Coverage for pygeodesy/booleans.py: 95%

966 statements  

« prev     ^ index     » next       coverage.py v7.6.1, created at 2025-04-09 11:05 -0400

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, fdot_, hypot, hypot2 

25# from pygeodesy.fsums import fsum1 # _MODS 

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

27 _composite_, _DOT_, _duplicate_, _e_, \ 

28 _ELLIPSIS_, _few_, _height_, _lat_, _LatLon_, \ 

29 _lon_, _not_, _points_, _SPACE_, _too_, _X_, \ 

30 _x_, _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__ = '24.11.07' 

47 

48_0EPS = EPS # near-zero, positive 

49_EPS0 = -EPS # near-zero, negative 

50_1EPS = _1_0 + EPS # near-one, over 

51_EPS1 = _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_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, wrap=False, **name): 

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

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

129 other C{LatLon} instance. 

130 

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

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

133 @kwarg lon: Longitude (C{scalar}), required B{C{lat_ll}} is scalar, 

134 ignored otherwise. 

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

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

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

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

139 ''' 

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

141 

142 if lon is None: 

143 y, x = lat_ll.lat, lat_ll.lon 

144 h = _xattr(lat_ll, height=h) 

145 c = _xattr(lat_ll, clipid=clipid) 

146 else: 

147 y, x, c = lat_ll, lon, clipid 

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

149 # don't duplicate defaults 

150 if self._height != h: 

151 self._height = h 

152 if self._clipid != c: 

153 self._clipid = c 

154 if name: 

155 self.name = name 

156 

157 def __abs__(self): 

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

159 

160 def __eq__(self, other): 

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

162 other.x == self.x and 

163 other.y == self.y) 

164 

165 def __ne__(self, other): # required for Python 2 # PYCHOK no cover 

166 return not self.__eq__(other) 

167 

168 def __repr__(self): 

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

170 ''' 

171 if self._prev or self._next: 

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

173 t = _SPACE_(self, Fmt.ANGLE(t)) 

174 else: 

175 t = str(self) 

176 return t 

177 

178 def __str__(self): 

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

180 ''' 

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

182 if self._height: 

183 X = _X_ if self.isintersection else NN 

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

185 if self._clipid: 

186 t += (_clipid_, self._clipid), 

187 if self._alpha is not None: 

188 t += (_alpha_, self._alpha), 

189# if self._dupof: # recursion risk 

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

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

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

193 if self._linked: 

194 k = _DOT_ if self._checked else _BANG_ 

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

196 return NN(self.name, t) 

197 

198 def __sub__(self, other): 

199 _other(self, other) 

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

201 self.x - other.x) 

202 

203 def _2A(self, p2, p3): 

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

205 x, y = self.x, self.y 

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

207 (p3.x - x) * (p2.y - y) 

208 

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

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

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

212 a = fabs(self._2A(p2, p3)) 

213 return 0 if a < eps else a 

214 

215 @property_RO 

216 def clipid(self): 

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

218 ''' 

219 return self._clipid 

220 

221 def _equi(self, llb, eps): 

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

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

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

225 fabs(llb.lat - self.y) > eps) 

226 

227 @property_RO 

228 def height(self): 

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

230 ''' 

231 h = self._height 

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

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

234 

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

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

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

238 

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

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

241 

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

243 

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

245 ''' 

246 try: 

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

248 except (AttributeError, TypeError, ValueError): 

249 raise _IsnotError(_LatLon_, other=other) 

250 

251 @property_RO 

252 def isintersection(self): 

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

254 ''' 

255 return bool(self._linked) 

256 

257 @property_RO 

258 def ispoint(self): 

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

260 ''' 

261 return self._alpha is None 

262 

263 @property_RO 

264 def lat(self): 

265 '''Get the latitude (C{scalar}). 

266 ''' 

267 return self.y 

268 

269 @property_RO 

270 def latlon(self): 

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

272 ''' 

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

274 

275 def _link(self, other): 

276 # Make this and an other point neighbors. 

277 # assert _other(self, other) 

278 self._linked = other 

279 other._linked = self 

280 

281 @property_RO 

282 def lon(self): 

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

284 ''' 

285 return self.x 

286 

287 def _toClas(self, Clas, clipid): 

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

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

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

291 

292 

293class LatLonFHP(_LatLonBool): 

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

295 ''' 

296 _en_ex = None 

297 _label = None 

298 _2split = None # or C{._Clip} 

299 _2xing = False 

300 

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

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

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

304 C{LatLon} instance. 

305 

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

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

308 

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

310 ''' 

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

312 

313 def __add__(self, other): 

314 _other(self, other) 

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

316 

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

318 _other(self, other) 

319 return fdot_(self.x, other.y, -self.y, other.x) 

320 

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

322 _other(self, other) 

323 return fdot_(self.x, other.x, self.y, other.y) 

324 

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

326 _xscalar(other=other) 

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

328 

329# def _edge2(self): 

330# # Return the start and end point of the 

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

332# n = p = self 

333# while p.isintersection: 

334# p = p._prev 

335# if p is self: 

336# break 

337# while n.isintersection: 

338# n = n._next 

339# if n is self: 

340# break 

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

342# return p, n 

343 

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

345 if self._label: 

346 t = NN(self._label, t) 

347 if self._en_ex: 

348 t = NN(t, self._en_ex) 

349 return t 

350 

351 @property_RO 

352 def _isduplicate(self): 

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

354 p = self._dupof 

355 return bool(p and self._linked 

356 and p is not self 

357 and p == self 

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

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

360 

361# @property_RO 

362# def _isduplicated(self): 

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

364# d, v = 0, self 

365# while v: 

366# if v._dupof is self: 

367# d += 1 

368# v = v._next 

369# if v is self: 

370# break 

371# return d 

372 

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

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

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

376 pii/S0925772101000128>}? 

377 

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

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

380 L{LatLonGH} or any C{LatLon}). 

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

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

383 

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

385 

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

387 article/pii/S0925772101000128>}. 

388 ''' 

389 class _Pseudo(object): 

390 # Pseudo-_CompositeBase._clips tuple 

391 

392 @property_RO 

393 def _clips(self): 

394 for cp in _Cps(_CompositeFHP, composites_points, 

395 LatLonFHP.isenclosedBy): # PYCHOK yield 

396 for c in cp._clips: 

397 yield c 

398 

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

400 

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

402 # Is this point inside a composite, excluding 

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

404 x, y, i = self.x, self.y, False 

405 for c in composite._clips: 

406 if c not in excludes: 

407 w = 0 

408 for p1, p2 in c._edges2(**wrap): 

409 # edge [p1,p2] must straddle y 

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

411 r = p2.x > x 

412 s = p2.y > p1.y 

413 if p1.x < x: 

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

415 else: 

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

417 if b: 

418 w += 1 if s else -1 

419 if isodd(w): 

420 i = not i 

421 return i 

422 

423 @property_RO 

424 def _prev_next2(self): 

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

426 p, n = self, self._next 

427 if self._isduplicate: # PYCHOK no cover 

428 p = self._dupof 

429 while p._isduplicate: 

430 p = p._dupof 

431 while n._isduplicate: 

432 n = n._next 

433 return p._prev, n 

434 

435 def _RPoracle(self, p1, p2, p3): 

436 # Relative Position oracle 

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

438 T = _RP.IS_Pm 

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

440 T = _RP.IS_Pp 

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

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

443 self._2A(p2, p3) > 0 else \ 

444 _RP.RIGHT # PYCHOK indent 

445 else: # right turn (or straight) 

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

447 self._2A(p2, p3) < 0 else \ 

448 _RP.LEFT # PYCHOK indent 

449 return T 

450 

451 

452class LatLonGH(_LatLonBool): 

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

454 ''' 

455 _entry = None # entry or exit iff intersection 

456 

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

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

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

460 C{LatLon} instance. 

461 

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

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

464 

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

466 ''' 

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

468 

469 def _check(self): 

470 # Check-mark this vertex and its link. 

471 self._checked = True 

472 k = self._linked 

473 if k and not k._checked: 

474 k._checked = True 

475 

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

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

478 (_e_ if self._entry else _x_)) 

479 

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

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

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

483 article/pii/S0925772101000128>}? 

484 

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

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

487 L{LatLonGH} or any C{LatLon}). 

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

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

490 

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

492 ''' 

493 class _Pseudo(object): 

494 # Pseudo-_CompositeBase._edges3 method 

495 

496 def _edges3(self, **kwds): 

497 for cp in _Cps(_CompositeGH, composites_points, 

498 LatLonGH.isenclosedBy): # PYCHOK yield 

499 for e in cp._edges3(**kwds): 

500 yield e 

501 

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

503 

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

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

506 

507 def _x(y, p1, p2): 

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

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

510 

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

512 # intersecting a ray emitted from this point to 

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

514 # inside, if I{even} outside. 

515 y, i = self.y, False 

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

517 x = self.x 

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

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

520 r = p2.x > x 

521 if p1.x < x: 

522 b = r and (_x(y, p1, p2) > x) 

523 else: 

524 b = r or (_x(y, p1, p2) > x) 

525 if b: 

526 i = not i 

527 return i 

528 

529 

530class _Clip(_Named): 

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

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

533 and intersections with other clips. 

534 ''' 

535 _composite = None 

536 _dups = 0 

537 _first = None 

538 _id = 0 

539 _identical = False 

540 _noInters = False 

541 _last = None 

542 _LL = None 

543 _len = 0 

544 _pushback = False 

545 

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

547 '''(INTERNAL) New C{_Clip}. 

548 ''' 

549 # assert isinstance(composite, _CompositeBase) 

550 if clipid in composite._clipids: 

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

552 self._composite = composite 

553 self._id = clipid 

554 self._LL = composite._LL 

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

556 

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

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

559 ''' 

560 for v in self: 

561 if v is point: # or ==? 

562 return True 

563 return False 

564 

565 def __eq__(self, other): 

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

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

568 the same order, possibly rotated? 

569 ''' 

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

571 

572 def __ge__(self, other): 

573 '''See method C{__lt__}. 

574 ''' 

575 return not self.__lt__(other) 

576 

577 def __gt__(self, other): 

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

579 located or stretched farther North or East? 

580 ''' 

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

582 

583 def __hash__(self): # PYCHOK no cover 

584 return hash(self._bltr4) 

585 

586 def __iter__(self): 

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

588 ''' 

589 v = f = self._first 

590 while v: 

591 yield v 

592 v = v._next 

593 if v is f: 

594 break 

595 

596 def __le__(self, other): 

597 '''See method C{__gt__}. 

598 ''' 

599 return not self.__gt__(other) 

600 

601 def __len__(self): 

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

603 intersections in this clip. 

604 ''' 

605 return self._len 

606 

607 def __lt__(self, other): 

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

609 located or stretched farther South or West? 

610 ''' 

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

612 

613 def __ne__(self, other): # required for Python 2 # PYCHOK no cover 

614 '''See method C{__eq__}. 

615 ''' 

616 return not self.__eq__(other) 

617 

618 _all = __iter__ 

619 

620 @property_RO 

621 def _all_ON_ON(self): 

622 # Check whether all vertices are ON_ON. 

623 L_ON_ON = _L.ON_ON 

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

625 

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

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

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

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

630 self._len += 1 

631 # assert v._clipid == self._id 

632 

633 v._next = n = self._first 

634 if n is None: # set ._first 

635 self._first = p = n = v 

636 else: # insert before ._first 

637 v._prev = p = n._prev 

638 p._next = n._prev = v 

639 return v 

640 

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

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

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

644# y, x, p = v.y, v.x, self._last 

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

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

647# if v._linked: 

648# p._linked = True # to force errors 

649# return p 

650 

651 @Property_RO 

652 def _bltr4(self): 

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

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

655 

656 def _bltr4eps(self, eps): 

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

658 if eps > 0: # > EPS 

659 yb, xl, yt, xr = self._bltr4 

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

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

662 t = yb, xl, yt, xr 

663 else: 

664 t = self._bltr4 

665 return t 

666 

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

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

669 p, f = self._last, self._first 

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

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

672 # un-close the clip 

673 f._prev = p = p._prev 

674 p._next = f 

675 self._len -= 1 

676# elif f and raiser: 

677# raise self._OpenClipError(p, f) 

678 if len(self) < 3: 

679 raise self._Error(_too_(_few_)) 

680 

681 def _dup(self, q): 

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

683 v = self._insert(q.y, q.x, q) 

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

685 v._dupof = q._dupof or q 

686 # assert v._prev is q 

687 # assert q._next is v 

688 return v 

689 

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

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

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

693 p1 = p = f = self._first 

694 while p: 

695 p2 = p = p._next 

696 if p.ispoint: 

697 if wrap and p is not f: 

698 p2 = _unrollon(p1, p) 

699 yield p1, p2 

700 p1 = p2 

701 if p is f: 

702 break 

703 

704 def _equi(self, clip, eps): 

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

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

707 r, f = len(self), self._first 

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

709 == clip._bltr4eps(eps): 

710 _equi = _LatLonBool._equi 

711 for v in clip: 

712 if _equi(f, v, eps): 

713 s, n = f, v 

714 for _ in range(r): 

715 s, n = s._next, n._next 

716 if not _equi(s, n, eps): 

717 break # next v 

718 else: # equivalent 

719 return True 

720 return False 

721 

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

723 # Build a C{ClipError} instance 

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

725 if self._dups: 

726 kwds.update(dups=self._dups) 

727 cp = self._composite 

728 if self._id: 

729 try: 

730 i = cp._clips.index(self) 

731 if i != self._id: 

732 kwds.update(clip=i) 

733 except ValueError: 

734 pass 

735 kwds[_clipid_] = self._id 

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

737 

738 def _index(self, clips, eps): 

739 # see _CompositeBase._equi 

740 for i, c in enumerate(clips): 

741 if c._equi(self, eps): 

742 return i 

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

744 

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

746 # insertVertex between points C{start} and 

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

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

749 n = start._next 

750 if end_alpha: 

751 end, alpha = end_alpha 

752 v._alpha = alpha 

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

754 # assert start is not end 

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

756 n = n._next 

757 v._next = n 

758 v._prev = p = n._prev 

759 p._next = n._prev = v 

760 self._len += 1 

761# _Clip._bltr4._update(self) 

762# _Clip._ishole._update(self) 

763 return v 

764 

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

766 # insert an intersection or make a point both 

767 if p1_p2_alpha: # intersection on edge 

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

769 else: # intersection at point 

770 v = q 

771 # assert not v._linked 

772 # assert v._alpha is None 

773 return v 

774 

775 def _intersections(self): 

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

777 for v in self: 

778 if v.isintersection: 

779 yield v 

780 

781 @Property_RO 

782 def _ishole(self): # PYCHOK no cover 

783 # Is this clip a hole inside its composite? 

784 v = self._first 

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

786 

787 @property_RO 

788 def _nodups(self): 

789 # Yield all non-duplicates. 

790 for v in self: 

791 if not v._dupof: 

792 yield v 

793 

794 def _noXings(self, Union): 

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

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

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

798 

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

800 # Return a C{CloseError} instance 

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

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

803 

804 def _point2(self, insert): 

805 # getNonIntersectionPoint and -Vertex 

806 if not (insert and self._noInters): 

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

808 return p, None 

809 for n in self._intersections(): 

810 p, _ = n._prev_next2 

811 k = p._linked 

812 if k: 

813 if n._linked not in k._prev_next2: 

814 # create a pseudo-point 

815 k = _0_5 * (p + n) 

816 if insert: 

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

818 r = k # to remove later 

819 else: # no ._prev, ._next 

820 k._clipid = n._clipid 

821 r = None 

822 return k, r 

823 return None, None 

824 

825 def _points(self, may_be=True): 

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

827 for v in self: 

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

829 yield v 

830 

831 def _remove2(self, v): 

832 # Remove vertex C{v}. 

833 # assert not v._isduplicated 

834 if len(self) > 1: 

835 p = v._prev 

836 p._next = n = v._next 

837 n._prev = p 

838 if self._first is v: 

839 self._first = n 

840 if self._last is v: 

841 self._last = p 

842 self._len -= 1 

843 else: 

844 n = self._last = \ 

845 p = self._first = None 

846 self._len = 0 

847 return p, n 

848 

849 def _update_all(self): # PYCHOK no cover 

850 # Zap the I{cached} properties. 

851 _Clip._bltr4._update( self) 

852 _Clip._ishole._update(self) 

853 return self # for _special_identicals 

854 

855 def _Xings(self): 

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

857 CROSSING = _L.CROSSING 

858 for v in self._intersections(): 

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

860 yield v 

861 

862 

863class _CompositeBase(_Named): 

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

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

866 ''' 

867 _clips = () # tuple of C{_Clips} 

868 _eps = EPS # null edges 

869 _kind = _corners_ 

870 _LL = _LatLonBool # shut up PyChecker 

871 _raiser = False 

872 _xtend = False 

873 

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

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

876 ''' 

877 n = _name__(name, _or_nameof=lls) 

878 if n: 

879 self.name = n 

880 if kind: 

881 self._kind = kind 

882 if self._eps < eps: 

883 self._eps = eps 

884 

885 c = _Clip(self) 

886 lp = None 

887 for ll in lls: 

888 ll = self._LL(ll) 

889 if lp is None: 

890 c._id = ll._clipid # keep clipid 

891 lp = c._append(ll) 

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

893 c._closed(self.raiser) 

894 c = _Clip(self, ll._clipid) 

895 lp = c._append(ll) 

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

897 lp = c._append(ll) 

898 else: 

899 c._dups += 1 

900 c._closed(self.raiser) 

901 

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

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

904 ''' 

905 for c in self._clips: 

906 if point in c: 

907 return True 

908 return False 

909 

910 def __eq__(self, other): 

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

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

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

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

915 possibly rotated. 

916 ''' 

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

918 

919 def __iter__(self): 

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

921 ''' 

922 for c in self._clips: 

923 for v in c: 

924 yield v 

925 

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

927 '''See method C{__eq__}. 

928 ''' 

929 return not self.__eq__(other) 

930 

931 def __len__(self): 

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

933 ''' 

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

935 

936 def __repr__(self): 

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

938 ''' 

939 c = len(self._clips) 

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

941 n = Fmt.SQUARE(len(self)) 

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

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

944 

945 def __str__(self): 

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

947 ''' 

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

949 

950 @property_RO 

951 def _bottom_top_eps2(self): 

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

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

954 max(v.y for v in self)) 

955 

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

957 # Return a new instance 

958 _g = kwds.get 

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

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

961 

962 @property_RO 

963 def _clipids(self): # PYCHOK no cover 

964 for c in self._clips: 

965 yield c._id 

966 

967 def clipids(self): 

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

969 ''' 

970 return tuple(self._clipids) 

971 

972# def _clipidups(self, other): 

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

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

975 

976 def _edges3(self, **raiser_wrap): 

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

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

979 for c in self._clips: 

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

981 yield p1, p2, c 

982 

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

984 # see function .points.isenclosedBy 

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

986 

987 @property 

988 def eps(self): 

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

990 ''' 

991 return self._eps 

992 

993 @eps.setter # PYCHOK setter! 

994 def eps(self, eps): 

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

996 ''' 

997 self._eps = eps 

998 

999 def _10eps(self, **eps_): 

1000 # Get eps for _LatLonBool._2Abs 

1001 e = _xkwds_get(eps_, eps=self._eps) 

1002 if e != EPS: 

1003 e *= _10EPS / EPS 

1004 else: 

1005 e = _10EPS 

1006 return e 

1007 

1008 def _equi(self, other, eps): 

1009 # Is this composite I{equivalent} to an B{C{other}} within 

1010 # the given, I{non-negative} tolerance B{C{eps}}? 

1011 cs, co = self._clips, other._clips 

1012 if cs and len(cs) == len(co): 

1013 if eps > 0: 

1014 _index = _Clip._index 

1015 else: 

1016 def _index(c, cs, unused): 

1017 return cs.index(c) 

1018 try: 

1019 cs = list(sorted(cs)) 

1020 for c in sorted(co): 

1021 cs.pop(_index(c, cs, eps)) 

1022 except ValueError: # from ._index 

1023 pass 

1024 return False if cs else True 

1025 else: # both null? 

1026 return False if cs or co else True 

1027 

1028 def _intersections(self): 

1029 # Yield all intersections. 

1030 for c in self._clips: 

1031 for v in c._intersections(): 

1032 yield v 

1033 

1034 def isequalTo(self, other, eps=None): 

1035 '''Is this boolean/composite equal to an B{C{other}} within 

1036 a given, I{non-negative} tolerance? 

1037 

1038 @arg other: The other boolean/composite (C{Boolean[FHP|GB]}). 

1039 @kwarg eps: Tolerance for equality (C{degrees} or C{None}). 

1040 

1041 @return: C{True} if equivalent, C{False} otherwise (C{bool}). 

1042 

1043 @raise TypeError: Invalid B{C{other}}. 

1044 

1045 @see: Method C{__eq__}. 

1046 ''' 

1047 if isinstance(other, _CompositeBase): 

1048 return self._equi(other, _eps0(eps)) 

1049 raise _IsnotError(_boolean_, _composite_, other=other) 

1050 

1051 def _kwds(self, op, **more): 

1052 # Get all keyword arguments as C{dict}. 

1053 kwds = dict(raiser=self.raiser, eps=self.eps, 

1054 name=self.name or op.__name__) 

1055 kwds.update(more) 

1056 return kwds 

1057 

1058 @property_RO 

1059 def _left_right_eps2(self): 

1060 # Get the left and right C{x} bounds, oversized. 

1061 return _min_max_eps2(min(v.x for v in self), 

1062 max(v.x for v in self)) 

1063 

1064 def _points(self, may_be=True): # PYCHOK no cover 

1065 # Yield all I{original} points, which may be intersections too. 

1066 for c in self._clips: 

1067 for v in c._points(may_be=may_be): 

1068 yield v 

1069 

1070 @property 

1071 def raiser(self): 

1072 '''Get the option to throw L{ClipError} exceptions (C{bool}). 

1073 ''' 

1074 return self._raiser 

1075 

1076 @raiser.setter # PYCHOK setter! 

1077 def raiser(self, throw): 

1078 '''Set the option to throw L{ClipError} exceptions (C{bool}). 

1079 ''' 

1080 self._raiser = bool(throw) 

1081 

1082 def _results(self, _presults, Clas, closed=False, inull=False, **eps): 

1083 # Yield the dedup'd results, as L{ClipFHP4Tuple}s 

1084 C = self._LL if Clas is None else Clas 

1085 e = self._10eps(**eps) 

1086 for clipid, ns in enumerate(_presults): 

1087 f = p = v = None 

1088 for n in ns: 

1089 if f is None: 

1090 yield n._toClas(C, clipid) 

1091 f = p = n 

1092 elif v is None: 

1093 v = n # got f, p, v 

1094 elif inull or p._2Abs(v, n, eps=e): 

1095 yield v._toClas(C, clipid) 

1096 p, v = v, n 

1097 else: # null, colinear, ... skipped 

1098 v = n 

1099 if v and (inull or p._2Abs(v, f, eps=e)): 

1100 yield v._toClas(C, clipid) 

1101 p = v 

1102 if f and p != f and closed: # close clip 

1103 yield f._toClas(C, clipid) 

1104 

1105 def _sum(self, other, op): 

1106 # Combine this and an C{other} composite 

1107 LL = self._LL 

1108 sp = self.copy(name=self.name or op.__name__) 

1109 sp._clips, sid = (), INT0 # new clips 

1110 for cp in (self, other): 

1111 for c in cp._clips: 

1112 _ap = _Clip(sp, sid)._append 

1113 for v in c._nodups: 

1114 _ap(LL(v.y, v.x, v.height, sid)) 

1115 sid += 1 

1116 return sp 

1117 

1118 def _sum1(self, _a_p, *args, **kwds): # in .karney, .points 

1119 # Sum the area or perimeter of all clips 

1120 return _MODS.fsums.fsum1((_a_p(c, *args, **kwds) for c in self._clips)) 

1121 

1122 def _sum2(self, LL, _a_p, *args, **kwds): # in .sphericalNvector, -Trigonometry 

1123 # Sum the area or perimeter of all clips 

1124 

1125 def _lls(clip): # convert clip to LLs 

1126 _LL = LL 

1127 for v in clip: 

1128 yield _LL(v.lat, v.lon) # datum=Sphere 

1129 

1130 return _MODS.fsums.fsum1((_a_p(_lls(c), *args, **kwds) for c in self._clips)) 

1131 

1132 def toLatLon(self, LatLon=None, closed=False, **LatLon_kwds): 

1133 '''Yield all (non-duplicate) points and intersections 

1134 as an instance of B{C{LatLon}}. 

1135 

1136 @kwarg LatLon: Class to use (C{LatLon}) or if C{None}, 

1137 L{LatLonFHP} or L{LatLonGH}. 

1138 @kwarg closed: If C{True}, close each clip (C{bool}). 

1139 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} 

1140 keyword arguments, ignore if 

1141 C{B{LatLon} is None}. 

1142 

1143 @raise TypeError: Invalid B{C{LatLon}}. 

1144 

1145 @note: For intersections, C{height} is an instance 

1146 of L{HeightX}, otherwise of L{Height}. 

1147 ''' 

1148 if LatLon is None: 

1149 LL, kwds = self._LL, {} 

1150 elif issubclassof(LatLon, _LatLonBool, LatLonBase): 

1151 LL, kwds = LatLon, LatLon_kwds 

1152 else: 

1153 raise _TypeError(LatLon=LatLon) 

1154 

1155 for c in self._clips: 

1156 lf, cid = None, c._id 

1157 for v in c._nodups: 

1158 ll = LL(v.y, v.x, **kwds) 

1159 ll._height = v.height 

1160 if ll._clipid != cid: 

1161 ll._clipid = cid 

1162 yield ll 

1163 if lf is None: 

1164 lf = ll 

1165 if closed and lf: 

1166 yield lf 

1167 

1168 

1169class _CompositeFHP(_CompositeBase): 

1170 '''(INTERNAL) A list of clips representing a I{composite} 

1171 of L{LatLonFHP} points, duplicates and intersections 

1172 with an other I{composite}. 

1173 ''' 

1174 _LL = LatLonFHP 

1175 _Union = False 

1176 

1177 def __init__(self, lls, raiser=False, **name_kind_eps): 

1178 # New L{_CompositeFHP}. 

1179 if raiser: 

1180 self._raiser = True 

1181 _CompositeBase.__init__(self, lls, **name_kind_eps) 

1182 

1183 def _classify(self): 

1184 # 2) Classify intersection chains. 

1185 L = _L 

1186 for v in self._intersections(): 

1187 n, b = v, v._label 

1188 if b in L.RIGHT_LEFT_ON: # next chain 

1189 while True: 

1190 n._label = None # _xkwds_pop(n.__dict__, _label=None) 

1191 n = n._next 

1192 if n is v or n._label is not L.ON_ON: # n._label and ... 

1193 break 

1194 a = L.LEFT_ON if n._label is L.ON_LEFT else L.RIGHT_ON 

1195 v._label = n._label = L.BOUNCING_D if a is b else L.CROSSING_D 

1196 

1197 # 3) Copy labels 

1198 for v in self._intersections(): 

1199 v._linked._label = v._label 

1200 

1201 def _clip(self, corners, Union=False, Clas=None, 

1202 **closed_inull_raiser_eps): 

1203 # Clip this composite with another one, C{corners}, 

1204 # using the Foster-Hormann-Popa's algorithm. 

1205 P = self 

1206 Q = self._class(corners, closed_inull_raiser_eps, 

1207 eps=P._eps, raiser=False) 

1208 if Union: 

1209 P._Union = Q._Union = True 

1210 

1211 bt = Q._bottom_top_eps2 

1212 lr = Q._left_right_eps2 

1213 # compute and insert intersections 

1214 for p1, p2, Pc in P._edges3(**closed_inull_raiser_eps): 

1215 if not (_outside(p1.x, p2.x, *lr) or 

1216 _outside(p1.y, p2.y, *bt)): 

1217 e = _EdgeFHP(p1, p2) 

1218 if e._dp2 > EPS2: # non-null edge 

1219 for q1, q2, Qc in Q._edges3(**closed_inull_raiser_eps): 

1220 for T, p, q in e._intersect3(q1, q2): 

1221 p = Pc._intersection(T, *p) 

1222 q = Qc._intersection(T, *q) 

1223 # assert not p._linked 

1224 # assert not q._linked 

1225 p._link(q) 

1226 

1227 # label and classify intersections 

1228 P._labelize() 

1229 P._classify() 

1230 

1231 # check for special cases 

1232 P._special_cases(Q) 

1233 Q._special_cases(P) 

1234 # handle identicals 

1235 P._special_identicals(Q) 

1236 

1237 # set Entry/Exit flags 

1238 P._set_entry_exits(Q) 

1239 Q._set_entry_exits(P) 

1240 

1241 # handle splits and crossings 

1242 P._splits_xings(Q) 

1243 

1244 # yield the results 

1245 return P._results(P._presults(Q), Clas, **closed_inull_raiser_eps) 

1246 

1247 @property_RO 

1248 def _identicals(self): 

1249 # Yield all clips marked C{._identical}. 

1250 for c in self._clips: 

1251 if c._identical: 

1252 yield c 

1253 

1254 def _labelize(self): 

1255 # 1) Intersections classification 

1256 for p in self._intersections(): 

1257 q = p._linked 

1258 # determine local configuration at this intersection 

1259 # and positions of Q- and Q+ relative to (P-, I, P+) 

1260 p1, p3 = p._prev_next2 

1261 q1, q3 = q._prev_next2 

1262 t = (q1._RPoracle(p1, p, p3), 

1263 q3._RPoracle(p1, p, p3)) 

1264 # check intersecting and overlapping cases 

1265 p._label = _RP2L.get(t, None) 

1266 

1267 def _presults(self, other): 

1268 # Yield the result clips, each as a generator 

1269 # of the L{_LatLonFHP}s in that clip 

1270 for cp in (self, other): 

1271 for c in cp._clips: 

1272 if c._pushback: 

1273 yield c._all() 

1274 for c in self._clips: 

1275 for X in c._Xings(): 

1276 yield self._resultX(X) 

1277 

1278 def _resultX(self, X): 

1279 # Yield the results from CROSSING C{X}. 

1280 L, U, v = _L, self._Union, X 

1281 while v: 

1282 v._checked = True 

1283 r = v # in P or Q 

1284 s = L.Toggle[v._en_ex] 

1285 e = (s is L.EXIT) ^ U 

1286 while True: 

1287 v = v._next if e else v._prev 

1288 yield v 

1289 v._checked = True 

1290 if v._en_ex is s or v is X: 

1291 break 

1292 if v is r: # full circle 

1293 raise ClipError(full_circle=v, clipid=v._clipid) 

1294 if v is not X: 

1295 v = v._linked 

1296 if v is X: 

1297 break 

1298 

1299 def _set_entry_exits(self, other): # MCCABE 14 

1300 # 4) Set entry/exit flags 

1301 L, U = _L, self._Union 

1302 for c in self._clips: 

1303 n, k = c._point2(True) 

1304 if n: 

1305 f = n 

1306 s = L.EXIT if n._isinside(other) else L.ENTRY 

1307 t = L.EXIT # first_chain_vertex = True 

1308 while True: 

1309 if n.isintersection: 

1310 b = n._label 

1311 if b is L.CROSSING: 

1312 n._en_ex = s 

1313 s = L.Toggle[s] 

1314 elif b is L.BOUNCING and ((s is L.EXIT) ^ U): 

1315 n._2split = c # see ._splits_xings 

1316 elif b is L.CROSSING_D: 

1317 n._en_ex = s 

1318 if (s is t) ^ U: 

1319 n._label = L.CROSSING 

1320 t = L.Toggle[t] 

1321 if t is L.EXIT: # first_chain_vertex == True 

1322 s = L.Toggle[s] 

1323 elif b is L.BOUNCING_D: 

1324 n._en_ex = s 

1325 if (s is t) ^ U: 

1326 n._2xing = True # see ._splits_xings 

1327 s = L.Toggle[s] 

1328 t = L.Toggle[t] 

1329 n = n._next # _, n = n._prev_next2 

1330 if n is f: 

1331 break # PYCHOK attr? 

1332 if k: 

1333 c._remove2(k) 

1334 

1335 def _special_cases(self, other): 

1336 # 3.5) Check special cases 

1337 U = self._Union 

1338 for c in self._clips: 

1339 if c._noXings(U): 

1340 c._noInters = True 

1341 if c._all_ON_ON: 

1342 c._identical = True 

1343 else: 

1344 p, _ = c._point2(False) 

1345 if p and (p._isinside(other) ^ U): 

1346 c._pushback = True 

1347 

1348 def _special_identicals(self, other): 

1349 # 3.5) Handle identicals 

1350 _u = _Clip._update_all 

1351 cds = dict((c._id, _u(c)) for c in other._identicals) 

1352 # assert len(cds) == len(other._identicals) 

1353 if cds: # PYCHOK no cover 

1354 for c in self._identicals: 

1355 c._update_all() 

1356 for v in c._intersections(): 

1357 d = cds.get(v._linked._clipid, None) 

1358 if d and d._ishole is c._ishole: 

1359 c._pushback = True 

1360 break # next c 

1361 

1362 @property_RO 

1363 def _2splits(self): 

1364 # Yield all intersections marked C{._2split} 

1365 for p in self._intersections(): 

1366 if p._2split: 

1367 # assert isinstance(p._2split, _Clip) 

1368 yield p 

1369 

1370 def _splits_xings(self, other): # MCCABE 15 

1371 # 5) Handle split pairs and 6) crossing candidates 

1372 

1373 def _2A_dup2(p, P): # PYCHOK unused 

1374 p1, p2 = p._prev_next2 

1375 ap = p1._2A(p, p2) 

1376 Pc = p._2split 

1377 # assert Pc in P._clips 

1378 # assert p in Pc 

1379 return ap, Pc._dup(p) 

1380 

1381 def _links2(ps, qs): # PYCHOK P unused? 

1382 # Yield each link as a 2-tuple(p, q) 

1383 id_qs = set(map(id, qs)) 

1384 if id_qs: 

1385 for p in ps: 

1386 q = p._linked 

1387 if q and id(q) in id_qs: 

1388 yield p, q 

1389 

1390 L = _L 

1391 E = L.ENTRY if self._Union else L.EXIT 

1392 X = L.Toggle[E] 

1393 for p, q in _links2(self._2splits, other._2splits): 

1394 ap, pp = _2A_dup2(p, self) 

1395 aq, qq = _2A_dup2(q, other) 

1396 if (ap * aq) > 0: # PYCHOK no cover 

1397 p._link(qq) # overwrites ... 

1398 q._link(pp) # ... p-q link 

1399 else: 

1400 pp._link(qq) 

1401 p._en_ex = q._en_ex = E 

1402 pp._en_ex = qq._en_ex = X 

1403 p._label = pp._label = \ 

1404 q._label = qq._label = L.CROSSING 

1405 

1406 for p, q in _links2(self._2xings, other._2xings): 

1407 p._label = q._label = L.CROSSING 

1408 

1409 @property_RO 

1410 def _2xings(self): 

1411 # Yield all intersections marked C{._2xing} 

1412 for p in self._intersections(): 

1413 if p._2xing: 

1414 yield p 

1415 

1416 

1417class _CompositeGH(_CompositeBase): 

1418 '''(INTERNAL) A list of clips representing a I{composite} 

1419 of L{LatLonGH} points, duplicates and intersections 

1420 with an other I{composite}. 

1421 ''' 

1422 _LL = LatLonGH 

1423 _xtend = False 

1424 

1425 def __init__(self, lls, raiser=False, xtend=False, **name_kind_eps): 

1426 # New L{_CompositeGH}. 

1427 if xtend: 

1428 self._xtend = True 

1429 elif raiser: 

1430 self._raiser = True 

1431 _CompositeBase.__init__(self, lls, **name_kind_eps) 

1432 

1433 def _clip(self, corners, s_entry, c_entry, Clas=None, 

1434 **closed_inull_raiser_xtend_eps): 

1435 # Clip this polygon with another one, C{corners}. 

1436 

1437 # Core of Greiner/Hormann's algorithm, enhanced U{Correia's 

1438 # <https://GitHub.com/helderco/univ-polyclip>} implementation*** 

1439 # and extended to optionally handle so-called "degenerate cases" 

1440 S = self 

1441 C = self._class(corners, closed_inull_raiser_xtend_eps, 

1442 raiser=False, xtend=False) 

1443 bt = C._bottom_top_eps2 

1444 lr = C._left_right_eps2 

1445 

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) > _0EPS: # non-parallel edges 

1555 aq1 = q1._2A(p1, p2) 

1556 aq2_1 = q2._2A(p1, p2) - aq1 

1557 if fabs(aq2_1) > _0EPS: 

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) < _0EPS: # 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 = fdot_(y, dy, x, dx) / self._hypot2 

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

1615 return a, fabs(d) 

1616 

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

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

1619 unstr(_EdgeGH._intersect4, *args, **kwds)) 

1620 return ClipError(_case_, n, txt=t) 

1621 

1622 @Property_RO 

1623 def _hypot0(self): 

1624 _, sx, _, sy = self._x_sx_y_sy 

1625 return hypot(sx, sy) * _0EPS 

1626 

1627 @Property_RO 

1628 def _hypot2(self): 

1629 _, sx, _, sy = self._x_sx_y_sy 

1630 return hypot2(sx, sy) 

1631 

1632 def _intersect4(self, c1, c2, parallel=True): # MCCABE 14 

1633 # Yield the intersection(s) of this and another edge. 

1634 

1635 # @return: None, 1 or 2 intersections, each a 4-Tuple 

1636 # (y, x, s_alpha, c_alpha) with intersection 

1637 # coordinates x and y and both alphas. 

1638 

1639 # @raise ClipError: Intersection unhandled. 

1640 

1641 # @see: U{Intersection point of two line segments 

1642 # <http://PaulBourke.net/geometry/pointlineplane/>}. 

1643 c1_x, c1_y = c1.x, c1.y 

1644 if not (_outside(c1_x, c2.x, *self._lr) or 

1645 _outside(c1_y, c2.y, *self._bt)): 

1646 x, sx, \ 

1647 y, sy = self._x_sx_y_sy 

1648 

1649 cx = c2.x - c1_x 

1650 cy = c2.y - c1_y 

1651 d = cy * sx - cx * sy 

1652 

1653 if fabs(d) > _0EPS: # non-parallel edges 

1654 dx = x - c1_x 

1655 dy = y - c1_y 

1656 ca = fdot_(sx, dy, -sy, dx) / d 

1657 if _0EPS < ca < _EPS1 or (self._xtend and 

1658 _EPS0 < ca < _1EPS): 

1659 sa = fdot_(cx, dy, -cy, dx) / d 

1660 if _0EPS < sa < _EPS1 or (self._xtend and 

1661 _EPS0 < sa < _1EPS): 

1662 yield (y + sa * sy), (x + sa * sx), sa, ca 

1663 

1664 # unhandled, "degenerate" cases 1, 2 or 3 

1665 elif self._raiser and not (sa < _EPS0 or sa > _1EPS): # PYCHOK no cover 

1666 raise self._Error(1, c1, c2, sa=sa) # intersection at s1 or s2 

1667 

1668 elif self._raiser and not (ca < _EPS0 or ca > _1EPS): # PYCHOK no cover 

1669 # intersection at c1 or c2 or at c1 or c2 and s1 or s2 

1670 sa = fdot_(cx, dy, -cy, dx) / d 

1671 e = 2 if sa < _EPS0 or sa > _1EPS else 3 

1672 raise self._Error(e, c1, c2, ca=ca) 

1673 

1674 elif parallel and (sx or sy) and (cx or cy): # PYCHOK no cover 

1675 # non-null, parallel or colinear edges 

1676 sa1, d1 = self._alpha2(c1_x - x, c1_y - y, sx, sy) 

1677 sa2, d2 = self._alpha2(c2.x - x, c2.y - y, sx, sy) 

1678 if max(d1, d2) < _0EPS: 

1679 if self._xtend and not _outside(sa1, sa2, _EPS0, _1EPS): 

1680 if sa1 > sa2: # anti-parallel 

1681 sa1, sa2 = sa2, sa1 

1682 ca1, ca2 = _1_0, _0_0 

1683 else: # parallel 

1684 ca1, ca2 = _0_0, _1_0 

1685 ca = fabs((sx / cx) if cx else (sy / cy)) 

1686 # = hypot(sx, sy) / hypot(cx, cy) 

1687 if sa1 < 0: # s1 is between c1 and c2 

1688 ca *= ca1 + sa1 

1689 yield y, x, ca1, _alpha1(ca) 

1690 else: # c1 is between s1 and s2 

1691 yield (y + sa1 * sy), (x + sa1 * sx), sa1, ca1 

1692 if sa2 > 1: # s2 is between c1 and c2 

1693 ca *= sa2 - _1_0 

1694 yield (y + sy), (x + sx), ca2, _alpha1(ca2 - ca) 

1695 else: # c2 is between s1 and s2 

1696 yield (y + sa2 * sy), (x + sa2 * sx), sa2, ca2 

1697 elif self._raiser and not _outside(sa1, sa2, _0_0, _1EPS): 

1698 raise self._Error(4, c1, c2, d1=d1, d2=d2) 

1699 

1700 

1701class _BooleanBase(object): 

1702 # Shared C{Boolean[FHP|GH]} methods. 

1703 

1704 def __add__(self, other): 

1705 '''Sum: C{this + other} clips. 

1706 ''' 

1707 return self._sum(_other(self, other), self.__add__) # PYCHOK OK 

1708 

1709 def __and__(self, other): 

1710 '''Intersection: C{this & other}. 

1711 ''' 

1712 return self._boolean(other, False, False, self.__and__) # PYCHOK OK 

1713 

1714 def __iadd__(self, other): 

1715 '''In-place sum: C{this += other} clips. 

1716 ''' 

1717 return self._inplace(self.__add__(other)) 

1718 

1719 def __iand__(self, other): 

1720 '''In-place intersection: C{this &= other}. 

1721 ''' 

1722 return self._inplace(self.__and__(other)) 

1723 

1724 def __ior__(self, other): 

1725 '''In-place union: C{this |= other}. 

1726 ''' 

1727 return self._inplace(self.__or__(other)) 

1728 

1729 def __or__(self, other): 

1730 '''Union: C{this | other}. 

1731 ''' 

1732 return self._boolean(other, True, True, self.__or__) # PYCHOK OK 

1733 

1734 def __radd__(self, other): 

1735 '''Reverse sum: C{other + this} clips. 

1736 ''' 

1737 return _other(self, other)._sum(self, self.__radd__) 

1738 

1739 def __rand__(self, other): 

1740 '''Reverse intersection: C{other & this} 

1741 ''' 

1742 return _other(self, other).__and__(self) 

1743 

1744 def __ror__(self, other): 

1745 '''Reverse union: C{other | this} 

1746 ''' 

1747 return _other(self, other).__or__(self) 

1748 

1749 def _boolean4(self, other, op): 

1750 # Set up a new C{Boolean[FHP|GH]}. 

1751 C = self.__class__ 

1752 kwds = C._kwds(self, op) 

1753 a = C(self, **kwds) 

1754 b = _other(self, other) 

1755 return a, b, C, kwds 

1756 

1757 def _inplace(self, r): 

1758 # Replace this with a L{Boolean*} result. 

1759 self._clips, r._clips = r._clips, None 

1760# if self._raiser != r._raiser: 

1761# self._raiser = r._raiser 

1762# if self._xtend != r._xtend: 

1763# self._xtend = r._xtend 

1764# if self._eps != r._eps: 

1765# self._eps = r._eps 

1766 return self 

1767 

1768 

1769class BooleanFHP(_CompositeFHP, _BooleanBase): 

1770 '''I{Composite} class providing I{boolean} operations between two 

1771 I{composites} using U{Forster-Hormann-Popa<https://www.ScienceDirect.com/ 

1772 science/article/pii/S259014861930007X>}'s C++ implementation, transcoded 

1773 to pure Python. 

1774 

1775 The supported operations between (composite) polygon A and B are: 

1776 

1777 - C = A & B or A &= B, intersection of A and B 

1778 

1779 - C = A + B or A += B, sum of A and B clips 

1780 

1781 - C = A | B or A |= B, union of A and B 

1782 

1783 - A == B or A != B, equivalent A and B clips 

1784 

1785 - A.isequalTo(B, eps), equivalent within tolerance 

1786 

1787 @see: Methods C{__eq__} and C{isequalTo}, function L{clipFHP4} 

1788 and class L{BooleanGH}. 

1789 ''' 

1790 _kind = _boolean_ 

1791 

1792 def __init__(self, lls, raiser=False, eps=EPS, **name): 

1793 '''New L{BooleanFHP} operand for I{boolean} operation. 

1794 

1795 @arg lls: The polygon points and clips (iterable of L{LatLonFHP}s, 

1796 L{ClipFHP4Tuple}s or other C{LatLon}s). 

1797 @kwarg raiser: If C{True}, throw L{ClipError} exceptions (C{bool}). 

1798 @kwarg esp: Tolerance for eliminating null edges (C{degrees}, same 

1799 units as the B{C{lls}} coordinates). 

1800 @kwarg name: Optional C{B{name}=NN} (C{str}). 

1801 ''' 

1802 _CompositeFHP.__init__(self, lls, raiser=raiser, eps=eps, **name) 

1803 

1804 def __isub__(self, other): 

1805 '''Not implemented.''' 

1806 return _NotImplemented(self, other) 

1807 

1808 def __rsub__(self, other): 

1809 '''Not implemented.''' 

1810 return _NotImplemented(self, other) 

1811 

1812 def __sub__(self, other): 

1813 '''Not implemented.''' 

1814 return _NotImplemented(self, other) 

1815 

1816 def _boolean(self, other, Union, unused, op): 

1817 # One C{BooleanFHP} operation. 

1818 p, q, C, kwds = self._boolean4(other, op) 

1819 r = p._clip(q, Union=Union, **kwds) 

1820 return C(r, **kwds) 

1821 

1822 

1823class BooleanGH(_CompositeGH, _BooleanBase): 

1824 '''I{Composite} class providing I{boolean} operations between two 

1825 I{composites} using the U{Greiner-Hormann<http://www.Inf.USI.CH/ 

1826 hormann/papers/Greiner.1998.ECO.pdf>} algorithm and U{Correia 

1827 <https://GitHub.com/helderco/univ-polyclip>}'s implementation, 

1828 modified and extended. 

1829 

1830 The supported operations between (composite) polygon A and B are: 

1831 

1832 - C = A - B or A -= B, difference A less B 

1833 

1834 - C = B - A or B -= A, difference B less B 

1835 

1836 - C = A & B or A &= B, intersection of A and B 

1837 

1838 - C = A + B or A += B, sum of A and B clips 

1839 

1840 - C = A | B or A |= B, union of A and B 

1841 

1842 - A == B or A != B, equivalent A and B clips 

1843 

1844 - A.isequalTo(B, eps), equivalent within tolerance 

1845 

1846 @note: To handle I{degenerate cases} like C{point-edge} and 

1847 C{point-point} intersections, use class L{BooleanFHP}. 

1848 

1849 @see: Methods C{__eq__} and C{isequalTo}, function L{clipGH4} 

1850 and class L{BooleanFHP}. 

1851 ''' 

1852 _kind = _boolean_ 

1853 

1854 def __init__(self, lls, raiser=True, xtend=False, eps=EPS, **name): 

1855 '''New L{BooleanFHP} operand for I{boolean} operation. 

1856 

1857 @arg lls: The polygon points and clips (iterable of L{LatLonGH}s, 

1858 L{ClipGH4Tuple}s or other C{LatLon}s). 

1859 @kwarg raiser: If C{True}, throw L{ClipError} exceptions (C{bool}). 

1860 @kwarg xtend: If C{True}, extend edges of I{degenerate cases}, an 

1861 attempt to handle the latter (C{bool}). 

1862 @kwarg esp: Tolerance for eliminating null edges (C{degrees}, same 

1863 units as the B{C{lls}} coordinates). 

1864 @kwarg name: Optional C{B{name}=NN} (C{str}). 

1865 ''' 

1866 _CompositeGH.__init__(self, lls, raiser=raiser, xtend=xtend, eps=eps, **name) 

1867 

1868 def _boolean(self, other, s_entry, c_entry, op): 

1869 # One C{BooleanGH} operation. 

1870 s, c, C, kwds = self._boolean4(other, op) 

1871 r = s._clip(c, s_entry, c_entry, **kwds) 

1872 return C(r, **kwds) 

1873 

1874 def __isub__(self, other): 

1875 '''In-place difference: C{this -= other}. 

1876 ''' 

1877 return self._inplace(self.__sub__(other)) 

1878 

1879 def __rsub__(self, other): 

1880 ''' Reverse difference: C{other - this} 

1881 ''' 

1882 return _other(self, other).__sub__(self) 

1883 

1884 def __sub__(self, other): 

1885 '''Difference: C{this - other}. 

1886 ''' 

1887 return self._boolean(other, True, False, self.__sub__) 

1888 

1889 

1890def _alpha1(alpha): # PYCHOK no cover 

1891 # Return C{alpha} in C{[0..1]} range 

1892 if _EPS0 < alpha < _1EPS: 

1893 return max(_0_0, min(alpha, _1_0)) 

1894 t = _not_(Fmt.SQUARE(_ELLIPSIS_(0, 1))) 

1895 raise ClipError(_alpha_, alpha, txt=t) 

1896 

1897 

1898def _alpha4(a): 

1899 # Return 4-tuple (alpha, -EPS < alpha < EPS, 

1900 # 0 < alpha < 1, 

1901 # not 0 < alpha < 1) 

1902 a_EPS = bool(_EPS0 < a < _0EPS) 

1903 a_0_1 = bool(_0EPS < a < _EPS1) 

1904 return a, a_EPS, a_0_1, (not a_0_1) 

1905 

1906 

1907def _Cps(Cp, composites_points, where): 

1908 # Yield composites and points as a C{Cp} composite. 

1909 try: 

1910 kwds = dict(kind=_points_, name__=where) 

1911 for cp in composites_points: 

1912 yield cp if isBoolean(cp) else Cp(cp, **kwds) 

1913 except (AttributeError, ClipError, TypeError, ValueError) as x: 

1914 raise _ValueError(points=cp, cause=x) 

1915 

1916 

1917def _eps0(eps): 

1918 # Adjust C{eps} or C{0}. 

1919 return eps if eps and eps > EPS else 0 

1920 

1921 

1922def isBoolean(obj): 

1923 '''Check for C{Boolean} composites. 

1924 

1925 @arg obj: The object (any C{type}). 

1926 

1927 @return: C{True} if B{C{obj}} is L{BooleanFHP}, L{BooleanGH} 

1928 or some other composite, C{False} otherwise. 

1929 ''' 

1930 return isinstance(obj, _CompositeBase) 

1931 

1932 

1933def _left_right_bottom_top_eps2(p1, p2): 

1934 '''(INTERNAL) Return 2-tuple C{((left, right), (bottom, top))}, both oversized. 

1935 ''' 

1936 return (_min_max_eps2(p1.x, p2.x), 

1937 _min_max_eps2(p1.y, p2.y)) 

1938 

1939 

1940def _low_high_eps2(lo, hi, eps): 

1941 '''(INTERNAL) Return 2-tuple C{(lo, hi)}, oversized. 

1942 ''' 

1943 # assert eps > 0 

1944 lo -= fabs(eps * lo) 

1945 hi += fabs(eps * hi) 

1946 if lo < hi: 

1947 pass 

1948 elif lo > hi: 

1949 lo, hi = hi, lo 

1950 else: 

1951 lo -= eps 

1952 hi += eps 

1953 return lo, hi 

1954 

1955 

1956def _min_max_eps2(*xs): 

1957 '''(INTERNAL) Return 2-tuple C{(min, max)}, oversized. 

1958 ''' 

1959 return _low_high_eps2(min(xs), max(xs), EPS) 

1960 

1961 

1962def _other(this, other): 

1963 '''(INTERNAL) Check for compatible C{type}s. 

1964 ''' 

1965 C = this.__class__ 

1966 if isinstance(other, C): 

1967 return other 

1968 raise _IsnotError(C, other=other) 

1969 

1970 

1971def _outside(x1, x2, lo, hi): 

1972 '''(INTERNAL) Are C{x1} and C{x2} outside C{(lo, hi)}? 

1973 ''' 

1974 # assert lo <= hi 

1975 return (x1 < lo or x2 > hi) if x1 > x2 else \ 

1976 (x2 < lo or x1 > hi) 

1977 

1978 

1979__all__ += _ALL_DOCS(_BooleanBase, _Clip, 

1980 _CompositeBase, _CompositeFHP, _CompositeGH, 

1981 _LatLonBool) 

1982 

1983# **) MIT License 

1984# 

1985# Copyright (C) 2018-2025 -- mrJean1 at Gmail -- All Rights Reserved. 

1986# 

1987# Permission is hereby granted, free of charge, to any person obtaining a 

1988# copy of this software and associated documentation files (the "Software"), 

1989# to deal in the Software without restriction, including without limitation 

1990# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1991# and/or sell copies of the Software, and to permit persons to whom the 

1992# Software is furnished to do so, subject to the following conditions: 

1993# 

1994# The above copyright notice and this permission notice shall be included 

1995# in all copies or substantial portions of the Software. 

1996# 

1997# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1998# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1999# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

2000# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

2001# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

2002# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

2003# OTHER DEALINGS IN THE SOFTWARE. 

2004 

2005# ***) GNU GPL 3 

2006# 

2007# Copyright (C) 2011-2012 Helder Correia <Helder.MC@Gmail.com> 

2008# 

2009# This program is free software: you can redistribute it and/or 

2010# modify it under the terms of the GNU General Public License as 

2011# published by the Free Software Foundation, either version 3 of 

2012# the License, or any later version. 

2013# 

2014# This program is distributed in the hope that it will be useful, 

2015# but WITHOUT ANY WARRANTY; without even the implied warranty of 

2016# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 

2017# GNU General Public License for more details. 

2018# 

2019# You should have received a copy of the GNU General Public License 

2020# along with this program. If not, see <http://www.GNU.org/licenses/>. 

2021# 

2022# You should have received the README file along with this program. 

2023# If not, see <https://GitHub.com/helderco/univ-polyclip>.