1

2# -*- coding: utf-8 -*-

3

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

5

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

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

8 C{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

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

19

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

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

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

23 _ValueError, _xattr, _xkwds_get

24 from pygeodesy.fmath import favg, hypot, hypot2

25# from pygeodesy.fsums import fsum1 # _MODS

26 from 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!

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

32 from pygeodesy.latlonBase import LatLonBase, \

33 LatLon2Tuple, Property_RO, property_RO

34 from 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

39 from pygeodesy.units import Height, HeightX

40 from 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

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

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

63

64

65 class _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

88 class _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

113 class _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

295 class 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

459 class 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

542 class _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

875 class _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

1181 class _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

1429 class _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

1530 class _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

1603 class _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

1713 class _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

1781 class 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

1836 class 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

1904 def _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

1912 def _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

1921 def _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

1931 def _eps0(eps):

1932 # Adjust C{eps} or C{None}.

1933 return eps if eps and eps > EPS else 0

1934

1935

1936 def 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

1948 def _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

1955 def _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

1963 def _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

1972 def _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

1981 def _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>.