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, isscalar, issubclassof, map2

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

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

23 _ValueError, _xkwds_get

24 from pygeodesy.fmath import fabs, favg, hypot, hypot2

25# from pygeodesy.fsums import fsum1 # from _MODS

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

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

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

29 _points_, _scalar_,_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 # from _MODS

33 from pygeodesy.named import Fmt, _Named, _NotImplemented, pairs, unstr

34# from pygeodesy.points import boundsOf # from _MODS

35 from pygeodesy.props import Property_RO, property_RO

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

37 from pygeodesy.units import Height, HeightX

38

39# from math import fabs # from .fmath

40

41__all__ = _ALL_LAZY.booleans

42__version__ = '23.04.02'

43

44_0_EPS = EPS # near-zero, positive

45_EPS_0 = -EPS # near-zero, negative

46_1_EPS = _1_0 + EPS # near-one, over

47_EPS_1 = _1_0 - EPS # near-one, under

48_10EPS = EPS * 10 # see ._2Abs, ._10eps

49

50_alpha_ = 'alpha'

51_boolean_ = 'boolean'

52_case_ = 'case'

53_corners_ = 'corners'

54_duplicate_ = 'duplicate'

55_open_ = 'open'

56

57

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

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

60

61

62 class _L(object): # Intersection labels

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

64 CROSSING_D = _Enum(_X_ + _d_, 8)

65 CROSSINGs = (CROSSING, CROSSING_D)

66 BOUNCING = _Enum(_B_, 2)

67 BOUNCING_D = _Enum(_B_ + _d_, 9)

68 BOUNCINGs = (BOUNCING, BOUNCING_D) + CROSSINGs

69 LEFT_ON = _Enum('Lo', 3)

70 ON_ON = _Enum('oo', 5)

71 ON_LEFT = _Enum('oL', 6)

72 ON_RIGHT = _Enum('oR', 7)

73 RIGHT_ON = _Enum('Ro', 4)

74 RIGHT_LEFT_ON = (RIGHT_ON, LEFT_ON)

75 # Entry/Exit flags

76 ENTRY = _Enum(_e_, 1)

77 EXIT = _Enum(_x_, 0)

78 Toggle = {ENTRY: EXIT,

79 EXIT: ENTRY,

80 None: None}

81

82_L = _L() # PYCHOK singleton

83

84

85 class _RP(object): # RelativePositions

86 IS_Pm = _Enum('Pm', 2) # C++ enum

87 IS_Pp = _Enum('Pp', 3)

88 LEFT = _Enum('L', 0)

89 RIGHT = _Enum(_R_, 1)

90

91_RP = _RP() # PYCHOK singleton

92

93_RP2L = {(_RP.LEFT, _RP.RIGHT): _L.CROSSING,

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

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

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

97 # overlapping cases

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

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

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

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

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

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

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

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

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

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

108

109

110 class _LatLonBool(_Named):

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

112 '''

113 _alpha = None # point AND intersection else length

114 _checked = False # checked in phase 3 iff intersection

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

116 _dupof = None # original of a duplicate

117# _e_x_str = NN # shut up PyChecker

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

119 _linked = None # link to neighbor iff intersection

120 _next = None # link to the next vertex

121 _prev = None # link to the previous vertex

122

123 def __init__(self, lat_ll, lon=None, height=0, clipid=INT0, name=NN):

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

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

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

127

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

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

130 or some other C{LatLon}).

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

132 scalar, ignored otherwise.

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

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

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

136 '''

137 if lon is None:

138 self.y, self.x = lat_ll.lat, lat_ll.lon

139 h = getattr(lat_ll, _height_, height)

140 c = getattr(lat_ll, _clipid_, clipid)

141 else:

142 self.y, self.x = lat_ll, lon

143 h, c = height, clipid

144 # don't duplicate defaults

145 if self._height != h:

146 self._height = h

147 if self._clipid != c:

148 self._clipid = c

149 if name:

150 self.name = name

151

152 def __abs__(self):

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

154

155 def __eq__(self, other):

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

157 other.x == self.x and

158 other.y == self.y)

159

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

161 return not self.__eq__(other)

162

163 def __repr__(self):

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

165 '''

166 if self._prev or self._next:

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

168 t = _SPACE_(self, Fmt.ANGLE(t))

169 else:

170 t = str(self)

171 return t

172

173 def __str__(self):

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

175 '''

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

177 if self._height:

178 X = _X_ if self.isintersection else NN

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

180 if self._clipid:

181 t += (_clipid_, self._clipid),

182 if self._alpha is not None:

183 t += (_alpha_, self._alpha),

184# if self._dupof: # recursion risk

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

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

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

188 if self._linked:

189 k = _DOT_ if self._checked else _BANG_

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

191 return NN(self.name, t)

192

193 def __sub__(self, other):

194 _other(self, other)

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

196 self.x - other.x)

197

198 def _2A(self, p2, p3):

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

200 x, y = self.x, self.y

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

202 (p3.x - x) * (p2.y - y)

203

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

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

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

207 a = fabs(self._2A(p2, p3))

208 return 0 if a < eps else a

209

210 @property_RO

211 def clipid(self):

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

213 '''

214 return self._clipid

215

216 def _equi(self, llb, eps):

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

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

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

220 fabs(llb.lat - self.y) > eps)

221

222 @property_RO

223 def height(self):

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

225 '''

226 h = self._height

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

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

229

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

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

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

233

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

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

236

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

238

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

240 '''

241 try:

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

243 except (AttributeError, TypeError, ValueError):

244 raise _IsnotError(_LatLon_, other=other)

245

246 @property_RO

247 def isintersection(self):

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

249 '''

250 return bool(self._linked)

251

252 @property_RO

253 def ispoint(self):

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

255 '''

256 return self._alpha is None

257

258 @property_RO

259 def lat(self):

260 '''Get the latitude (C{scalar}).

261 '''

262 return self.y

263

264 def _link(self, other):

265 # Make this and an other point are neighbors.

266 # assert _other(self, other)

267 self._linked = other

268 other._linked = self

269

270 @property_RO

271 def lon(self):

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

273 '''

274 return self.x

275

276 def _toClas(self, Clas, clipid):

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

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

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

280

281

282 class LatLonFHP(_LatLonBool):

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

284 '''

285 _en_ex = None

286 _label = None

287 _2split = None # or C{._Clip}

288 _2xing = False

289

290 def __init__(self, lat_ll, *lon_h_clipid, **name):

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

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

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

294

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

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

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

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

299 ignored otherwise.

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

301 '''

302 _LatLonBool.__init__(self, lat_ll, *lon_h_clipid, **name)

303

304 def __add__(self, other):

305 _other(self, other)

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

307

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

309 _other(self, other)

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

311

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

313 _other(self, other)

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

315

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

317 if not isscalar(other):

318 raise _IsnotError(_scalar_, other=other)

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

320

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

322 if self._label:

323 t = NN(self._label, t)

324 if self._en_ex:

325 t = NN(t, self._en_ex)

326 return t

327

328 @property_RO

329 def _isduplicate(self):

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

331 p = self._dupof

332 return bool(p and self._linked

333 and p is not self

334 and p == self

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

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

337

338# @property_RO

339# def _isduplicated(self):

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

341# d, v = 0, self

342# while v:

343# if v._dupof is self:

344# d += 1

345# v = v._next

346# if v is self:

347# break

348# return d

349

350 def isenclosedBy(self, *composites_points):

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

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

353 article/pii/S0925772101000128>}?

354

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

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

357 L{LatLonGH} or any C{LatLon}).

358

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

360

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

362 article/pii/S0925772101000128>}.

363 '''

364 class _Clips(object):

365 # Pseudo-_CompositeBase._clips tuple

366

367 @property_RO

368 def _clips(self):

369 for cp in _Cps(_CompositeFHP, composites_points,

370 LatLonFHP.isenclosedBy): # PYCHOK yield

371 for c in cp._clips:

372 yield c

373

374 return self._isinside(_Clips())

375

376 def _isinside(self, composite, *excludes):

377 # Is this point inside a composite I{winding number},

378 # excluding certain C{_Clip}s?

379 x, y, i = self.x, self.y, False

380 for c in composite._clips:

381 if c not in excludes:

382 w = 0

383 for p1, p2 in c._edges2():

384 # edge [p1,p2] must straddle y

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

386 r = p2.x > x

387 s = p2.y > p1.y

388 if p1.x < x:

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

390 else:

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

392 if b:

393 w += 1 if s else -1

394 if isodd(w):

395 i = not i

396 return i

397

398 @property_RO

399 def _prev_next2(self):

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

401 p, n = self, self._next

402 if self._isduplicate:

403 p = self._dupof

404 while p._isduplicate:

405 p = p._dupof

406 while n._isduplicate:

407 n = n._next

408 return p._prev, n

409

410# def _edge2(self):

411# # Return the start and end point of the

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

413# n = p = self

414# while p.isintersection:

415# p = p._prev

416# if p is self:

417# break

418# while n.isintersection:

419# n = n._next

420# if n is self:

421# break

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

423# return p, n

424

425 def _RPoracle(self, p1, p2, p3):

426 # Relative Position oracle

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

428 T = _RP.IS_Pm

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

430 T = _RP.IS_Pp

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

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

433 self._2A(p2, p3) > 0 else \

434 _RP.RIGHT # PYCHOK indent

435 else: # right turn (or straight)

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

437 self._2A(p2, p3) < 0 else \

438 _RP.LEFT # PYCHOK indent

439 return T

440

441

442 class LatLonGH(_LatLonBool):

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

444 '''

445 _entry = None # entry or exit iff intersection

446

447 def __init__(self, lat_ll, *lon_h_clipid, **name):

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

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

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

451

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

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

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

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

456 ignored otherwise.

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

458 '''

459 _LatLonBool.__init__(self, lat_ll, *lon_h_clipid, **name)

460

461 def _check(self):

462 # Check-mark this vertex and its link.

463 self._checked = True

464 k = self._linked

465 if k and not k._checked:

466 k._checked = True

467

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

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

470 (_e_ if self._entry else _x_))

471

472 def isenclosedBy(self, *composites_points):

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

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

475 article/pii/S0925772101000128>}?

476

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

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

479 L{LatLonGH} or any C{LatLon}).

480

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

482 '''

483 class _Edges(object):

484 # Pseudo-_CompositeBase._edges3 method

485

486 def _edges3(self, **kwds):

487 for cp in _Cps(_CompositeGH, composites_points,

488 LatLonGH.isenclosedBy): # PYCHOK yield

489 for e in cp._edges3(**kwds):

490 yield e

491

492 return self._isinside(_Edges())

493

494 def _isinside(self, composite, *bottom_top):

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

496

497 def _x(y, p1, p2):

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

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

500

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

502 # intersecting a ray emitted from this point to

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

504 # inside, if I{even} outside.

505 o, y = False, self.y

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

507 x = self.x

508 for p1, p2, _ in composite._edges3():

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

510 r = p2.x > x

511 if p1.x < x:

512 b = r and (_x(y, p1, p2) > x)

513 else:

514 b = r or (_x(y, p1, p2) > x)

515 if b:

516 o = not o

517 return o

518

519

520 class _Clip(_Named):

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

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

523 and intersections with other clips.

524 '''

525 _composite = None

526 _dups = 0

527 _first = None

528 _id = 0

529 _identical = False

530 _noInters = False

531 _last = None

532 _LL = None

533 _len = 0

534 _pushback = False

535

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

537 '''(INTERNAL) New C{_Clip}.

538 '''

539 # assert isinstance(composite, _CompositeBase)

540 if clipid in composite._clipids:

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

542 self._composite = composite

543 self._id = clipid

544 self._LL = composite._LL

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

546

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

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

549 '''

550 for v in self:

551 if v is point: # or ==?

552 return True

553 return False

554

555 def __eq__(self, other):

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

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

558 the same order, possibly rotated?

559 '''

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

561

562 def __ge__(self, other):

563 '''See method C{__lt__}.

564 '''

565 return not self.__lt__(other)

566

567 def __gt__(self, other):

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

569 located or stretched farther North or East?

570 '''

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

572

573 def __hash__(self): # PYCHOK no over

574 return hash(self._bltr4)

575

576 def __iter__(self):

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

578 '''

579 v = f = self._first

580 while v:

581 yield v

582 v = v._next

583 if v is f:

584 break

585

586 def __le__(self, other):

587 '''See method C{__gt__}.

588 '''

589 return not self.__gt__(other)

590

591 def __len__(self):

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

593 intersections in this clip.

594 '''

595 return self._len

596

597 def __lt__(self, other):

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

599 located or stretched farther South or West?

600 '''

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

602

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

604 '''See method C{__eq__}.

605 '''

606 return not self.__eq__(other)

607

608 _all = __iter__

609

610 @property_RO

611 def _all_ON_ON(self):

612 # Check whether all vertices are ON_ON.

613 L_ON_ON = _L.ON_ON

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

615

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

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

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

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

620 self._len += 1

621 # assert v._clipid == self._id

622

623 v._next = n = self._first

624 if n is None: # set ._first

625 self._first = p = n = v

626 else: # insert before ._first

627 v._prev = p = n._prev

628 p._next = n._prev = v

629 return v

630

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

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

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

634# y, x, p = v.y, v.x, self._last

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

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

637# if v._linked:

638# p._linked = True # to force errors

639# return p

640

641 @Property_RO

642 def _bltr4(self):

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

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

645

646 def _bltr4eps(self, eps):

647 # Get the ._bltr4 bounds tuple, oversized.

648 if eps > 0: # > EPS

649 yb, xl, yt, xr = self._bltr4

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

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

652 t = yb, xl, yt, xr

653 else:

654 t = self._bltr4

655 return t

656

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

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

659 p, f = self._last, self._first

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

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

662 # un-close the clip

663 f._prev = p = p._prev

664 p._next = f

665 self._len -= 1

666# elif f and raiser:

667# raise self._OpenClipError(p, f)

668 if len(self) < 3:

669 raise self._Error(_too_(_few_))

670

671 def _dup(self, q):

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

673 v = self._insert(q.y, q.x, q)

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

675 v._dupof = q._dupof or q

676 # assert v._prev is q

677 # assert q._next is v

678 return v

679

680 def _edges2(self, **unused):

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

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

683 p1 = p2 = f = self._first

684 while p2:

685 p2 = p2._next

686 if p2.ispoint:

687 yield p1, p2

688 p1 = p2

689 if p2 is f:

690 break

691

692 def _equi(self, clip, eps):

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

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

695 r, f = len(self), self._first

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

697 == clip._bltr4eps(eps):

698 _equi = _LatLonBool._equi

699 for v in clip:

700 if _equi(f, v, eps):

701 s, n = f, v

702 for _ in range(r):

703 s, n = s._next, n._next

704 if not _equi(s, n, eps):

705 break # next v

706 else: # equivalent

707 return True

708 return False

709

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

711 # Build a C{ClipError} instance

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

713 if self._dups:

714 kwds.update(dups=self._dups)

715 cp = self._composite

716 if self._id:

717 try:

718 i = cp._clips.index(self)

719 if i != self._id:

720 kwds[_clip_] = i

721 except ValueError:

722 pass

723 kwds[_clipid_] = self._id

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

725

726 def _index(self, clips, eps):

727 # see _CompositeBase._equi

728 for i, c in enumerate(clips):

729 if c._equi(self, eps):

730 return i

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

732

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

734 # insertVertex between points C{start} and

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

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

737 n = start._next

738 if end_alpha:

739 end, alpha = end_alpha

740 v._alpha = alpha

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

742 # assert start is not end

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

744 n = n._next

745 v._next = n

746 v._prev = p = n._prev

747 p._next = n._prev = v

748 self._len += 1

749# _Clip._bltr4._update(self)

750# _Clip._ishole._update(self)

751 return v

752

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

754 # insert an intersection or make a point both

755 if p1_p2_alpha: # intersection on edge

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

757 else: # intersection at point

758 v = q

759 # assert not v._linked

760 # assert v._alpha is None

761 return v

762

763 def _intersections(self):

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

765 for v in self:

766 if v.isintersection:

767 yield v

768

769 @Property_RO

770 def _ishole(self): # PYCHOK no cover

771 # Is this clip a hole inside its composite?

772 v = self._first

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

774

775 @property_RO

776 def _nodups(self):

777 # Yield all non-duplicates.

778 for v in self:

779 if not v._dupof:

780 yield v

781

782 def _noXings(self, Union):

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

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

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

786

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

788 # Return a C{CloseError} instance

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

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

791

792 def _point2(self, insert):

793 # getNonIntersectionPoint and -Vertex

794 if not (insert and self._noInters):

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

796 return p, None

797 for n in self._intersections():

798 p, _ = n._prev_next2

799 k = p._linked

800 if k:

801 if n._linked not in k._prev_next2:

802 # create a pseudo-point

803 k = _0_5 * (p + n)

804 if insert:

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

806 r = k # to remove later

807 else: # no ._prev, ._next

808 k._clipid = n._clipid

809 r = None

810 return k, r

811 return None, None

812

813 def _points(self, may_be=True):

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

815 for v in self:

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

817 yield v

818

819 def _remove2(self, v):

820 # Remove vertex C{v}.

821 # assert not v._isduplicated

822 if len(self) > 1:

823 p = v._prev

824 p._next = n = v._next

825 n._prev = p

826 if self._first is v:

827 self._first = n

828 if self._last is v:

829 self._last = p

830 self._len -= 1

831 else:

832 n = self._last = \

833 p = self._first = None

834 self._len = 0

835 return p, n

836

837 def _update_all(self): # PYCHOK no cover

838 # Zap the I{cached} properties.

839 _Clip._bltr4._update( self)

840 _Clip._ishole._update(self)

841 return self # for _special_identicals

842

843 def _Xings(self):

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

845 CROSSING = _L.CROSSING

846 for v in self._intersections():

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

848 yield v

849

850

851 class _CompositeBase(_Named):

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

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

854 '''

855 _clips = () # tuple of C{_Clips}

856 _eps = EPS # null edges

857 _kind = _corners_

858 _LL = _LatLonBool # shut up PyChecker

859 _raiser = False

860 _xtend = False

861

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

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

864 '''

865 n = name or getattr(lls, _name_, NN)

866 if n:

867 self.name = n

868 if kind:

869 self._kind = kind

870 if self._eps < eps:

871 self._eps = eps

872

873 c = _Clip(self)

874 lp = None

875 for ll in lls:

876 ll = self._LL(ll)

877 if lp is None:

878 c._id = ll._clipid # keep clipid

879 lp = c._append(ll)

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

881 c._closed(self.raiser)

882 c = _Clip(self, ll._clipid)

883 lp = c._append(ll)

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

885 lp = c._append(ll)

886 else:

887 c._dups += 1

888 c._closed(self.raiser)

889

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

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

892 '''

893 for c in self._clips:

894 if point in c:

895 return True

896 return False

897

898 def __eq__(self, other):

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

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

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

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

903 possibly rotated.

904 '''

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

906

907 def __iter__(self):

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

909 '''

910 for c in self._clips:

911 for v in c:

912 yield v

913

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

915 '''See method C{__eq__}.

916 '''

917 return not self.__eq__(other)

918

919 def __len__(self):

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

921 '''

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

923

924 def __repr__(self):

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

926 '''

927 c = len(self._clips)

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

929 n = Fmt.SQUARE(len(self))

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

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

932

933 def __str__(self):

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

935 '''

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

937

938 @property_RO

939 def _bottom_top_eps2(self):

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

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

942 max(v.y for v in self))

943

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

945 # Return a new instance

946 _g = kwds.get

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

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

949

950 @property_RO

951 def _clipids(self): # PYCHOK no cover

952 for c in self._clips:

953 yield c._id

954

955 def clipids(self):

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

957 '''

958 return tuple(self._clipids)

959

960# def _clipidups(self, other):

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

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

963

964 def _edges3(self, **raiser):

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

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

967 for c in self._clips:

968 for p1, p2 in c._edges2(**raiser):

969 yield p1, p2, c

970

971 def _encloses(self, lat, lon):

972 # see function .points.isenclosedBy

973 return self._LL(lat, lon).isenclosedBy(self)

974

975 @property

976 def eps(self):

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

978 '''

979 return self._eps

980

981 @eps.setter # PYCHOK setter!

982 def eps(self, eps):

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

984 '''

985 self._eps = eps

986

987 def _10eps(self, **eps):

988 # Get eps for _LatLonBool._2Abs

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

990 if e != EPS:

991 e *= _10EPS / EPS

992 else:

993 e = _10EPS

994 return e

995

996 def _equi(self, other, eps):

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

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

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

1000 if cs and len(cs) == len(co):

1001 if eps > 0:

1002 _index = _Clip._index

1003 else:

1004 def _index(c, cs, unused):

1005 return cs.index(c)

1006 try:

1007 cs = list(sorted(cs))

1008 for c in sorted(co):

1009 cs.pop(_index(c, cs, eps))

1010 except ValueError: # from ._index

1011 pass

1012 return False if cs else True

1013 else: # both null?

1014 return False if cs or co else True

1015

1016 def _intersections(self):

1017 # Yield all intersections.

1018 for c in self._clips:

1019 for v in c._intersections():

1020 yield v

1021

1022 def isequalTo(self, other, eps=None):

1023 '''Is this boolean/composite equal to an B{C{other}} within

1024 a given, I{non-negative} tolerance?

1025

1026 @arg other: The other boolean/composite (C{Boolean[FHP|GB]}).

1027 @kwarg eps: Tolerance for equality (C{degrees} or C{None}).

1028

1029 @return: C{True} if equivalent, C{False} otherwise (C{bool}).

1030

1031 @raise TypeError: Invalid B{C{other}}.

1032

1033 @see: Method C{__eq__}.

1034 '''

1035 if isinstance(other, _CompositeBase):

1036 return self._equi(other, _eps0(eps))

1037 raise _IsnotError(_boolean_, _composite_, other=other)

1038

1039 def _kwds(self, op, **more):

1040 # Get all keyword arguments as C{dict}.

1041 kwds = dict(raiser=self.raiser, eps=self.eps,

1042 name=self.name or op.__name__)

1043 kwds.update(more)

1044 return kwds

1045

1046 @property_RO

1047 def _left_right_eps2(self):

1048 # Get the left and right C{x} bounds, oversized.

1049 return _min_max_eps2(min(v.x for v in self),

1050 max(v.x for v in self))

1051

1052 def _points(self, may_be=True): # PYCHOK no cover

1053 # Yield all I{original} points, which may be intersections too.

1054 for c in self._clips:

1055 for v in c._points(may_be=may_be):

1056 yield v

1057

1058 @property

1059 def raiser(self):

1060 '''Get the option to throw L{ClipError} exceptions (C{bool}).

1061 '''

1062 return self._raiser

1063

1064 @raiser.setter # PYCHOK setter!

1065 def raiser(self, throw):

1066 '''Set the option to throw L{ClipError} exceptions (C{bool}).

1067 '''

1068 self._raiser = bool(throw)

1069

1070 def _results(self, _presults, Clas, closed=False, inull=False, **eps):

1071 # Yield the dedup'd results, as L{ClipFHP4Tuple}s

1072 C = self._LL if Clas is None else Clas

1073 e = self._10eps(**eps)

1074 for clipid, ns in enumerate(_presults):

1075 f = p = v = None

1076 for n in ns:

1077 if f is None:

1078 yield n._toClas(C, clipid)

1079 f = p = n

1080 elif v is None:

1081 v = n # got f, p, v

1082 elif inull or p._2Abs(v, n, eps=e):

1083 yield v._toClas(C, clipid)

1084 p, v = v, n

1085 else: # null, colinear, ... skipped

1086 v = n

1087 if v and (inull or p._2Abs(v, f, eps=e)):

1088 yield v._toClas(C, clipid)

1089 p = v

1090 if f and p != f and closed: # close clip

1091 yield f._toClas(C, clipid)

1092

1093 def _sum(self, other, op):

1094 # Combine this and an C{other} composite

1095 LL = self._LL

1096 sp = self.copy(name=self.name or op.__name__)

1097 sp._clips, sid = (), INT0 # new clips

1098 for cp in (self, other):

1099 for c in cp._clips:

1100 _ap = _Clip(sp, sid)._append

1101 for v in c._nodups:

1102 _ap(LL(v.y, v.x, v.height, sid))

1103 sid += 1

1104 return sp

1105

1106 def _sum1(self, _a_p, *args, **kwds): # in .karney, .points

1107 # Sum the area or perimeter of all clips

1108 return _MODS.fsums.fsum1((_a_p(c, *args, **kwds) for c in self._clips),

1109 floats=True)

1110

1111 def _sum2(self, LL, _a_p, *args, **kwds): # in .sphericalNvector, -Trigonometry

1112 # Sum the area or perimeter of all clips

1113

1114 def _lls(clip): # convert clip to LLs

1115 for v in clip:

1116 yield LL(v.lat, v.lon) # datum=Sphere

1117

1118 return _MODS.fsums.fsum1((_a_p(_lls(c), *args, **kwds) for c in self._clips),

1119 floats=True)

1120

1121 def toLatLon(self, LatLon=None, closed=False, **LatLon_kwds):

1122 '''Yield all (non-duplicate) points and intersections

1123 as an instance of B{C{LatLon}}.

1124

1125 @kwarg LatLon: Class to use (C{LatLon}) or if C{None},

1126 L{LatLonFHP} or L{LatLonGH}.

1127 @kwarg closed: If C{True}, close each clip (C{bool}).

1128 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}}

1129 keyword arguments, ignore if

1130 C{B{LatLon} is None}.

1131

1132 @raise TypeError: Invalid B{C{LatLon}}.

1133

1134 @note: For intersections, C{height} is an instance

1135 of L{HeightX}, otherwise of L{Height}.

1136 '''

1137 if LatLon is None:

1138 LL, kwds = self._LL, {}

1139 elif issubclassof(LatLon, _LatLonBool,

1140 _MODS.latlonBase.LatLonBase):

1141 LL, kwds = LatLon, LatLon_kwds

1142 else:

1143 raise _TypeError(LatLon=LatLon)

1144

1145 for c in self._clips:

1146 lf, cid = None, c._id

1147 for v in c._nodups:

1148 ll = LL(v.y, v.x, **kwds)

1149 ll._height = v.height

1150 if ll._clipid != cid:

1151 ll._clipid = cid

1152 yield ll

1153 if lf is None:

1154 lf = ll

1155 if closed and lf:

1156 yield lf

1157

1158

1159 class _CompositeFHP(_CompositeBase):

1160 '''(INTERNAL) A list of clips representing a I{composite}

1161 of L{LatLonFHP} points, duplicates and intersections

1162 with an other I{composite}.

1163 '''

1164 _LL = LatLonFHP

1165 _Union = False

1166

1167 def __init__(self, lls, raiser=False, **name_kind_eps):

1168 # New L{_CompositeFHP}.

1169 if raiser:

1170 self._raiser = True

1171 _CompositeBase.__init__(self, lls, **name_kind_eps)

1172

1173 def _classify(self):

1174 # 2) Classify intersection chains.

1175 L = _L

1176 for v in self._intersections():

1177 n, b = v, v._label

1178 if b in L.RIGHT_LEFT_ON: # next chain

1179 while True:

1180 n._label = None # n.__dict__.pop('_label')

1181 n = n._next

1182 if n is v or n._label is not L.ON_ON: # n._label and ...

1183 break

1184 a = L.LEFT_ON if n._label is L.ON_LEFT else L.RIGHT_ON

1185 v._label = n._label = L.BOUNCING_D if a is b else L.CROSSING_D

1186

1187 # 3) Copy labels

1188 for v in self._intersections():

1189 v._linked._label = v._label

1190

1191 def _clip(self, corners, Union=False, Clas=None,

1192 **closed_inull_raiser_eps):

1193 # Clip this composite with another one, C{corners},

1194 # using Foster-Hormann-Popa's algorithm.

1195 P = self

1196 Q = self._class(corners, closed_inull_raiser_eps,

1197 eps=P._eps, raiser=False)

1198 if Union:

1199 P._Union = Q._Union = True

1200

1201 bt = Q._bottom_top_eps2

1202 lr = Q._left_right_eps2

1203 # compute and insert intersections

1204 for p1, p2, Pc in P._edges3(**closed_inull_raiser_eps):

1205 if not (_outside(p1.x, p2.x, *lr) or

1206 _outside(p1.y, p2.y, *bt)):

1207 e = _EdgeFHP(p1, p2)

1208 if e._dp2 > EPS2: # non-null edge

1209 for q1, q2, Qc in Q._edges3(**closed_inull_raiser_eps):

1210 for T, p, q in e._intersect3(q1, q2):

1211 p = Pc._intersection(T, *p)

1212 q = Qc._intersection(T, *q)

1213 # assert not p._linked

1214 # assert not q._linked

1215 p._link(q)

1216

1217 # label and classify intersections

1218 P._labelize()

1219 P._classify()

1220

1221 # check for special cases

1222 P._special_cases(Q)

1223 Q._special_cases(P)

1224 # handle identicals

1225 P._special_identicals(Q)

1226

1227 # set Entry/Exit flags

1228 P._set_entry_exits(Q)

1229 Q._set_entry_exits(P)

1230

1231 # handle splits and crossings

1232 P._splits_xings(Q)

1233

1234 # yield the results

1235 return P._results(P._presults(Q), Clas, **closed_inull_raiser_eps)

1236

1237 @property_RO

1238 def _identicals(self):

1239 # Yield all clips marked C{._identical}.

1240 for c in self._clips:

1241 if c._identical:

1242 yield c

1243

1244 def _labelize(self):

1245 # 1) Intersections classification

1246 for p in self._intersections():

1247 q = p._linked

1248 # determine local configuration at this intersection

1249 # and positions of Q- and Q+ relative to (P-, I, P+)

1250 p1, p3 = p._prev_next2

1251 q1, q3 = q._prev_next2

1252 t = (q1._RPoracle(p1, p, p3),

1253 q3._RPoracle(p1, p, p3))

1254 # check intersecting and overlapping cases

1255 p._label = _RP2L.get(t, None)

1256

1257 def _presults(self, other):

1258 # Yield the result clips, each as a generator

1259 # of the L{_LatLonFHP}s in that clip

1260 for cp in (self, other):

1261 for c in cp._clips:

1262 if c._pushback:

1263 yield c._all()

1264 for c in self._clips:

1265 for X in c._Xings():

1266 yield self._resultX(X)

1267

1268 def _resultX(self, X):

1269 # Yield the results from CROSSING C{X}.

1270 L, U, v = _L, self._Union, X

1271 while v:

1272 v._checked = True

1273 r = v # in P or Q

1274 s = L.Toggle[v._en_ex]

1275 e = (s is L.EXIT) ^ U

1276 while True:

1277 v = v._next if e else v._prev

1278 yield v

1279 v._checked = True

1280 if v._en_ex is s or v is X:

1281 break

1282 if v is r: # full circle

1283 raise ClipError(full_circle=v, clipid=v._clipid)

1284 if v is not X:

1285 v = v._linked

1286 if v is X:

1287 break

1288

1289 def _set_entry_exits(self, other): # MCCABE 14

1290 # 4) Set entry/exit flags

1291 L, U = _L, self._Union

1292 for c in self._clips:

1293 n, k = c._point2(True)

1294 if n:

1295 f = n

1296 s = L.EXIT if n._isinside(other) else L.ENTRY

1297 t = L.EXIT # first_chain_vertex = True

1298 while True:

1299 if n.isintersection:

1300 b = n._label

1301 if b is L.CROSSING:

1302 n._en_ex = s

1303 s = L.Toggle[s]

1304 elif b is L.BOUNCING and ((s is L.EXIT) ^ U):

1305 n._2split = c # see ._splits_xings

1306 elif b is L.CROSSING_D:

1307 n._en_ex = s

1308 if (s is t) ^ U:

1309 n._label = L.CROSSING

1310 t = L.Toggle[t]

1311 if t is L.EXIT: # first_chain_vertex == True

1312 s = L.Toggle[s]

1313 elif b is L.BOUNCING_D:

1314 n._en_ex = s

1315 if (s is t) ^ U:

1316 n._2xing = True # see ._splits_xings

1317 s = L.Toggle[s]

1318 t = L.Toggle[t]

1319 n = n._next # _, n = n._prev_next2

1320 if n is f:

1321 break # PYCHOK attr?

1322 if k:

1323 c._remove2(k)

1324

1325 def _special_cases(self, other):

1326 # 3.5) Check special cases

1327 U = self._Union

1328 for c in self._clips:

1329 if c._noXings(U):

1330 c._noInters = True

1331 if c._all_ON_ON:

1332 c._identical = True

1333 else:

1334 p, _ = c._point2(False)

1335 if p and (p._isinside(other) ^ U):

1336 c._pushback = True

1337

1338 def _special_identicals(self, other):

1339 # 3.5) Handle identicals

1340 _u = _Clip._update_all

1341 cds = dict((c._id, _u(c)) for c in other._identicals)

1342 # assert len(cds) == len(other._identicals)

1343 if cds: # PYCHOK no cover

1344 for c in self._identicals:

1345 c._update_all()

1346 for v in c._intersections():

1347 d = cds.get(v._linked._clipid, None)

1348 if d and d._ishole is c._ishole:

1349 c._pushback = True

1350 break # next c

1351

1352 @property_RO

1353 def _2splits(self):

1354 # Yield all intersections marked C{._2split}

1355 for p in self._intersections():

1356 if p._2split:

1357 # assert isinstance(p._2split, _Clip)

1358 yield p

1359

1360 def _splits_xings(self, other): # MCCABE 15

1361 # 5) Handle split pairs and 6) crossing candidates

1362

1363 def _2A_dup2(p, P): # PYCHOK unused

1364 p1, p2 = p._prev_next2

1365 ap = p1._2A(p, p2)

1366 Pc = p._2split

1367 # assert Pc in P._clips

1368 # assert p in Pc

1369 return ap, Pc._dup(p)

1370

1371 def _links2(ps, qs): # PYCHOK P unused?

1372 # Yield each link as a 2-tuple(p, q)

1373 id_qs = set(map(id, qs))

1374 if id_qs:

1375 for p in ps:

1376 q = p._linked

1377 if q and id(q) in id_qs:

1378 yield p, q

1379

1380 L = _L

1381 E = L.ENTRY if self._Union else L.EXIT

1382 X = L.Toggle[E]

1383 for p, q in _links2(self._2splits, other._2splits):

1384 ap, pp = _2A_dup2(p, self)

1385 aq, qq = _2A_dup2(q, other)

1386 if (ap * aq) > 0: # PYCHOK no cover

1387 p._link(qq) # overwrites ...

1388 q._link(pp) # ... p-q link

1389 else:

1390 pp._link(qq)

1391 p._en_ex = q._en_ex = E

1392 pp._en_ex = qq._en_ex = X

1393 p._label = pp._label = \

1394 q._label = qq._label = L.CROSSING

1395

1396 for p, q in _links2(self._2xings, other._2xings):

1397 p._label = q._label = L.CROSSING

1398

1399 @property_RO

1400 def _2xings(self):

1401 # Yield all intersections marked C{._2xing}

1402 for p in self._intersections():

1403 if p._2xing:

1404 yield p

1405

1406

1407 class _CompositeGH(_CompositeBase):

1408 '''(INTERNAL) A list of clips representing a I{composite}

1409 of L{LatLonGH} points, duplicates and intersections

1410 with an other I{composite}.

1411 '''

1412 _LL = LatLonGH

1413 _xtend = False

1414

1415 def __init__(self, lls, raiser=False, xtend=False, **name_kind_eps):

1416 # New L{_CompositeGH}.

1417 if xtend:

1418 self._xtend = True

1419 elif raiser:

1420 self._raiser = True

1421 _CompositeBase.__init__(self, lls, **name_kind_eps)

1422

1423 def _clip(self, corners, s_entry, c_entry, Clas=None,

1424 **closed_inull_raiser_xtend_eps):

1425 # Clip this polygon with another one, C{corners}.

1426

1427 # Core of Greiner/Hormann's algorithm, enhanced U{Correia's

1428 # <https://GitHub.com/helderco/univ-polyclip>} implementation***

1429 # and extended to optionally handle so-called "degenerate cases"

1430 S = self

1431 C = self._class(corners, closed_inull_raiser_xtend_eps,

1432 raiser=False, xtend=False)

1433 bt = C._bottom_top_eps2

1434 lr = C._left_right_eps2

1435 # 1. find intersections

1436 for s1, s2, Sc in S._edges3(**closed_inull_raiser_xtend_eps):

1437 if not (_outside(s1.x, s2.x, *lr) or

1438 _outside(s1.y, s2.y, *bt)):

1439 e = _EdgeGH(s1, s2, **closed_inull_raiser_xtend_eps)

1440 if e._hypot2 > EPS2: # non-null edge

1441 for c1, c2, Cc in C._edges3(**closed_inull_raiser_xtend_eps):

1442 for y, x, sa, ca in e._intersect4(c1, c2):

1443 s = Sc._insert(y, x, s1, s2, sa)

1444 c = Cc._insert(y, x, c1, c2, ca)

1445 s._link(c)

1446

1447 # 2. identify entry/exit intersections

1448 if S._first:

1449 s_entry ^= S._first._isinside(C, *bt)

1450 for v in S._intersections():

1451 v._entry = s_entry = not s_entry

1452

1453 if C._first:

1454 c_entry ^= C._first._isinside(S)

1455 for v in C._intersections():

1456 v._entry = c_entry = not c_entry

1457

1458 # 3. yield the result(s)

1459 return S._results(S._presults(), Clas, **closed_inull_raiser_xtend_eps)

1460

1461 @property_RO

1462 def _first(self):

1463 # Get the very first vertex of the first clip

1464 for v in self:

1465 return v

1466 return None # PYCHOK no cover

1467

1468 def _kwds(self, op, **more):

1469 # Get the kwds C{dict}.

1470 return _CompositeBase._kwds(self, op, xtend=self.xtend, **more)

1471

1472 def _presults(self):

1473 # Yield the unchecked intersection(s).

1474 for c in self._clips:

1475 for v in c._intersections():

1476 if not v._checked:

1477 yield self._resultU(v)

1478

1479 def _resultU(self, v):

1480 # Yield the result from an un-checked intersection.

1481 while v and not v._checked:

1482 v._check()

1483 yield v

1484 r = v

1485 e = v._entry

1486 while True:

1487 v = v._next if e else v._prev

1488 yield v

1489 if v._linked:

1490 break

1491 if v is r:

1492 raise ClipError(full_circle=v, clipid=v._clipid)

1493 v = v._linked # switch

1494

1495 @property

1496 def xtend(self):

1497 '''Get the option to handle I{degenerate cases} (C{bool}).

1498 '''

1499 return self._xtend

1500

1501 @xtend.setter # PYCHOK setter!

1502 def xtend(self, xtend):

1503 '''Set the option to handle I{degenerate cases} (C{bool}).

1504 '''

1505 self._xtend = bool(xtend)

1506

1507

1508 class _EdgeFHP(object):

1509 # An edge between two L{LatLonFHP} points.

1510

1511 X_INTERSECT = _Enum('Xi', 1) # C++ enum

1512 X_OVERLAP = _Enum('Xo', 5)

1513 P_INTERSECT = _Enum('Pi', 3)

1514 P_OVERLAP = _Enum('Po', 7)

1515 Ps = (P_INTERSECT, P_OVERLAP, X_OVERLAP)

1516 Q_INTERSECT = _Enum('Qi', 2)

1517 Q_OVERLAP = _Enum('Qo', 6)

1518 Qs = (Q_INTERSECT, Q_OVERLAP, X_OVERLAP)

1519 V_INTERSECT = _Enum('Vi', 4)

1520 V_OVERLAP = _Enum('Vo', 8)

1521 Vs = (V_INTERSECT, V_OVERLAP)

1522

1523 def __init__(self, p1, p2, **unused):

1524 # New edge between points C{p1} and C{p2}, each a L{LatLonFHP}.

1525 self._p1_p2 = p1, p2

1526 self._dp = dp = p2 - p1

1527 self._dp2 = dp * dp # dot product, hypot2

1528

1529 self._lr, \

1530 self._bt = _left_right_bottom_top_eps2(p1, p2)

1531

1532 def _intersect3(self, q1, q2):

1533 # Return intersection Type or C{None}

1534 if not (_outside(q1.x, q2.x, *self._lr) or

1535 _outside(q1.y, q2.y, *self._bt)):

1536 dq = q2 - q1

1537 dq2 = dq * dq # dot product, hypot2

1538 if dq2 > EPS2: # like ._clip

1539 T, E = None, _EdgeFHP # self.__class__

1540 p1, p2 = self._p1_p2

1541 ap1 = p1._2A(q1, q2)

1542 ap2_1 = p2._2A(q1, q2) - ap1

1543 if fabs(ap2_1) > _0_EPS: # non-parallel edges

1544 aq1 = q1._2A(p1, p2)

1545 aq2_1 = q2._2A(p1, p2) - aq1

1546 if fabs(aq2_1) > _0_EPS:

1547 # compute and classify alpha and beta

1548 a, a_0, a_0_1, _ = _alpha4(-ap1 / ap2_1)

1549 b, b_0, b_0_1, _ = _alpha4(-aq1 / aq2_1)

1550 # distinguish intersection types

1551 T = E.X_INTERSECT if a_0_1 and b_0_1 else (

1552 E.P_INTERSECT if a_0_1 and b_0 else (

1553 E.Q_INTERSECT if a_0 and b_0_1 else (

1554 E.V_INTERSECT if a_0 and b_0 else None)))

1555

1556 elif fabs(ap1) < _0_EPS: # parallel or colinear edges

1557 dp = self._dp

1558 d1 = q1 - p1

1559 # compute and classify alpha and beta

1560 a, a_0, a_0_1, _a_0_1 = _alpha4((d1 * dp) / self._dp2)

1561 b, b_0, b_0_1, _b_0_1 = _alpha4((d1 * dq) / (-dq2))

1562 # distinguish overlap type

1563 T = E.X_OVERLAP if a_0_1 and b_0_1 else (

1564 E.P_OVERLAP if a_0_1 and _b_0_1 else (

1565 E.Q_OVERLAP if _a_0_1 and b_0_1 else (

1566 E.V_OVERLAP if a_0 and b_0 else None)))

1567

1568 if T:

1569 if T is E.X_INTERSECT:

1570 v = p1 + a * self._dp

1571 yield T, (v, p1, p2, a), (v, q1, q2, b)

1572 elif T in E.Vs:

1573 yield T, (p1,), (q1,)

1574 else:

1575 if T in E.Qs:

1576 yield T, (p1,), (p1, q1, q2, b)

1577 if T in E.Ps:

1578 yield T, (q1, p1, p2, a), (q1,)

1579

1580

1581 class _EdgeGH(object):

1582 # An edge between two L{LatLonGH} points.

1583

1584 _raiser = False

1585 _xtend = False

1586

1587 def __init__(self, s1, s2, raiser=False, xtend=False, **unused):

1588 # New edge between points C{s1} and C{s2}, each a L{LatLonGH}.

1589 self._s1, self._s2 = s1, s2

1590 self._x_sx_y_sy = (s1.x, s2.x - s1.x,

1591 s1.y, s2.y - s1.y)

1592 self._lr, \

1593 self._bt = _left_right_bottom_top_eps2(s1, s2)

1594

1595 if xtend:

1596 self._xtend = True

1597 elif raiser:

1598 self._raiser = True

1599

1600 def _alpha2(self, x, y, dx, dy):

1601 # Return C{(alpha)}, see .points.nearestOn5

1602 a = (y * dy + x * dx) / self._hypot2

1603 d = (y * dx - x * dy) / self._hypot0

1604 return a, fabs(d)

1605

1606 def _Error(self, n, *args, **kwds): # PYCHOK no cover

1607 t = unstr(_EdgeGH.__name__, self._s1, self._s2)

1608 t = _DOT_(t, _EdgeGH._intersect4.__name__)

1609 t = unstr(t, *args, **kwds)

1610 return ClipError(_case_, n, txt=t)

1611

1612 @Property_RO

1613 def _hypot0(self):

1614 _, sx, _, sy = self._x_sx_y_sy

1615 return hypot(sx, sy) * _0_EPS

1616

1617 @Property_RO

1618 def _hypot2(self):

1619 _, sx, _, sy = self._x_sx_y_sy

1620 return hypot2(sx, sy)

1621

1622 def _intersect4(self, c1, c2, parallel=True): # MCCABE 14

1623 # Yield the intersections of this and another edge.

1624

1625 # @return: None, 1 or 2 intersections, each a 4-Tuple

1626 # (y, x, s_alpha, c_alpha) with intersection

1627 # coordinates x and y and both alphas.

1628

1629 # @raise ClipError: Intersection unhandled.

1630

1631 # @see: U{Intersection point of two line segments

1632 # <http://PaulBourke.net/geometry/pointlineplane/>}.

1633 c1_x, c1_y = c1.x, c1.y

1634 if not (_outside(c1_x, c2.x, *self._lr) or

1635 _outside(c1_y, c2.y, *self._bt)):

1636 x, sx, \

1637 y, sy = self._x_sx_y_sy

1638

1639 cx = c2.x - c1_x

1640 cy = c2.y - c1_y

1641 d = cy * sx - cx * sy

1642

1643 if fabs(d) > _0_EPS: # non-parallel edges

1644 dx = x - c1_x

1645 dy = y - c1_y

1646 ca = (sx * dy - sy * dx) / d

1647 if _0_EPS < ca < _EPS_1 or (self._xtend and

1648 _EPS_0 < ca < _1_EPS):

1649 sa = (cx * dy - cy * dx) / d

1650 if _0_EPS < sa < _EPS_1 or (self._xtend and

1651 _EPS_0 < sa < _1_EPS):

1652 yield (y + sa * sy), (x + sa * sx), sa, ca

1653

1654 # unhandled, "degenerate" cases 1, 2 or 3

1655 elif self._raiser and not (sa < _EPS_0 or sa > _1_EPS): # PYCHOK no cover

1656 raise self._Error(1, c1, c2, sa=sa) # intersection at s1 or s2

1657

1658 elif self._raiser and not (ca < _EPS_0 or ca > _1_EPS): # PYCHOK no cover

1659 # intersection at c1 or c2 or at c1 or c2 and s1 or s2

1660 sa = (cx * dy - cy * dx) / d

1661 e = 2 if sa < _EPS_0 or sa > _1_EPS else 3

1662 raise self._Error(e, c1, c2, ca=ca)

1663

1664 elif parallel and (sx or sy) and (cx or cy): # PYCHOK no cover

1665 # non-null, parallel or colinear edges

1666 sa1, d1 = self._alpha2(c1_x - x, c1_y - y, sx, sy)

1667 sa2, d2 = self._alpha2(c2.x - x, c2.y - y, sx, sy)

1668 if max(d1, d2) < _0_EPS:

1669 if self._xtend and not _outside(sa1, sa2, _EPS_0, _1_EPS):

1670 if sa1 > sa2: # anti-parallel

1671 sa1, sa2 = sa2, sa1

1672 ca1, ca2 = _1_0, _0_0

1673 else: # parallel

1674 ca1, ca2 = _0_0, _1_0

1675 ca = fabs((sx / cx) if cx else (sy / cy))

1676 # = hypot(sx, sy) / hypot(cx, cy)

1677 if sa1 < 0: # s1 is between c1 and c2

1678 ca *= ca1 + sa1

1679 yield y, x, ca1, _alpha1(ca)

1680 else: # c1 is between s1 and s2

1681 yield (y + sa1 * sy), (x + sa1 * sx), sa1, ca1

1682 if sa2 > 1: # s2 is between c1 and c2

1683 ca *= sa2 - _1_0

1684 yield (y + sy), (x + sx), ca2, _alpha1(ca2 - ca)

1685 else: # c2 is between s1 and s2

1686 yield (y + sa2 * sy), (x + sa2 * sx), sa2, ca2

1687 elif self._raiser and not _outside(sa1, sa2, _0_0, _1_EPS):

1688 raise self._Error(4, c1, c2, d1=d1, d2=d2)

1689

1690

1691 class _BooleanBase(object):

1692 # Shared C{Boolean[FHP|GH]} methods.

1693

1694 def __add__(self, other):

1695 '''Sum: C{this + other} clips.

1696 '''

1697 return self._sum(_other(self, other), self.__add__) # PYCHOK OK

1698

1699 def __and__(self, other):

1700 '''Intersection: C{this & other}.

1701 '''

1702 return self._boolean(other, False, False, self.__and__) # PYCHOK OK

1703

1704 def __iadd__(self, other):

1705 '''In-place sum: C{this += other} clips.

1706 '''

1707 return self._inplace(self.__add__(other))

1708

1709 def __iand__(self, other):

1710 '''In-place intersection: C{this &= other}.

1711 '''

1712 return self._inplace(self.__and__(other))

1713

1714 def __ior__(self, other):

1715 '''In-place union: C{this |= other}.

1716 '''

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

1718

1719 def __or__(self, other):

1720 '''Union: C{this | other}.

1721 '''

1722 return self._boolean(other, True, True, self.__or__) # PYCHOK OK

1723

1724 def __radd__(self, other):

1725 '''Reverse sum: C{other + this} clips.

1726 '''

1727 return _other(self, other)._sum(self, self.__radd__)

1728

1729 def __rand__(self, other):

1730 '''Reverse intersection: C{other & this}

1731 '''

1732 return _other(self, other).__and__(self)

1733

1734 def __ror__(self, other):

1735 '''Reverse union: C{other | this}

1736 '''

1737 return _other(self, other).__or__(self)

1738

1739 def _boolean4(self, other, op):

1740 # Set up a new C{Boolean[FHP|GH]}.

1741 C = self.__class__

1742 kwds = C._kwds(self, op)

1743 a = C(self, **kwds)

1744 b = _other(self, other)

1745 return a, b, C, kwds

1746

1747 def _inplace(self, r):

1748 # Replace this with a L{Boolean*} result.

1749 self._clips, r._clips = r._clips, None

1750# if self._raiser != r._raiser:

1751# self._raiser = r._raiser

1752# if self._xtend != r._xtend:

1753# self._xtend = r._xtend

1754# if self._eps != r._eps:

1755# self._eps = r._eps

1756 return self

1757

1758

1759 class BooleanFHP(_CompositeFHP, _BooleanBase):

1760 '''I{Composite} class providing I{boolean} operations between two

1761 I{composites} using U{Forster-Hormann-Popa<https://www.ScienceDirect.com/

1762 science/article/pii/S259014861930007X>}'s C++ implementation, transcoded

1763 to pure Python.

1764

1765 The supported operations between (composite) polygon A and B are:

1766

1767 - C = A & B or A &= B, intersection of A and B

1768

1769 - C = A + B or A += B, sum of A and B clips

1770

1771 - C = A | B or A |= B, union of A and B

1772

1773 - A == B or A != B, equivalent A and B clips

1774

1775 - A.isequalTo(B, eps), equivalent within tolerance

1776

1777 @see: Methods C{__eq__} and C{isequalTo}, function L{clipFHP4}

1778 and class L{BooleanGH}.

1779 '''

1780 _kind = _boolean_

1781

1782 def __init__(self, lls, raiser=False, eps=EPS, name=NN):

1783 '''New L{BooleanFHP} operand for I{boolean} operation.

1784

1785 @arg lls: The polygon points and clips (iterable of L{LatLonFHP}s,

1786 L{ClipFHP4Tuple}s or other C{LatLon}s).

1787 @kwarg raiser: If C{True}, throw L{ClipError} exceptions (C{bool}).

1788 @kwarg esp: Tolerance for eliminating null edges (C{degrees}, same

1789 units as the B{C{lls}} coordinates).

1790 @kwarg name: Optional name (C{str}).

1791 '''

1792 _CompositeFHP.__init__(self, lls, raiser=raiser,

1793 eps=eps, name=name)

1794

1795 def __isub__(self, other):

1796 '''Not implemented.'''

1797 return _NotImplemented(self, other)

1798

1799 def __rsub__(self, other):

1800 '''Not implemented.'''

1801 return _NotImplemented(self, other)

1802

1803 def __sub__(self, other):

1804 '''Not implemented.'''

1805 return _NotImplemented(self, other)

1806

1807 def _boolean(self, other, Union, unused, op):

1808 # One C{BooleanFHP} operation.

1809 p, q, C, kwds = self._boolean4(other, op)

1810 r = p._clip(q, Union=Union, **kwds)

1811 return C(r, **kwds)

1812

1813

1814 class BooleanGH(_CompositeGH, _BooleanBase):

1815 '''I{Composite} class providing I{boolean} operations between two

1816 I{composites} using the U{Greiner-Hormann<http://www.Inf.USI.CH/

1817 hormann/papers/Greiner.1998.ECO.pdf>} algorithm and U{Correia

1818 <https://GitHub.com/helderco/univ-polyclip>}'s implementation,

1819 modified and extended.

1820

1821 The supported operations between (composite) polygon A and B are:

1822

1823 - C = A - B or A -= B, difference A less B

1824

1825 - C = B - A or B -= A, difference B less B

1826

1827 - C = A & B or A &= B, intersection of A and B

1828

1829 - C = A + B or A += B, sum of A and B clips

1830

1831 - C = A | B or A |= B, union of A and B

1832

1833 - A == B or A != B, equivalent A and B clips

1834

1835 - A.isequalTo(B, eps), equivalent within tolerance

1836

1837 @note: To handle I{degenerate cases} like C{point-edge} and

1838 C{point-point} intersections, use class L{BooleanFHP}.

1839

1840 @see: Methods C{__eq__} and C{isequalTo}, function L{clipGH4}

1841 and class L{BooleanFHP}.

1842 '''

1843 _kind = _boolean_

1844

1845 def __init__(self, lls, raiser=True, xtend=False, eps=EPS, name=NN):

1846 '''New L{BooleanFHP} operand for I{boolean} operation.

1847

1848 @arg lls: The polygon points and clips (iterable of L{LatLonGH}s,

1849 L{ClipGH4Tuple}s or other C{LatLon}s).

1850 @kwarg raiser: If C{True}, throw L{ClipError} exceptions (C{bool}).

1851 @kwarg xtend: If C{True}, extend edges of I{degenerate cases}, an

1852 attempt to handle the latter (C{bool}).

1853 @kwarg esp: Tolerance for eliminating null edges (C{degrees}, same

1854 units as the B{C{lls}} coordinates).

1855 @kwarg name: Optional name (C{str}).

1856 '''

1857 _CompositeGH.__init__(self, lls, raiser=raiser, xtend=xtend,

1858 eps=eps, name=name)

1859

1860 def _boolean(self, other, s_entry, c_entry, op):

1861 # One C{BooleanGH} operation.

1862 s, c, C, kwds = self._boolean4(other, op)

1863 r = s._clip(c, s_entry, c_entry, **kwds)

1864 return C(r, **kwds)

1865

1866 def __isub__(self, other):

1867 '''In-place difference: C{this -= other}.

1868 '''

1869 return self._inplace(self.__sub__(other))

1870

1871 def __rsub__(self, other):

1872 ''' Reverse difference: C{other - this}

1873 '''

1874 return _other(self, other).__sub__(self)

1875

1876 def __sub__(self, other):

1877 '''Difference: C{this - other}.

1878 '''

1879 return self._boolean(other, True, False, self.__sub__)

1880

1881

1882 def _alpha1(alpha):

1883 # Return C{alpha} in C{[0..1]} range

1884 if _EPS_0 < alpha < _1_EPS:

1885 return max(_0_0, min(alpha, _1_0))

1886 t = _not_(Fmt.SQUARE(_ELLIPSIS_(0, 1)))

1887 raise ClipError(_alpha_, alpha, txt=t)

1888

1889

1890 def _alpha4(a):

1891 # Return 4-tuple (alpha, -EPS < alpha < EPS,

1892 # 0 < alpha < 1,

1893 # not 0 < alpha < 1)

1894 return (a, False, True, False) if _0_EPS < a < _EPS_1 else (

1895 (a, False, False, True) if _0_EPS < fabs(a) else

1896 (a, True, False, False))

1897

1898

1899 def _Cps(Cp, composites_points, where):

1900 # Yield composites and points as a C{Cp} composite.

1901 try:

1902 kwds = dict(kind=_points_, name=where.__name__)

1903 for cp in composites_points:

1904 yield cp if isBoolean(cp) else Cp(cp, **kwds)

1905 except (AttributeError, ClipError, TypeError, ValueError) as x:

1906 raise _ValueError(points=cp, cause=x)

1907

1908

1909 def _eps0(eps):

1910 # Adjust C{eps} or C{None}.

1911 return eps if eps and eps > EPS else 0

1912

1913

1914 def isBoolean(obj):

1915 '''Check for C{Boolean} composites.

1916

1917 @arg obj: The object (any C{type}).

1918

1919 @return: C{True} if B{C{obj}} is L{BooleanFHP},

1920 L{BooleanGH} oe some other composite,

1921 C{False} otherwise.

1922 '''

1923 return isinstance(obj, _CompositeBase)

1924

1925

1926 def _left_right_bottom_top_eps2(p1, p2):

1927 '''(INTERNAL) Return 2-tuple C{(left, right), (bottom, top)}, oversized.

1928 '''

1929 return (_min_max_eps2(p1.x, p2.x),

1930 _min_max_eps2(p1.y, p2.y))

1931

1932

1933 def _low_high_eps2(lo, hi, eps):

1934 '''(INTERNAL) Return 2-tuple C{(lo, hi)}, oversized.

1935 '''

1936 lo *= (_1_0 + eps) if lo < 0 else (_1_0 - eps)

1937 hi *= (_1_0 - eps) if hi < 0 else (_1_0 + eps)

1938 return (lo or -eps), (hi or eps)

1939

1940

1941 def _min_max_eps2(*xs):

1942 '''(INTERNAL) Return 2-tuple C{(min, max)}, oversized.

1943 '''

1944 lo, hi = min(xs), max(xs)

1945 lo *= _1_EPS if lo < 0 else _EPS_1

1946 hi *= _EPS_1 if hi < 0 else _1_EPS

1947 return (lo or _EPS_0), (hi or _0_EPS)

1948

1949

1950 def _other(this, other):

1951 '''(INTERNAL) Check for compatible C{type}s.

1952 '''

1953 C = this.__class__

1954 if isinstance(other, C):

1955 return other

1956 raise _IsnotError(C.__name__, other=other)

1957

1958

1959 def _outside(x1, x2, lo, hi):

1960 '''(INTERNAL) Is C{(x1, x2)} outside C{(lo, hi)}?

1961 '''

1962 return max(x1, x2) < lo or min(x1, x2) > hi

1963

1964

1965__all__ += _ALL_DOCS(_BooleanBase, _Clip,

1966 _CompositeBase, _CompositeFHP, _CompositeGH,

1967 _LatLonBool)

1968

1969# **) MIT License

1970#

1971# Copyright (C) 2018-2023 -- mrJean1 at Gmail -- All Rights Reserved.

1972#

1973# Permission is hereby granted, free of charge, to any person obtaining a

1974# copy of this software and associated documentation files (the "Software"),

1975# to deal in the Software without restriction, including without limitation

1976# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1977# and/or sell copies of the Software, and to permit persons to whom the

1978# Software is furnished to do so, subject to the following conditions:

1979#

1980# The above copyright notice and this permission notice shall be included

1981# in all copies or substantial portions of the Software.

1982#

1983# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1984# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1985# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1986# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1987# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1988# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1989# OTHER DEALINGS IN THE SOFTWARE.

1990

1991# ***) GNU GPL 3

1992#

1993# Copyright (C) 2011-2012 Helder Correia <Helder.MC@Gmail.com>

1994#

1995# This program is free software: you can redistribute it and/or

1996# modify it under the terms of the GNU General Public License as

1997# published by the Free Software Foundation, either version 3 of

1998# the License, or any later version.

1999#

2000# This program is distributed in the hope that it will be useful,

2001# but WITHOUT ANY WARRANTY; without even the implied warranty of

2002# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the

2003# GNU General Public License for more details.

2004#

2005# You should have received a copy of the GNU General Public License

2006# along with this program. If not, see <http://www.GNU.org/licenses/>.

2007#

2008# You should have received the README file along with this program.

2009# If not, see <https://GitHub.com/helderco/univ-polyclip>.