 sa = (cx * dy - cy * dx) / d 

1672 if _0_EPS < sa < _EPS_1 or (self._xtend and 

1673 _EPS_0 < sa < _1_EPS): 

1674 yield (y + sa * sy), (x + sa * sx), sa, ca 

1675 

1676 # unhandled, "degenerate" cases 1, 2 or 3 

1677 elif self._raiser and not (sa < _EPS_0 or sa > _1_EPS): # PYCHOK no cover 

1678 raise self._Error(1, c1, c2, sa=sa) # intersection at s1 or s2 

1679 

1680 elif self._raiser and not (ca < _EPS_0 or ca > _1_EPS): # PYCHOK no cover 

1681 # intersection at c1 or c2 or at c1 or c2 and s1 or s2 

1682 sa = (cx * dy - cy * dx) / d 

1683 e = 2 if sa < _EPS_0 or sa > _1_EPS else 3 

1684 raise self._Error(e, c1, c2, ca=ca) 

1685 

1686 elif parallel and (sx or sy) and (cx or cy): # PYCHOK no cover 

1687 # non-null, parallel or colinear edges 

1688 sa1, d1 = self._alpha2(c1_x - x, c1_y - y, sx, sy) 

1689 sa2, d2 = self._alpha2(c2.x - x, c2.y - y, sx, sy) 

1690 if max(d1, d2) < _0_EPS: 

1691 if self._xtend and not _outside(sa1, sa2, _EPS_0, _1_EPS): 

1692 if sa1 > sa2: # anti-parallel 

1693 sa1, sa2 = sa2, sa1 

1694 ca1, ca2 = _1_0, _0_0 

1695 else: # parallel 

1696 ca1, ca2 = _0_0, _1_0 

1697 ca = fabs((sx / cx) if cx else (sy / cy)) 

1698 # = hypot(sx, sy) / hypot(cx, cy) 

1699 if sa1 < 0: # s1 is between c1 and c2 

1700 ca *= ca1 + sa1 

1701 yield y, x, ca1, _alpha1(ca) 

1702 else: # c1 is between s1 and s2 

1703 yield (y + sa1 * sy), (x + sa1 * sx), sa1, ca1 

1704 if sa2 > 1: # s2 is between c1 and c2 

1705 ca *= sa2 - _1_0 

1706 yield (y + sy), (x + sx), ca2, _alpha1(ca2 - ca) 

1707 else: # c2 is between s1 and s2 

1708 yield (y + sa2 * sy), (x + sa2 * sx), sa2, ca2 

1709 elif self._raiser and not _outside(sa1, sa2, _0_0, _1_EPS): 

1710 raise self._Error(4, c1, c2, d1=d1, d2=d2) 

1711 

1712 

1713class _BooleanBase(object): 

1714 # Shared C{Boolean[FHP|GH]} methods. 

1715 

1716 def __add__(self, other): 

1717 '''Sum: C{this + other} clips. 

1718 ''' 

1719 return self._sum(_other(self, other), self.__add__) # PYCHOK OK 

1720 

1721 def __and__(self, other): 

1722 '''Intersection: C{this & other}. 

1723 ''' 

1724 return self._boolean(other, False, False, self.__and__) # PYCHOK OK 

1725 

1726 def __iadd__(self, other): 

1727 '''In-place sum: C{this += other} clips. 

1728 ''' 

1729 return self._inplace(self.__add__(other)) 

1730 

1731 def __iand__(self, other): 

1732 '''In-place intersection: C{this &= other}. 

1733 ''' 

1734 return self._inplace(self.__and__(other)) 

1735 

1736 def __ior__(self, other): 

1737 '''In-place union: C{this |= other}. 

1738 ''' 

1739 return self._inplace(self.__or__(other)) 

1740 

1741 def __or__(self, other): 

1742 '''Union: C{this | other}. 

1743 ''' 

1744 return self._boolean(other, True, True, self.__or__) # PYCHOK OK 

1745 

1746 def __radd__(self, other): 

1747 '''Reverse sum: C{other + this} clips. 

1748 ''' 

1749 return _other(self, other)._sum(self, self.__radd__) 

1750 

1751 def __rand__(self, other): 

1752 '''Reverse intersection: C{other & this} 

1753 ''' 

1754 return _other(self, other).__and__(self) 

1755 

1756 def __ror__(self, other): 

1757 '''Reverse union: C{other | this} 

1758 ''' 

1759 return _other(self, other).__or__(self) 

1760 

1761 def _boolean4(self, other, op): 

1762 # Set up a new C{Boolean[FHP|GH]}. 

1763 C = self.__class__ 

1764 kwds = C._kwds(self, op) 

1765 a = C(self, **kwds) 

1766 b = _other(self, other) 

1767 return a, b, C, kwds 

1768 

1769 def _inplace(self, r): 

1770 # Replace this with a L{Boolean*} result. 

1771 self._clips, r._clips = r._clips, None 

1772# if self._raiser != r._raiser: 

1773# self._raiser = r._raiser 

1774# if self._xtend != r._xtend: 

1775# self._xtend = r._xtend 

1776# if self._eps != r._eps: 

1777# self._eps = r._eps 

1778 return self 

1779 

1780 

1781class BooleanFHP(_CompositeFHP, _BooleanBase): 

1782 '''I{Composite} class providing I{boolean} operations between two 

1783 I{composites} using U{Forster-Hormann-Popa<https://www.ScienceDirect.com/ 

1784 science/article/pii/S259014861930007X>}'s C++ implementation, transcoded 

1785 to pure Python. 

1786 

1787 The supported operations between (composite) polygon A and B are: 

1788 

1789 - C = A & B or A &= B, intersection of A and B 

1790 

1791 - C = A + B or A += B, sum of A and B clips 

1792 

1793 - C = A | B or A |= B, union of A and B 

1794 

1795 - A == B or A != B, equivalent A and B clips 

1796 

1797 - A.isequalTo(B, eps), equivalent within tolerance 

1798 

1799 @see: Methods C{__eq__} and C{isequalTo}, function L{clipFHP4} 

1800 and class L{BooleanGH}. 

1801 ''' 

1802 _kind = _boolean_ 

1803 

1804 def __init__(self, lls, raiser=False, eps=EPS, name=NN): 

1805 '''New L{BooleanFHP} operand for I{boolean} operation. 

1806 

1807 @arg lls: The polygon points and clips (iterable of L{LatLonFHP}s, 

1808 L{ClipFHP4Tuple}s or other C{LatLon}s). 

1809 @kwarg raiser: If C{True}, throw L{ClipError} exceptions (C{bool}). 

1810 @kwarg esp: Tolerance for eliminating null edges (C{degrees}, same 

1811 units as the B{C{lls}} coordinates). 

1812 @kwarg name: Optional name (C{str}). 

1813 ''' 

1814 _CompositeFHP.__init__(self, lls, raiser=raiser, 

1815 eps=eps, name=name) 

1816 

1817 def __isub__(self, other): 

1818 '''Not implemented.''' 

1819 return _NotImplemented(self, other) 

1820 

1821 def __rsub__(self, other): 

1822 '''Not implemented.''' 

1823 return _NotImplemented(self, other) 

1824 

1825 def __sub__(self, other): 

1826 '''Not implemented.''' 

1827 return _NotImplemented(self, other) 

1828 

1829 def _boolean(self, other, Union, unused, op): 

1830 # One C{BooleanFHP} operation. 

1831 p, q, C, kwds = self._boolean4(other, op) 

1832 r = p._clip(q, Union=Union, **kwds) 

1833 return C(r, **kwds) 

1834 

1835 

1836class BooleanGH(_CompositeGH, _BooleanBase): 

1837 '''I{Composite} class providing I{boolean} operations between two 

1838 I{composites} using the U{Greiner-Hormann<http://www.Inf.USI.CH/ 

1839 hormann/papers/Greiner.1998.ECO.pdf>} algorithm and U{Correia 

1840 <https://GitHub.com/helderco/univ-polyclip>}'s implementation, 

1841 modified and extended. 

1842 

1843 The supported operations between (composite) polygon A and B are: 

1844 

1845 - C = A - B or A -= B, difference A less B 

1846 

1847 - C = B - A or B -= A, difference B less B 

1848 

1849 - C = A & B or A &= B, intersection of A and B 

1850 

1851 - C = A + B or A += B, sum of A and B clips 

1852 

1853 - C = A | B or A |= B, union of A and B 

1854 

1855 - A == B or A != B, equivalent A and B clips 

1856 

1857 - A.isequalTo(B, eps), equivalent within tolerance 

1858 

1859 @note: To handle I{degenerate cases} like C{point-edge} and 

1860 C{point-point} intersections, use class L{BooleanFHP}. 

1861 

1862 @see: Methods C{__eq__} and C{isequalTo}, function L{clipGH4} 

1863 and class L{BooleanFHP}. 

1864 ''' 

1865 _kind = _boolean_ 

1866 

1867 def __init__(self, lls, raiser=True, xtend=False, eps=EPS, name=NN): 

1868 '''New L{BooleanFHP} operand for I{boolean} operation. 

1869 

1870 @arg lls: The polygon points and clips (iterable of L{LatLonGH}s, 

1871 L{ClipGH4Tuple}s or other C{LatLon}s). 

1872 @kwarg raiser: If C{True}, throw L{ClipError} exceptions (C{bool}). 

1873 @kwarg xtend: If C{True}, extend edges of I{degenerate cases}, an 

1874 attempt to handle the latter (C{bool}). 

1875 @kwarg esp: Tolerance for eliminating null edges (C{degrees}, same 

1876 units as the B{C{lls}} coordinates). 

1877 @kwarg name: Optional name (C{str}). 

1878 ''' 

1879 _CompositeGH.__init__(self, lls, raiser=raiser, xtend=xtend, 

1880 eps=eps, name=name) 

1881 

1882 def _boolean(self, other, s_entry, c_entry, op): 

1883 # One C{BooleanGH} operation. 

1884 s, c, C, kwds = self._boolean4(other, op) 

1885 r = s._clip(c, s_entry, c_entry, **kwds) 

1886 return C(r, **kwds) 

1887 

1888 def __isub__(self, other): 

1889 '''In-place difference: C{this -= other}. 

1890 ''' 

1891 return self._inplace(self.__sub__(other)) 

1892 

1893 def __rsub__(self, other): 

1894 ''' Reverse difference: C{other - this} 

1895 ''' 

1896 return _other(self, other).__sub__(self) 

1897 

1898 def __sub__(self, other): 

1899 '''Difference: C{this - other}. 

1900 ''' 

1901 return self._boolean(other, True, False, self.__sub__) 

1902 

1903 

1904def _alpha1(alpha): 

1905 # Return C{alpha} in C{[0..1]} range 

1906 if _EPS_0 < alpha < _1_EPS: 

1907 return max(_0_0, min(alpha, _1_0)) 

1908 t = _not_(Fmt.SQUARE(_ELLIPSIS_(0, 1))) 

1909 raise ClipError(_alpha_, alpha, txt=t) 

1910 

1911 

1912def _alpha4(a): 

1913 # Return 4-tuple (alpha, -EPS < alpha < EPS, 

1914 # 0 < alpha < 1, 

1915 # not 0 < alpha < 1) 

1916 return (a, False, True, False) if _0_EPS < a < _EPS_1 else ( 

1917 (a, False, False, True) if _0_EPS < fabs(a) else 

1918 (a, True, False, False)) 

1919 

1920 

1921def _Cps(Cp, composites_points, where): 

1922 # Yield composites and points as a C{Cp} composite. 

1923 try: 

1924 kwds = dict(kind=_points_, name=where.__name__) 

1925 for cp in composites_points: 

1926 yield cp if isBoolean(cp) else Cp(cp, **kwds) 

1927 except (AttributeError, ClipError, TypeError, ValueError) as x: 

1928 raise _ValueError(points=cp, cause=x) 

1929 

1930 

1931def _eps0(eps): 

1932 # Adjust C{eps} or C{None}. 

1933 return eps if eps and eps > EPS else 0 

1934 

1935 

1936def isBoolean(obj): 

1937 '''Check for C{Boolean} composites. 

1938 

1939 @arg obj: The object (any C{type}). 

1940 

1941 @return: C{True} if B{C{obj}} is L{BooleanFHP}, 

1942 L{BooleanGH} oe some other composite, 

1943 C{False} otherwise. 

1944 ''' 

1945 return isinstance(obj, _CompositeBase) 

1946 

1947 

1948def _left_right_bottom_top_eps2(p1, p2): 

1949 '''(INTERNAL) Return 2-tuple C{(left, right), (bottom, top)}, oversized. 

1950 ''' 

1951 return (_min_max_eps2(p1.x, p2.x), 

1952 _min_max_eps2(p1.y, p2.y)) 

1953 

1954 

1955def _low_high_eps2(lo, hi, eps): 

1956 '''(INTERNAL) Return 2-tuple C{(lo, hi)}, oversized. 

1957 ''' 

1958 lo *= (_1_0 + eps) if lo < 0 else (_1_0 - eps) 

1959 hi *= (_1_0 - eps) if hi < 0 else (_1_0 + eps) 

1960 return (lo or -eps), (hi or eps) 

1961 

1962 

1963def _min_max_eps2(*xs): 

1964 '''(INTERNAL) Return 2-tuple C{(min, max)}, oversized. 

1965 ''' 

1966 lo, hi = min(xs), max(xs) 

1967 lo *= _1_EPS if lo < 0 else _EPS_1 

1968 hi *= _EPS_1 if hi < 0 else _1_EPS 

1969 return (lo or _EPS_0), (hi or _0_EPS) 

1970 

1971 

1972def _other(this, other): 

1973 '''(INTERNAL) Check for compatible C{type}s. 

1974 ''' 

1975 C = this.__class__ 

1976 if isinstance(other, C): 

1977 return other 

1978 raise _IsnotError(C.__name__, other=other) 

1979 

1980 

1981def _outside(x1, x2, lo, hi): 

1982 '''(INTERNAL) Is C{(x1, x2)} outside C{(lo, hi)}? 

1983 ''' 

1984 return max(x1, x2) < lo or min(x1, x2) > hi 

1985 

1986 

1987__all__ += _ALL_DOCS(_BooleanBase, _Clip, 

1988 _CompositeBase, _CompositeFHP, _CompositeGH, 

1989 _LatLonBool) 

1990 

1991# **) MIT License 

1992# 

1993# Copyright (C) 2018-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1994# 

1995# Permission is hereby granted, free of charge, to any person obtaining a 

1996# copy of this software and associated documentation files (the "Software"), 

1997# to deal in the Software without restriction, including without limitation 

1998# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1999# and/or sell copies of the Software, and to permit persons to whom the 

2000# Software is furnished to do so, subject to the following conditions: 

2001# 

2002# The above copyright notice and this permission notice shall be included 

2003# in all copies or substantial portions of the Software. 

2004# 

2005# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

2006# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

2007# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

2008# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

2009# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

2010# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

2011# OTHER DEALINGS IN THE SOFTWARE. 

2012 

2013# ***) GNU GPL 3 

2014# 

2015# Copyright (C) 2011-2012 Helder Correia <Helder.MC@Gmail.com> 

2016# 

2017# This program is free software: you can redistribute it and/or 

2018# modify it under the terms of the GNU General Public License as 

2019# published by the Free Software Foundation, either version 3 of 

2020# the License, or any later version. 

2021# 

2022# This program is distributed in the hope that it will be useful, 

2023# but WITHOUT ANY WARRANTY; without even the implied warranty of 

2024# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 

2025# GNU General Public License for more details. 

2026# 

2027# You should have received a copy of the GNU General Public License 

2028# along with this program. If not, see <http://www.GNU.org/licenses/>. 

2029# 

2030# You should have received the README file along with this program. 

2031# If not, see <https://GitHub.com/helderco/univ-polyclip>.