Coverage for pygeodesy/booleans.py: 94%
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« prev ^ index » next coverage.py v7.2.2, created at 2024-06-10 14:08 -0400
2# -*- coding: utf-8 -*-
4u'''I{Boolean} operations on I{composite} polygons and I{clip}s.
6Classes L{BooleanFHP} and L{BooleanGH} are I{composites} and
7provide I{boolean} operations C{intersection}, C{difference},
8C{reverse-difference}, C{sum} and C{union}.
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.
13@see: U{Forster-Hormann-Popa<https://www.ScienceDirect.com/science/
14 article/pii/S259014861930007X>} and U{Greiner-Hormann
15 <http://www.Inf.USI.CH/hormann/papers/Greiner.1998.ECO.pdf>}.
16'''
17# make sure int/int division yields float quotient, see .basics
18from __future__ import division as _; del _ # PYCHOK semicolon
20from pygeodesy.basics import isodd, issubclassof, map2, _xscalar
21from pygeodesy.constants import EPS, EPS2, INT0, _0_0, _0_5, _1_0
22from pygeodesy.errors import ClipError, _IsnotError, _TypeError, \
23 _ValueError, _xattr, _xkwds_get, _xkwds_pop2
24from pygeodesy.fmath import favg, hypot, hypot2
25# from pygeodesy.fsums import fsum1 # _MODS
26from pygeodesy.interns import NN, _BANG_, _clip_, _clipid_, _COMMASPACE_, \
27 _composite_, _DOT_, _e_, _ELLIPSIS_, _few_, \
28 _height_, _lat_, _LatLon_, _lon_, _not_, \
29 _points_, _SPACE_, _too_, _X_, _x_, \
30 _B_, _d_, _R_ # PYCHOK used!
31from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
32from pygeodesy.latlonBase import LatLonBase, \
33 LatLon2Tuple, Property_RO, property_RO
34from pygeodesy.named import _name__, _Named, _NotImplemented, \
35 Fmt, pairs, unstr
36# from pygeodesy.namedTuples import LatLon2Tupe # from .latlonBase
37# from pygeodesy.points import boundsOf # _MODS
38# from pygeodesy.props import Property_RO, property_RO # from .latlonBase
39# from pygeodesy.streprs import Fmt, pairs, unstr # from .named
40from pygeodesy.units import Height, HeightX
41from pygeodesy.utily import fabs, _unrollon, _Wrap
43# from math import fabs # from .utily
45__all__ = _ALL_LAZY.booleans
46__version__ = '24.06.06'
48_0_EPS = EPS # near-zero, positive
49_EPS_0 = -EPS # near-zero, negative
50_1_EPS = _1_0 + EPS # near-one, over
51_EPS_1 = _1_0 - EPS # near-one, under
52_10EPS = EPS * 10 # see ._2Abs, ._10eps
54_alpha_ = 'alpha'
55_boolean_ = 'boolean'
56_case_ = 'case'
57_corners_ = 'corners'
58_duplicate_ = 'duplicate'
59_open_ = 'open'
62def _Enum(txt, enum): # PYCHOK unused
63 return txt # NN(txt, _TILDE_, enum)
66class _L(object): # Intersection labels
67 CROSSING = _Enum(_X_, 1) # C++ enum
68 CROSSING_D = _Enum(_X_ + _d_, 8)
69 CROSSINGs = (CROSSING, CROSSING_D)
70 BOUNCING = _Enum(_B_, 2)
71 BOUNCING_D = _Enum(_B_ + _d_, 9)
72 BOUNCINGs = (BOUNCING, BOUNCING_D) + CROSSINGs
73 LEFT_ON = _Enum('Lo', 3)
74 ON_ON = _Enum('oo', 5)
75 ON_LEFT = _Enum('oL', 6)
76 ON_RIGHT = _Enum('oR', 7)
77 RIGHT_ON = _Enum('Ro', 4)
78 RIGHT_LEFT_ON = (RIGHT_ON, LEFT_ON)
79 # Entry/Exit flags
80 ENTRY = _Enum(_e_, 1)
81 EXIT = _Enum(_x_, 0)
82 Toggle = {ENTRY: EXIT,
83 EXIT: ENTRY,
84 None: None}
86_L = _L() # PYCHOK singleton
89class _RP(object): # RelativePositions
90 IS_Pm = _Enum('Pm', 2) # C++ enum
91 IS_Pp = _Enum('Pp', 3)
92 LEFT = _Enum('L', 0)
93 RIGHT = _Enum(_R_, 1)
95_RP = _RP() # PYCHOK singleton
97_RP2L = {(_RP.LEFT, _RP.RIGHT): _L.CROSSING,
98 (_RP.RIGHT, _RP.LEFT): _L.CROSSING,
99 (_RP.LEFT, _RP.LEFT): _L.BOUNCING,
100 (_RP.RIGHT, _RP.RIGHT): _L.BOUNCING,
101 # overlapping cases
102 (_RP.RIGHT, _RP.IS_Pp): _L.LEFT_ON,
103 (_RP.IS_Pp, _RP.RIGHT): _L.LEFT_ON,
104 (_RP.LEFT, _RP.IS_Pp): _L.RIGHT_ON,
105 (_RP.IS_Pp, _RP.LEFT): _L.RIGHT_ON,
106 (_RP.IS_Pm, _RP.IS_Pp): _L.ON_ON,
107 (_RP.IS_Pp, _RP.IS_Pm): _L.ON_ON,
108 (_RP.IS_Pm, _RP.RIGHT): _L.ON_LEFT,
109 (_RP.RIGHT, _RP.IS_Pm): _L.ON_LEFT,
110 (_RP.LEFT, _RP.IS_Pm): _L.ON_RIGHT,
111 (_RP.IS_Pm, _RP.LEFT): _L.ON_RIGHT}
114class _LatLonBool(_Named):
115 '''(INTERNAL) Base class for L{LatLonFHP} and L{LatLonGH}.
116 '''
117 _alpha = None # point AND intersection else length
118 _checked = False # checked in phase 3 iff intersection
119 _clipid = INT0 # (polygonal) clip identifier, number
120 _dupof = None # original of a duplicate
121# _e_x_str = NN # shut up PyChecker
122 _height = Height(0) # interpolated height, usually meter
123 _linked = None # link to neighbor iff intersection
124 _next = None # link to the next vertex
125 _prev = None # link to the previous vertex
127 def __init__(self, lat_ll, lon=None, height=0, clipid=INT0, wrap=False, **name):
128 '''New C{LatLon[FHP|GH]} from separate C{lat}, C{lon}, C{height} and C{clipid}
129 scalars or from a previous C{LatLon[FHP|GH]}, C{Clip[FHP|GH]4Tuple} or some
130 other C{LatLon} instance.
132 @arg lat_ll: Latitude (C{scalar}) or a lat-/longitude (C{LatLon[FHP|GH]},
133 C{Clip[FHP|GH]4Tuple} or some other C{LatLon}).
134 @kwarg lon: Longitude (C{scalar}), iff B{C{lat_ll}} is scalar, ignored
135 otherwise.
136 @kwarg height: Height (C{scalar}), conventionally C{meter}.
137 @kwarg clipid: Clip identifier (C{int}).
138 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{lat}} and B{C{lon}} (C{bool}).
139 @kwarg name: Optional C{B{name}=NN} (C{str}).
140 '''
141 h, name = _xkwds_pop2(name, h=height) if name else (height, name)
143 if lon is None:
144 y, x = lat_ll.lat, lat_ll.lon
145 h = _xattr(lat_ll, height=h)
146 c = _xattr(lat_ll, clipid=clipid)
147 else:
148 y, x, c = lat_ll, lon, clipid
149 self.y, self.x = _Wrap.latlon(y, x) if wrap else (y, x)
150 # don't duplicate defaults
151 if self._height != h:
152 self._height = h
153 if self._clipid != c:
154 self._clipid = c
155 if name:
156 self.name = name
158 def __abs__(self):
159 return max(fabs(self.x), fabs(self.y))
161 def __eq__(self, other):
162 return other is self or bool(_other(self, other) and
163 other.x == self.x and
164 other.y == self.y)
166 def __ne__(self, other): # required for Python 2
167 return not self.__eq__(other)
169 def __repr__(self):
170 '''String C{repr} of this lat-/longitude.
171 '''
172 if self._prev or self._next:
173 t = _ELLIPSIS_(self._prev, self._next)
174 t = _SPACE_(self, Fmt.ANGLE(t))
175 else:
176 t = str(self)
177 return t
179 def __str__(self):
180 '''String C{str} of this lat-/longitude.
181 '''
182 t = (_lat_, self.lat), (_lon_, self.lon)
183 if self._height:
184 X = _X_ if self.isintersection else NN
185 t += (_height_ + X, self._height),
186 if self._clipid:
187 t += (_clipid_, self._clipid),
188 if self._alpha is not None:
189 t += (_alpha_, self._alpha),
190# if self._dupof: # recursion risk
191# t += (_dupof_, self._dupof.name),
192 t = pairs(t, prec=8, fmt=Fmt.g, ints=True)
193 t = Fmt.PAREN(_COMMASPACE_.join(t))
194 if self._linked:
195 k = _DOT_ if self._checked else _BANG_
196 t = NN(t, self._e_x_str(k)) # PYCHOK expected
197 return NN(self.name, t)
199 def __sub__(self, other):
200 _other(self, other)
201 return self.__class__(self.y - other.y, # classof
202 self.x - other.x)
204 def _2A(self, p2, p3):
205 # I{Signed} area of a triangle, I{doubled}.
206 x, y = self.x, self.y
207 return (p2.x - x) * (p3.y - y) - \
208 (p3.x - x) * (p2.y - y)
210 def _2Abs(self, p2, p3, eps=_10EPS):
211 # I{Unsigned} area of a triangle, I{doubled}
212 # or 0 if below the given threshold C{eps}.
213 a = fabs(self._2A(p2, p3))
214 return 0 if a < eps else a
216 @property_RO
217 def clipid(self):
218 '''Get the I{clipid} (C{int} or C{0}).
219 '''
220 return self._clipid
222 def _equi(self, llb, eps):
223 # Is this LLB I{equivalent} to B{C{llb}} within
224 # the given I{non-negative} tolerance B{C{eps}}?
225 return not (fabs(llb.lon - self.x) > eps or
226 fabs(llb.lat - self.y) > eps)
228 @property_RO
229 def height(self):
230 '''Get the I{height} (C{Height} or C{int}).
231 '''
232 h = self._height
233 return HeightX(h) if self.isintersection else (
234 Height(h) if h else _LatLonBool._height)
236 def isequalTo(self, other, eps=None):
237 '''Is this point equal to an B{C{other}} within a given,
238 I{non-negative} tolerance, ignoring C{height}?
240 @arg other: The other point (C{LatLon}).
241 @kwarg eps: Tolerance for equality (C{degrees} or C{None}).
243 @return: C{True} if equivalent, C{False} otherwise (C{bool}).
245 @raise TypeError: Invalid B{C{other}}.
246 '''
247 try:
248 return self._equi(other, _eps0(eps))
249 except (AttributeError, TypeError, ValueError):
250 raise _IsnotError(_LatLon_, other=other)
252 @property_RO
253 def isintersection(self):
254 '''Is this an intersection? May be C{ispoint} too!
255 '''
256 return bool(self._linked)
258 @property_RO
259 def ispoint(self):
260 '''Is this an I{original} point? May be C{isintersection} too!
261 '''
262 return self._alpha is None
264 @property_RO
265 def lat(self):
266 '''Get the latitude (C{scalar}).
267 '''
268 return self.y
270 @property_RO
271 def latlon(self):
272 '''Get the lat- and longitude (L{LatLon2Tuple}).
273 '''
274 return LatLon2Tuple(self.y, self.x)
276 def _link(self, other):
277 # Make this and an other point neighbors.
278 # assert _other(self, other)
279 self._linked = other
280 other._linked = self
282 @property_RO
283 def lon(self):
284 '''Get the longitude (C{scalar}).
285 '''
286 return self.x
288 def _toClas(self, Clas, clipid):
289 # Return this vertex as a C{Clas} instance
290 # (L{Clip[FHP|GH]4Tuple} or L{LatLon[FHP|GH]}).
291 return Clas(self.lat, self.lon, self.height, clipid)
294class LatLonFHP(_LatLonBool):
295 '''A point or intersection in a L{BooleanFHP} clip or composite.
296 '''
297 _en_ex = None
298 _label = None
299 _2split = None # or C{._Clip}
300 _2xing = False
302 def __init__(self, lat_ll, lon=None, height=0, clipid=INT0, **wrap_name):
303 '''New C{LatLonFHP} from separate C{lat}, C{lon}, C{h}eight and C{clipid}
304 scalars, or from a previous L{LatLonFHP}, L{ClipFHP4Tuple} or some other
305 C{LatLon} instance.
307 @arg lat_ll: Latitude (C{scalar}) or a lat-/longitude (L{LatLonFHP},
308 L{ClipFHP4Tuple} or some other C{LatLon}).
310 @see: L{Here<_LatLonBool.__init__>} for further details.
311 '''
312 _LatLonBool.__init__(self, lat_ll, lon, height, clipid, **wrap_name)
314 def __add__(self, other):
315 _other(self, other)
316 return self.__class__(self.y + other.y, self.x + other.x)
318 def __mod__(self, other): # cross product
319 _other(self, other)
320 return self.x * other.y - self.y * other.x
322 def __mul__(self, other): # dot product
323 _other(self, other)
324 return self.x * other.x + self.y * other.y
326 def __rmul__(self, other): # scalar product
327 _xscalar(other=other)
328 return self.__class__(self.y * other, self.x * other)
330 def _e_x_str(self, t): # PYCHOK no cover
331 if self._label:
332 t = NN(self._label, t)
333 if self._en_ex:
334 t = NN(t, self._en_ex)
335 return t
337 @property_RO
338 def _isduplicate(self):
339 # Is this point a I{duplicate} intersection?
340 p = self._dupof
341 return bool(p and self._linked
342 and p is not self
343 and p == self
344# and p._alpha in (None, self._alpha)
345 and self._alpha in (_0_0, p._alpha))
347# @property_RO
348# def _isduplicated(self):
349# # Return the number of I{duplicates}?
350# d, v = 0, self
351# while v:
352# if v._dupof is self:
353# d += 1
354# v = v._next
355# if v is self:
356# break
357# return d
359 def isenclosedBy(self, *composites_points, **wrap):
360 '''Is this point inside one or more composites or polygons based on
361 the U{winding number<https://www.ScienceDirect.com/science/article/
362 pii/S0925772101000128>}?
364 @arg composites_points: Composites and/or iterables of points
365 (L{ClipFHP4Tuple}, L{ClipGH4Tuple}, L{LatLonFHP},
366 L{LatLonGH} or any C{LatLon}).
367 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True},
368 wrap or I{normalize} and unroll all C{points} (C{bool}).
370 @raise ValueError: Some C{points} invalid.
372 @see: U{Algorithm 6<https://www.ScienceDirect.com/science/
373 article/pii/S0925772101000128>}.
374 '''
375 class _Pseudo(object):
376 # Pseudo-_CompositeBase._clips tuple
378 @property_RO
379 def _clips(self):
380 for cp in _Cps(_CompositeFHP, composites_points,
381 LatLonFHP.isenclosedBy): # PYCHOK yield
382 for c in cp._clips:
383 yield c
385 return self._isinside(_Pseudo(), **wrap)
387 def _isinside(self, composite, *excludes, **wrap):
388 # Is this point inside a composite, excluding
389 # certain C{_Clip}s? I{winding number}?
390 x, y, i = self.x, self.y, False
391 for c in composite._clips:
392 if c not in excludes:
393 w = 0
394 for p1, p2 in c._edges2(**wrap):
395 # edge [p1,p2] must straddle y
396 if (p1.y < y) is not (p2.y < y): # or ^
397 r = p2.x > x
398 s = p2.y > p1.y
399 if p1.x < x:
400 b = r and (s is (p1._2A(p2, self) > 0))
401 else:
402 b = r or (s is (p1._2A(p2, self) > 0))
403 if b:
404 w += 1 if s else -1
405 if isodd(w):
406 i = not i
407 return i
409 @property_RO
410 def _prev_next2(self):
411 # Adjust 2-tuple (._prev, ._next) iff a I{duplicate} intersection
412 p, n = self, self._next
413 if self._isduplicate:
414 p = self._dupof
415 while p._isduplicate:
416 p = p._dupof
417 while n._isduplicate:
418 n = n._next
419 return p._prev, n
421# def _edge2(self):
422# # Return the start and end point of the
423# # edge containing I{intersection} C{v}.
424# n = p = self
425# while p.isintersection:
426# p = p._prev
427# if p is self:
428# break
429# while n.isintersection:
430# n = n._next
431# if n is self:
432# break
433# # assert p == self or not p._2Abs(self, n)
434# return p, n
436 def _RPoracle(self, p1, p2, p3):
437 # Relative Position oracle
438 if p1._linked is self: # or p1._linked2(self):
439 T = _RP.IS_Pm
440 elif p3._linked is self: # or p3._linked2(self):
441 T = _RP.IS_Pp
442 elif p1._2A(p2, p3) > 0: # left turn
443 T = _RP.LEFT if self._2A(p1, p2) > 0 and \
444 self._2A(p2, p3) > 0 else \
445 _RP.RIGHT # PYCHOK indent
446 else: # right turn (or straight)
447 T = _RP.RIGHT if self._2A(p1, p2) < 0 and \
448 self._2A(p2, p3) < 0 else \
449 _RP.LEFT # PYCHOK indent
450 return T
453class LatLonGH(_LatLonBool):
454 '''A point or intersection in a L{BooleanGH} clip or composite.
455 '''
456 _entry = None # entry or exit iff intersection
458 def __init__(self, lat_ll, lon=None, height=0, clipid=INT0, **wrap_name):
459 '''New C{LatLonGH} from separate C{lat}, C{lon}, C{h}eight and C{clipid}
460 scalars, or from a previous L{LatLonGH}, L{ClipGH4Tuple} or some other
461 C{LatLon} instance.
463 @arg lat_ll: Latitude (C{scalar}) or a lat-/longitude (L{LatLonGH},
464 L{ClipGH4Tuple} or some other C{LatLon}).
466 @see: L{Here<_LatLonBool.__init__>} for further details.
467 '''
468 _LatLonBool.__init__(self, lat_ll, lon, height, clipid, **wrap_name)
470 def _check(self):
471 # Check-mark this vertex and its link.
472 self._checked = True
473 k = self._linked
474 if k and not k._checked:
475 k._checked = True
477 def _e_x_str(self, t): # PYCHOK no cover
478 return t if self._entry is None else NN(t,
479 (_e_ if self._entry else _x_))
481 def isenclosedBy(self, *composites_points, **wrap):
482 '''Is this point inside one or more composites or polygons based
483 on the U{even-odd-rule<https://www.ScienceDirect.com/science/
484 article/pii/S0925772101000128>}?
486 @arg composites_points: Composites and/or iterables of points
487 (L{ClipFHP4Tuple}, L{ClipGH4Tuple}, L{LatLonFHP},
488 L{LatLonGH} or any C{LatLon}).
489 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True},
490 wrap or I{normalize} and unroll all C{points} (C{bool}).
492 @raise ValueError: Some B{C{points}} invalid.
493 '''
494 class _Pseudo(object):
495 # Pseudo-_CompositeBase._edges3 method
497 def _edges3(self, **kwds):
498 for cp in _Cps(_CompositeGH, composites_points,
499 LatLonGH.isenclosedBy): # PYCHOK yield
500 for e in cp._edges3(**kwds):
501 yield e
503 return self._isinside(_Pseudo(), **wrap)
505 def _isinside(self, composite, *bottom_top, **wrap):
506 # Is this vertex inside the composite? I{even-odd rule}?
508 def _x(y, p1, p2):
509 # return C{x} at given C{y} on edge [p1,p2]
510 return (y - p1.y) / (p2.y - p1.y) * (p2.x - p1.x)
512 # The I{even-odd} rule counts the number of edges
513 # intersecting a ray emitted from this point to
514 # east-bound infinity. When I{odd} this point lies
515 # inside, if I{even} outside.
516 y, i = self.y, False
517 if not (bottom_top and _outside(y, y, *bottom_top)):
518 x = self.x
519 for p1, p2, _ in composite._edges3(**wrap):
520 if (p1.y < y) is not (p2.y < y): # or ^
521 r = p2.x > x
522 if p1.x < x:
523 b = r and (_x(y, p1, p2) > x)
524 else:
525 b = r or (_x(y, p1, p2) > x)
526 if b:
527 i = not i
528 return i
531class _Clip(_Named):
532 '''(INTERNAL) A I{doubly-linked} list representing a I{closed}
533 polygon of L{LatLonFHP} or L{LatLonGH} points, duplicates
534 and intersections with other clips.
535 '''
536 _composite = None
537 _dups = 0
538 _first = None
539 _id = 0
540 _identical = False
541 _noInters = False
542 _last = None
543 _LL = None
544 _len = 0
545 _pushback = False
547 def __init__(self, composite, clipid=INT0):
548 '''(INTERNAL) New C{_Clip}.
549 '''
550 # assert isinstance(composite, _CompositeBase)
551 if clipid in composite._clipids:
552 raise ClipError(clipid=clipid, txt=_duplicate_)
553 self._composite = composite
554 self._id = clipid
555 self._LL = composite._LL
556 composite._clips = composite._clips + (self,)
558 def __contains__(self, point): # PYCHOK no cover
559 '''Is the B{C{point}} in this clip?
560 '''
561 for v in self:
562 if v is point: # or ==?
563 return True
564 return False
566 def __eq__(self, other):
567 '''Is this clip I{equivalent} to an B{C{other}} clip,
568 do both have the same C{len}, the same points, in
569 the same order, possibly rotated?
570 '''
571 return self._equi(_other(self, other), 0)
573 def __ge__(self, other):
574 '''See method C{__lt__}.
575 '''
576 return not self.__lt__(other)
578 def __gt__(self, other):
579 '''Is this clip C{"above"} an B{C{other}} clip,
580 located or stretched farther North or East?
581 '''
582 return self._bltr4 > _other(self, other)._bltr4
584 def __hash__(self): # PYCHOK no over
585 return hash(self._bltr4)
587 def __iter__(self):
588 '''Yield the points, duplicates and intersections.
589 '''
590 v = f = self._first
591 while v:
592 yield v
593 v = v._next
594 if v is f:
595 break
597 def __le__(self, other):
598 '''See method C{__gt__}.
599 '''
600 return not self.__gt__(other)
602 def __len__(self):
603 '''Return the number of points, duplicates and
604 intersections in this clip.
605 '''
606 return self._len
608 def __lt__(self, other):
609 '''Is this clip C{"below"} an B{C{other}} clip,
610 located or stretched farther South or West?
611 '''
612 return self._bltr4 < _other(self, other)._bltr4
614 def __ne__(self, other): # required for Python 2
615 '''See method C{__eq__}.
616 '''
617 return not self.__eq__(other)
619 _all = __iter__
621 @property_RO
622 def _all_ON_ON(self):
623 # Check whether all vertices are ON_ON.
624 L_ON_ON = _L.ON_ON
625 return all(v._label is L_ON_ON for v in self)
627 def _append(self, y_v, *x_h_clipid):
628 # Append a point given as C{y}, C{x}, C{h}eight and
629 # C{clipid} args or as a C{LatLon[FHP|GH]}.
630 self._last = v = self._LL(y_v, *x_h_clipid) if x_h_clipid else y_v
631 self._len += 1
632 # assert v._clipid == self._id
634 v._next = n = self._first
635 if n is None: # set ._first
636 self._first = p = n = v
637 else: # insert before ._first
638 v._prev = p = n._prev
639 p._next = n._prev = v
640 return v
642# def _appendedup(self, v, clipid=0):
643# # Like C{._append}, but only append C{v} if not a
644# # duplicate of the one previously append[edup]'ed.
645# y, x, p = v.y, v.x, self._last
646# if p is None or y != p.y or x != p.x or clipid != p._clipid:
647# p = self._append(y, x, v._height, clipid)
648# if v._linked:
649# p._linked = True # to force errors
650# return p
652 @Property_RO
653 def _bltr4(self):
654 # Get the bounds as 4-tuple C{(bottom, left, top, right)}.
655 return map2(float, _MODS.points.boundsOf(self, wrap=False))
657 def _bltr4eps(self, eps):
658 # Get the ._bltr4 bounds tuple, slightly oversized.
659 if eps > 0: # > EPS
660 yb, xl, yt, xr = self._bltr4
661 yb, yt = _low_high_eps2(yb, yt, eps)
662 xl, xr = _low_high_eps2(xl, xr, eps)
663 t = yb, xl, yt, xr
664 else:
665 t = self._bltr4
666 return t
668 def _closed(self, raiser): # PYCHOK unused
669 # End a clip, un-close it and check C{len}.
670 p, f = self._last, self._first
671 if f and f._prev is p and p is not f and \
672 p._next is f and p == f: # PYCHOK no cover
673 # un-close the clip
674 f._prev = p = p._prev
675 p._next = f
676 self._len -= 1
677# elif f and raiser:
678# raise self._OpenClipError(p, f)
679 if len(self) < 3:
680 raise self._Error(_too_(_few_))
682 def _dup(self, q):
683 # Duplicate a point (or intersection) as intersection.
684 v = self._insert(q.y, q.x, q)
685 v._alpha = q._alpha or _0_0 # _0_0 replaces None
686 v._dupof = q._dupof or q
687 # assert v._prev is q
688 # assert q._next is v
689 return v
691 def _edges2(self, wrap=False, **unused):
692 # Yield each I{original} edge as a 2-tuple
693 # (p1, p2), a pair of C{LatLon[FHP|GH])}s.
694 p1 = p = f = self._first
695 while p:
696 p2 = p = p._next
697 if p.ispoint:
698 if wrap and p is not f:
699 p2 = _unrollon(p1, p)
700 yield p1, p2
701 p1 = p2
702 if p is f:
703 break
705 def _equi(self, clip, eps):
706 # Is this clip I{equivalent} to B{C{clip}} within
707 # the given I{non-negative} tolerance B{C{eps}}?
708 r, f = len(self), self._first
709 if f and r == len(clip) and self._bltr4eps(eps) \
710 == clip._bltr4eps(eps):
711 _equi = _LatLonBool._equi
712 for v in clip:
713 if _equi(f, v, eps):
714 s, n = f, v
715 for _ in range(r):
716 s, n = s._next, n._next
717 if not _equi(s, n, eps):
718 break # next v
719 else: # equivalent
720 return True
721 return False
723 def _Error(self, txt): # PYCHOK no cover
724 # Build a C{ClipError} instance
725 kwds = dict(len=len(self), txt=txt)
726 if self._dups:
727 kwds.update(dups=self._dups)
728 cp = self._composite
729 if self._id:
730 try:
731 i = cp._clips.index(self)
732 if i != self._id:
733 kwds[_clip_] = i
734 except ValueError:
735 pass
736 kwds[_clipid_] = self._id
737 return ClipError(cp._kind, cp.name, **kwds)
739 def _index(self, clips, eps):
740 # see _CompositeBase._equi
741 for i, c in enumerate(clips):
742 if c._equi(self, eps):
743 return i
744 raise ValueError(NN) # like clips.index(self)
746 def _insert(self, y, x, start, *end_alpha):
747 # insertVertex between points C{start} and
748 # C{end}, ordered by C{alpha} iff given.
749 v = self._LL(y, x, start._height, start._clipid)
750 n = start._next
751 if end_alpha:
752 end, alpha = end_alpha
753 v._alpha = alpha
754 v._height = favg(v._height, end._height, f=alpha)
755 # assert start is not end
756 while n is not end and n._alpha < alpha:
757 n = n._next
758 v._next = n
759 v._prev = p = n._prev
760 p._next = n._prev = v
761 self._len += 1
762# _Clip._bltr4._update(self)
763# _Clip._ishole._update(self)
764 return v
766 def _intersection(self, unused, q, *p1_p2_alpha):
767 # insert an intersection or make a point both
768 if p1_p2_alpha: # intersection on edge
769 v = self._insert(q.y, q.x, *p1_p2_alpha)
770 else: # intersection at point
771 v = q
772 # assert not v._linked
773 # assert v._alpha is None
774 return v
776 def _intersections(self):
777 # Yield all intersections, some may be points too.
778 for v in self:
779 if v.isintersection:
780 yield v
782 @Property_RO
783 def _ishole(self): # PYCHOK no cover
784 # Is this clip a hole inside its composite?
785 v = self._first
786 return v._isinside(self._composite, self) if v else False
788 @property_RO
789 def _nodups(self):
790 # Yield all non-duplicates.
791 for v in self:
792 if not v._dupof:
793 yield v
795 def _noXings(self, Union):
796 # Are all intersections non-CROSSINGs, -BOUNCINGs?
797 Xings = _L.BOUNCINGs if Union else _L.CROSSINGs
798 return all(v._label not in Xings for v in self._intersections())
800 def _OpenClipError(self, s, e): # PYCHOK no cover
801 # Return a C{CloseError} instance
802 t = NN(s, _ELLIPSIS_(_COMMASPACE_, e))
803 return self._Error(_SPACE_(_open_, t))
805 def _point2(self, insert):
806 # getNonIntersectionPoint and -Vertex
807 if not (insert and self._noInters):
808 for p in self._points(may_be=False): # not p._isduplicated?
809 return p, None
810 for n in self._intersections():
811 p, _ = n._prev_next2
812 k = p._linked
813 if k:
814 if n._linked not in k._prev_next2:
815 # create a pseudo-point
816 k = _0_5 * (p + n)
817 if insert:
818 k = self._insert(k.y, k.x, n._prev)
819 r = k # to remove later
820 else: # no ._prev, ._next
821 k._clipid = n._clipid
822 r = None
823 return k, r
824 return None, None
826 def _points(self, may_be=True):
827 # Yield all points I{in original order}, which may be intersections too.
828 for v in self:
829 if v.ispoint and (may_be or not v.isintersection):
830 yield v
832 def _remove2(self, v):
833 # Remove vertex C{v}.
834 # assert not v._isduplicated
835 if len(self) > 1:
836 p = v._prev
837 p._next = n = v._next
838 n._prev = p
839 if self._first is v:
840 self._first = n
841 if self._last is v:
842 self._last = p
843 self._len -= 1
844 else:
845 n = self._last = \
846 p = self._first = None
847 self._len = 0
848 return p, n
850 def _update_all(self): # PYCHOK no cover
851 # Zap the I{cached} properties.
852 _Clip._bltr4._update( self)
853 _Clip._ishole._update(self)
854 return self # for _special_identicals
856 def _Xings(self):
857 # Yield all I{un-checked} CROSSING intersections.
858 CROSSING = _L.CROSSING
859 for v in self._intersections():
860 if v._label is CROSSING and not v._checked:
861 yield v
864class _CompositeBase(_Named):
865 '''(INTERNAL) Base class for L{BooleanFHP} and L{BooleanGH}
866 (C{_CompositeFHP} and C{_CompositeGH}).
867 '''
868 _clips = () # tuple of C{_Clips}
869 _eps = EPS # null edges
870 _kind = _corners_
871 _LL = _LatLonBool # shut up PyChecker
872 _raiser = False
873 _xtend = False
875 def __init__(self, lls, kind=NN, eps=EPS, **name):
876 '''(INTERNAL) See L{BooleanFHP} and L{BooleanGH}.
877 '''
878 n = _name__(name, _or_nameof=lls)
879 if n:
880 self.name = n
881 if kind:
882 self._kind = kind
883 if self._eps < eps:
884 self._eps = eps
886 c = _Clip(self)
887 lp = None
888 for ll in lls:
889 ll = self._LL(ll)
890 if lp is None:
891 c._id = ll._clipid # keep clipid
892 lp = c._append(ll)
893 elif ll._clipid != lp._clipid: # new clip
894 c._closed(self.raiser)
895 c = _Clip(self, ll._clipid)
896 lp = c._append(ll)
897 elif abs(ll - lp) > eps: # PYCHOK lp
898 lp = c._append(ll)
899 else:
900 c._dups += 1
901 c._closed(self.raiser)
903 def __contains__(self, point): # PYCHOK no cover
904 '''Is the B{C{point}} in one of the clips?
905 '''
906 for c in self._clips:
907 if point in c:
908 return True
909 return False
911 def __eq__(self, other):
912 '''Is this I{composite} equivalent to an B{C{other}}, i.e.
913 do both contain I{equivalent} clips in the same or in a
914 different order? Two clips are considered I{equivalent}
915 if both have the same points etc. in the same order,
916 possibly rotated.
917 '''
918 return self._equi(_other(self, other), 0)
920 def __iter__(self):
921 '''Yield all points, duplicates and intersections.
922 '''
923 for c in self._clips:
924 for v in c:
925 yield v
927 def __ne__(self, other): # required for Python 2
928 '''See method C{__eq__}.
929 '''
930 return not self.__eq__(other)
932 def __len__(self):
933 '''Return the I{total} number of points.
934 '''
935 return sum(map(len, self._clips)) if self._clips else 0
937 def __repr__(self):
938 '''String C{repr} of this composite.
939 '''
940 c = len(self._clips)
941 c = Fmt.SQUARE(c) if c > 1 else NN
942 n = Fmt.SQUARE(len(self))
943 t = Fmt.PAREN(self) # XXX not unstr
944 return NN(self.__class__.__name__, c, n, t)
946 def __str__(self):
947 '''String C{str} of this composite.
948 '''
949 return _COMMASPACE_.join(map(str, self))
951 @property_RO
952 def _bottom_top_eps2(self):
953 # Get the bottom and top C{y} bounds, oversized.
954 return _min_max_eps2(min(v.y for v in self),
955 max(v.y for v in self))
957 def _class(self, corners, kwds, **dflts):
958 # Return a new instance
959 _g = kwds.get
960 kwds = dict((n, _g(n, v)) for n, v in dflts.items())
961 return self.__class__(corners or (), **kwds)
963 @property_RO
964 def _clipids(self): # PYCHOK no cover
965 for c in self._clips:
966 yield c._id
968 def clipids(self):
969 '''Return a tuple with all C{clipid}s, I{ordered}.
970 '''
971 return tuple(self._clipids)
973# def _clipidups(self, other):
974# # Number common C{clipid}s between this and an C{other} composite
975# return len(set(self._clipids).intersection(set(other._clipids)))
977 def _edges3(self, **raiser_wrap):
978 # Yield each I{original} edge as a 3-tuple
979 # C{(LatLon[FHP|GH], LatLon[FHP|GH], _Clip)}.
980 for c in self._clips:
981 for p1, p2 in c._edges2(**raiser_wrap):
982 yield p1, p2, c
984 def _encloses(self, lat, lon, **wrap):
985 # see function .points.isenclosedBy
986 return self._LL(lat, lon).isenclosedBy(self, **wrap)
988 @property
989 def eps(self):
990 '''Get the null edges tolerance (C{degrees}, usually).
991 '''
992 return self._eps
994 @eps.setter # PYCHOK setter!
995 def eps(self, eps):
996 '''Set the null edges tolerance (C{degrees}, usually).
997 '''
998 self._eps = eps
1000 def _10eps(self, **eps_):
1001 # Get eps for _LatLonBool._2Abs
1002 e = _xkwds_get(eps_, eps=self._eps)
1003 if e != EPS:
1004 e *= _10EPS / EPS
1005 else:
1006 e = _10EPS
1007 return e
1009 def _equi(self, other, eps):
1010 # Is this composite I{equivalent} to an B{C{other}} within
1011 # the given, I{non-negative} tolerance B{C{eps}}?
1012 cs, co = self._clips, other._clips
1013 if cs and len(cs) == len(co):
1014 if eps > 0:
1015 _index = _Clip._index
1016 else:
1017 def _index(c, cs, unused):
1018 return cs.index(c)
1019 try:
1020 cs = list(sorted(cs))
1021 for c in sorted(co):
1022 cs.pop(_index(c, cs, eps))
1023 except ValueError: # from ._index
1024 pass
1025 return False if cs else True
1026 else: # both null?
1027 return False if cs or co else True
1029 def _intersections(self):
1030 # Yield all intersections.
1031 for c in self._clips:
1032 for v in c._intersections():
1033 yield v
1035 def isequalTo(self, other, eps=None):
1036 '''Is this boolean/composite equal to an B{C{other}} within
1037 a given, I{non-negative} tolerance?
1039 @arg other: The other boolean/composite (C{Boolean[FHP|GB]}).
1040 @kwarg eps: Tolerance for equality (C{degrees} or C{None}).
1042 @return: C{True} if equivalent, C{False} otherwise (C{bool}).
1044 @raise TypeError: Invalid B{C{other}}.
1046 @see: Method C{__eq__}.
1047 '''
1048 if isinstance(other, _CompositeBase):
1049 return self._equi(other, _eps0(eps))
1050 raise _IsnotError(_boolean_, _composite_, other=other)
1052 def _kwds(self, op, **more):
1053 # Get all keyword arguments as C{dict}.
1054 kwds = dict(raiser=self.raiser, eps=self.eps,
1055 name=self.name or op.__name__)
1056 kwds.update(more)
1057 return kwds
1059 @property_RO
1060 def _left_right_eps2(self):
1061 # Get the left and right C{x} bounds, oversized.
1062 return _min_max_eps2(min(v.x for v in self),
1063 max(v.x for v in self))
1065 def _points(self, may_be=True): # PYCHOK no cover
1066 # Yield all I{original} points, which may be intersections too.
1067 for c in self._clips:
1068 for v in c._points(may_be=may_be):
1069 yield v
1071 @property
1072 def raiser(self):
1073 '''Get the option to throw L{ClipError} exceptions (C{bool}).
1074 '''
1075 return self._raiser
1077 @raiser.setter # PYCHOK setter!
1078 def raiser(self, throw):
1079 '''Set the option to throw L{ClipError} exceptions (C{bool}).
1080 '''
1081 self._raiser = bool(throw)
1083 def _results(self, _presults, Clas, closed=False, inull=False, **eps):
1084 # Yield the dedup'd results, as L{ClipFHP4Tuple}s
1085 C = self._LL if Clas is None else Clas
1086 e = self._10eps(**eps)
1087 for clipid, ns in enumerate(_presults):
1088 f = p = v = None
1089 for n in ns:
1090 if f is None:
1091 yield n._toClas(C, clipid)
1092 f = p = n
1093 elif v is None:
1094 v = n # got f, p, v
1095 elif inull or p._2Abs(v, n, eps=e):
1096 yield v._toClas(C, clipid)
1097 p, v = v, n
1098 else: # null, colinear, ... skipped
1099 v = n
1100 if v and (inull or p._2Abs(v, f, eps=e)):
1101 yield v._toClas(C, clipid)
1102 p = v
1103 if f and p != f and closed: # close clip
1104 yield f._toClas(C, clipid)
1106 def _sum(self, other, op):
1107 # Combine this and an C{other} composite
1108 LL = self._LL
1109 sp = self.copy(name=self.name or op.__name__)
1110 sp._clips, sid = (), INT0 # new clips
1111 for cp in (self, other):
1112 for c in cp._clips:
1113 _ap = _Clip(sp, sid)._append
1114 for v in c._nodups:
1115 _ap(LL(v.y, v.x, v.height, sid))
1116 sid += 1
1117 return sp
1119 def _sum1(self, _a_p, *args, **kwds): # in .karney, .points
1120 # Sum the area or perimeter of all clips
1121 return _MODS.fsums.fsum1((_a_p(c, *args, **kwds) for c in self._clips), floats=True)
1123 def _sum2(self, LL, _a_p, *args, **kwds): # in .sphericalNvector, -Trigonometry
1124 # Sum the area or perimeter of all clips
1126 def _lls(clip): # convert clip to LLs
1127 _LL = LL
1128 for v in clip:
1129 yield _LL(v.lat, v.lon) # datum=Sphere
1131 return _MODS.fsums.fsum1((_a_p(_lls(c), *args, **kwds) for c in self._clips), floats=True)
1133 def toLatLon(self, LatLon=None, closed=False, **LatLon_kwds):
1134 '''Yield all (non-duplicate) points and intersections
1135 as an instance of B{C{LatLon}}.
1137 @kwarg LatLon: Class to use (C{LatLon}) or if C{None},
1138 L{LatLonFHP} or L{LatLonGH}.
1139 @kwarg closed: If C{True}, close each clip (C{bool}).
1140 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}}
1141 keyword arguments, ignore if
1142 C{B{LatLon} is None}.
1144 @raise TypeError: Invalid B{C{LatLon}}.
1146 @note: For intersections, C{height} is an instance
1147 of L{HeightX}, otherwise of L{Height}.
1148 '''
1149 if LatLon is None:
1150 LL, kwds = self._LL, {}
1151 elif issubclassof(LatLon, _LatLonBool, LatLonBase):
1152 LL, kwds = LatLon, LatLon_kwds
1153 else:
1154 raise _TypeError(LatLon=LatLon)
1156 for c in self._clips:
1157 lf, cid = None, c._id
1158 for v in c._nodups:
1159 ll = LL(v.y, v.x, **kwds)
1160 ll._height = v.height
1161 if ll._clipid != cid:
1162 ll._clipid = cid
1163 yield ll
1164 if lf is None:
1165 lf = ll
1166 if closed and lf:
1167 yield lf
1170class _CompositeFHP(_CompositeBase):
1171 '''(INTERNAL) A list of clips representing a I{composite}
1172 of L{LatLonFHP} points, duplicates and intersections
1173 with an other I{composite}.
1174 '''
1175 _LL = LatLonFHP
1176 _Union = False
1178 def __init__(self, lls, raiser=False, **name_kind_eps):
1179 # New L{_CompositeFHP}.
1180 if raiser:
1181 self._raiser = True
1182 _CompositeBase.__init__(self, lls, **name_kind_eps)
1184 def _classify(self):
1185 # 2) Classify intersection chains.
1186 L = _L
1187 for v in self._intersections():
1188 n, b = v, v._label
1189 if b in L.RIGHT_LEFT_ON: # next chain
1190 while True:
1191 n._label = None # n.__dict__.pop('_label')
1192 n = n._next
1193 if n is v or n._label is not L.ON_ON: # n._label and ...
1194 break
1195 a = L.LEFT_ON if n._label is L.ON_LEFT else L.RIGHT_ON
1196 v._label = n._label = L.BOUNCING_D if a is b else L.CROSSING_D
1198 # 3) Copy labels
1199 for v in self._intersections():
1200 v._linked._label = v._label
1202 def _clip(self, corners, Union=False, Clas=None,
1203 **closed_inull_raiser_eps):
1204 # Clip this composite with another one, C{corners},
1205 # using Foster-Hormann-Popa's algorithm.
1206 P = self
1207 Q = self._class(corners, closed_inull_raiser_eps,
1208 eps=P._eps, raiser=False)
1209 if Union:
1210 P._Union = Q._Union = True
1212 bt = Q._bottom_top_eps2
1213 lr = Q._left_right_eps2
1214 # compute and insert intersections
1215 for p1, p2, Pc in P._edges3(**closed_inull_raiser_eps):
1216 if not (_outside(p1.x, p2.x, *lr) or
1217 _outside(p1.y, p2.y, *bt)):
1218 e = _EdgeFHP(p1, p2)
1219 if e._dp2 > EPS2: # non-null edge
1220 for q1, q2, Qc in Q._edges3(**closed_inull_raiser_eps):
1221 for T, p, q in e._intersect3(q1, q2):
1222 p = Pc._intersection(T, *p)
1223 q = Qc._intersection(T, *q)
1224 # assert not p._linked
1225 # assert not q._linked
1226 p._link(q)
1228 # label and classify intersections
1229 P._labelize()
1230 P._classify()
1232 # check for special cases
1233 P._special_cases(Q)
1234 Q._special_cases(P)
1235 # handle identicals
1236 P._special_identicals(Q)
1238 # set Entry/Exit flags
1239 P._set_entry_exits(Q)
1240 Q._set_entry_exits(P)
1242 # handle splits and crossings
1243 P._splits_xings(Q)
1245 # yield the results
1246 return P._results(P._presults(Q), Clas, **closed_inull_raiser_eps)
1248 @property_RO
1249 def _identicals(self):
1250 # Yield all clips marked C{._identical}.
1251 for c in self._clips:
1252 if c._identical:
1253 yield c
1255 def _labelize(self):
1256 # 1) Intersections classification
1257 for p in self._intersections():
1258 q = p._linked
1259 # determine local configuration at this intersection
1260 # and positions of Q- and Q+ relative to (P-, I, P+)
1261 p1, p3 = p._prev_next2
1262 q1, q3 = q._prev_next2
1263 t = (q1._RPoracle(p1, p, p3),
1264 q3._RPoracle(p1, p, p3))
1265 # check intersecting and overlapping cases
1266 p._label = _RP2L.get(t, None)
1268 def _presults(self, other):
1269 # Yield the result clips, each as a generator
1270 # of the L{_LatLonFHP}s in that clip
1271 for cp in (self, other):
1272 for c in cp._clips:
1273 if c._pushback:
1274 yield c._all()
1275 for c in self._clips:
1276 for X in c._Xings():
1277 yield self._resultX(X)
1279 def _resultX(self, X):
1280 # Yield the results from CROSSING C{X}.
1281 L, U, v = _L, self._Union, X
1282 while v:
1283 v._checked = True
1284 r = v # in P or Q
1285 s = L.Toggle[v._en_ex]
1286 e = (s is L.EXIT) ^ U
1287 while True:
1288 v = v._next if e else v._prev
1289 yield v
1290 v._checked = True
1291 if v._en_ex is s or v is X:
1292 break
1293 if v is r: # full circle
1294 raise ClipError(full_circle=v, clipid=v._clipid)
1295 if v is not X:
1296 v = v._linked
1297 if v is X:
1298 break
1300 def _set_entry_exits(self, other): # MCCABE 14
1301 # 4) Set entry/exit flags
1302 L, U = _L, self._Union
1303 for c in self._clips:
1304 n, k = c._point2(True)
1305 if n:
1306 f = n
1307 s = L.EXIT if n._isinside(other) else L.ENTRY
1308 t = L.EXIT # first_chain_vertex = True
1309 while True:
1310 if n.isintersection:
1311 b = n._label
1312 if b is L.CROSSING:
1313 n._en_ex = s
1314 s = L.Toggle[s]
1315 elif b is L.BOUNCING and ((s is L.EXIT) ^ U):
1316 n._2split = c # see ._splits_xings
1317 elif b is L.CROSSING_D:
1318 n._en_ex = s
1319 if (s is t) ^ U:
1320 n._label = L.CROSSING
1321 t = L.Toggle[t]
1322 if t is L.EXIT: # first_chain_vertex == True
1323 s = L.Toggle[s]
1324 elif b is L.BOUNCING_D:
1325 n._en_ex = s
1326 if (s is t) ^ U:
1327 n._2xing = True # see ._splits_xings
1328 s = L.Toggle[s]
1329 t = L.Toggle[t]
1330 n = n._next # _, n = n._prev_next2
1331 if n is f:
1332 break # PYCHOK attr?
1333 if k:
1334 c._remove2(k)
1336 def _special_cases(self, other):
1337 # 3.5) Check special cases
1338 U = self._Union
1339 for c in self._clips:
1340 if c._noXings(U):
1341 c._noInters = True
1342 if c._all_ON_ON:
1343 c._identical = True
1344 else:
1345 p, _ = c._point2(False)
1346 if p and (p._isinside(other) ^ U):
1347 c._pushback = True
1349 def _special_identicals(self, other):
1350 # 3.5) Handle identicals
1351 _u = _Clip._update_all
1352 cds = dict((c._id, _u(c)) for c in other._identicals)
1353 # assert len(cds) == len(other._identicals)
1354 if cds: # PYCHOK no cover
1355 for c in self._identicals:
1356 c._update_all()
1357 for v in c._intersections():
1358 d = cds.get(v._linked._clipid, None)
1359 if d and d._ishole is c._ishole:
1360 c._pushback = True
1361 break # next c
1363 @property_RO
1364 def _2splits(self):
1365 # Yield all intersections marked C{._2split}
1366 for p in self._intersections():
1367 if p._2split:
1368 # assert isinstance(p._2split, _Clip)
1369 yield p
1371 def _splits_xings(self, other): # MCCABE 15
1372 # 5) Handle split pairs and 6) crossing candidates
1374 def _2A_dup2(p, P): # PYCHOK unused
1375 p1, p2 = p._prev_next2
1376 ap = p1._2A(p, p2)
1377 Pc = p._2split
1378 # assert Pc in P._clips
1379 # assert p in Pc
1380 return ap, Pc._dup(p)
1382 def _links2(ps, qs): # PYCHOK P unused?
1383 # Yield each link as a 2-tuple(p, q)
1384 id_qs = set(map(id, qs))
1385 if id_qs:
1386 for p in ps:
1387 q = p._linked
1388 if q and id(q) in id_qs:
1389 yield p, q
1391 L = _L
1392 E = L.ENTRY if self._Union else L.EXIT
1393 X = L.Toggle[E]
1394 for p, q in _links2(self._2splits, other._2splits):
1395 ap, pp = _2A_dup2(p, self)
1396 aq, qq = _2A_dup2(q, other)
1397 if (ap * aq) > 0: # PYCHOK no cover
1398 p._link(qq) # overwrites ...
1399 q._link(pp) # ... p-q link
1400 else:
1401 pp._link(qq)
1402 p._en_ex = q._en_ex = E
1403 pp._en_ex = qq._en_ex = X
1404 p._label = pp._label = \
1405 q._label = qq._label = L.CROSSING
1407 for p, q in _links2(self._2xings, other._2xings):
1408 p._label = q._label = L.CROSSING
1410 @property_RO
1411 def _2xings(self):
1412 # Yield all intersections marked C{._2xing}
1413 for p in self._intersections():
1414 if p._2xing:
1415 yield p
1418class _CompositeGH(_CompositeBase):
1419 '''(INTERNAL) A list of clips representing a I{composite}
1420 of L{LatLonGH} points, duplicates and intersections
1421 with an other I{composite}.
1422 '''
1423 _LL = LatLonGH
1424 _xtend = False
1426 def __init__(self, lls, raiser=False, xtend=False, **name_kind_eps):
1427 # New L{_CompositeGH}.
1428 if xtend:
1429 self._xtend = True
1430 elif raiser:
1431 self._raiser = True
1432 _CompositeBase.__init__(self, lls, **name_kind_eps)
1434 def _clip(self, corners, s_entry, c_entry, Clas=None,
1435 **closed_inull_raiser_xtend_eps):
1436 # Clip this polygon with another one, C{corners}.
1438 # Core of Greiner/Hormann's algorithm, enhanced U{Correia's
1439 # <https://GitHub.com/helderco/univ-polyclip>} implementation***
1440 # and extended to optionally handle so-called "degenerate cases"
1441 S = self
1442 C = self._class(corners, closed_inull_raiser_xtend_eps,
1443 raiser=False, xtend=False)
1444 bt = C._bottom_top_eps2
1445 lr = C._left_right_eps2
1446 # 1. find intersections
1447 for s1, s2, Sc in S._edges3(**closed_inull_raiser_xtend_eps):
1448 if not (_outside(s1.x, s2.x, *lr) or
1449 _outside(s1.y, s2.y, *bt)):
1450 e = _EdgeGH(s1, s2, **closed_inull_raiser_xtend_eps)
1451 if e._hypot2 > EPS2: # non-null edge
1452 for c1, c2, Cc in C._edges3(**closed_inull_raiser_xtend_eps):
1453 for y, x, sa, ca in e._intersect4(c1, c2):
1454 s = Sc._insert(y, x, s1, s2, sa)
1455 c = Cc._insert(y, x, c1, c2, ca)
1456 s._link(c)
1458 # 2. identify entry/exit intersections
1459 if S._first:
1460 s_entry ^= S._first._isinside(C, *bt)
1461 for v in S._intersections():
1462 v._entry = s_entry = not s_entry
1464 if C._first:
1465 c_entry ^= C._first._isinside(S)
1466 for v in C._intersections():
1467 v._entry = c_entry = not c_entry
1469 # 3. yield the result(s)
1470 return S._results(S._presults(), Clas, **closed_inull_raiser_xtend_eps)
1472 @property_RO
1473 def _first(self):
1474 # Get the very first vertex of the first clip
1475 for v in self:
1476 return v
1477 return None # PYCHOK no cover
1479 def _kwds(self, op, **more):
1480 # Get the kwds C{dict}.
1481 return _CompositeBase._kwds(self, op, xtend=self.xtend, **more)
1483 def _presults(self):
1484 # Yield the unchecked intersection(s).
1485 for c in self._clips:
1486 for v in c._intersections():
1487 if not v._checked:
1488 yield self._resultU(v)
1490 def _resultU(self, v):
1491 # Yield the result from an un-checked intersection.
1492 while v and not v._checked:
1493 v._check()
1494 yield v
1495 r = v
1496 e = v._entry
1497 while True:
1498 v = v._next if e else v._prev
1499 yield v
1500 if v._linked:
1501 break
1502 if v is r:
1503 raise ClipError(full_circle=v, clipid=v._clipid)
1504 v = v._linked # switch
1506 @property
1507 def xtend(self):
1508 '''Get the option to handle I{degenerate cases} (C{bool}).
1509 '''
1510 return self._xtend
1512 @xtend.setter # PYCHOK setter!
1513 def xtend(self, xtend):
1514 '''Set the option to handle I{degenerate cases} (C{bool}).
1515 '''
1516 self._xtend = bool(xtend)
1519class _EdgeFHP(object):
1520 # An edge between two L{LatLonFHP} points.
1522 X_INTERSECT = _Enum('Xi', 1) # C++ enum
1523 X_OVERLAP = _Enum('Xo', 5)
1524 P_INTERSECT = _Enum('Pi', 3)
1525 P_OVERLAP = _Enum('Po', 7)
1526 Ps = (P_INTERSECT, P_OVERLAP, X_OVERLAP)
1527 Q_INTERSECT = _Enum('Qi', 2)
1528 Q_OVERLAP = _Enum('Qo', 6)
1529 Qs = (Q_INTERSECT, Q_OVERLAP, X_OVERLAP)
1530 V_INTERSECT = _Enum('Vi', 4)
1531 V_OVERLAP = _Enum('Vo', 8)
1532 Vs = (V_INTERSECT, V_OVERLAP)
1534 def __init__(self, p1, p2, **unused):
1535 # New edge between points C{p1} and C{p2}, each a L{LatLonFHP}.
1536 self._p1_p2 = p1, p2
1537 self._dp = dp = p2 - p1
1538 self._dp2 = dp * dp # dot product, hypot2
1540 self._lr, \
1541 self._bt = _left_right_bottom_top_eps2(p1, p2)
1543 def _intersect3(self, q1, q2):
1544 # Yield intersection(s) Type or C{None}
1545 if not (_outside(q1.x, q2.x, *self._lr) or
1546 _outside(q1.y, q2.y, *self._bt)):
1547 dq = q2 - q1
1548 dq2 = dq * dq # dot product, hypot2
1549 if dq2 > EPS2: # like ._clip
1550 T, E = None, _EdgeFHP # self.__class__
1551 p1, p2 = self._p1_p2
1552 ap1 = p1._2A(q1, q2)
1553 ap2_1 = p2._2A(q1, q2) - ap1
1554 if fabs(ap2_1) > _0_EPS: # non-parallel edges
1555 aq1 = q1._2A(p1, p2)
1556 aq2_1 = q2._2A(p1, p2) - aq1
1557 if fabs(aq2_1) > _0_EPS:
1558 # compute and classify alpha and beta
1559 a, a_0, a_0_1, _ = _alpha4(-ap1 / ap2_1)
1560 b, b_0, b_0_1, _ = _alpha4(-aq1 / aq2_1)
1561 # distinguish intersection types
1562 T = E.X_INTERSECT if a_0_1 and b_0_1 else (
1563 E.P_INTERSECT if a_0_1 and b_0 else (
1564 E.Q_INTERSECT if a_0 and b_0_1 else (
1565 E.V_INTERSECT if a_0 and b_0 else None)))
1567 elif fabs(ap1) < _0_EPS: # parallel or colinear edges
1568 dp = self._dp
1569 d1 = q1 - p1
1570 # compute and classify alpha and beta
1571 a, a_0, a_0_1, _a_0_1 = _alpha4((d1 * dp) / self._dp2)
1572 b, b_0, b_0_1, _b_0_1 = _alpha4((d1 * dq) / (-dq2))
1573 # distinguish overlap type
1574 T = E.X_OVERLAP if a_0_1 and b_0_1 else (
1575 E.P_OVERLAP if a_0_1 and _b_0_1 else (
1576 E.Q_OVERLAP if _a_0_1 and b_0_1 else (
1577 E.V_OVERLAP if a_0 and b_0 else None)))
1579 if T:
1580 if T is E.X_INTERSECT:
1581 v = p1 + a * self._dp
1582 yield T, (v, p1, p2, a), (v, q1, q2, b)
1583 elif T in E.Vs:
1584 yield T, (p1,), (q1,)
1585 else:
1586 if T in E.Qs:
1587 yield T, (p1,), (p1, q1, q2, b)
1588 if T in E.Ps:
1589 yield T, (q1, p1, p2, a), (q1,)
1592class _EdgeGH(object):
1593 # An edge between two L{LatLonGH} points.
1595 _raiser = False
1596 _xtend = False
1598 def __init__(self, s1, s2, raiser=False, xtend=False, **unused):
1599 # New edge between points C{s1} and C{s2}, each a L{LatLonGH}.
1600 self._s1, self._s2 = s1, s2
1601 self._x_sx_y_sy = (s1.x, s2.x - s1.x,
1602 s1.y, s2.y - s1.y)
1603 self._lr, \
1604 self._bt = _left_right_bottom_top_eps2(s1, s2)
1606 if xtend:
1607 self._xtend = True
1608 elif raiser:
1609 self._raiser = True
1611 def _alpha2(self, x, y, dx, dy):
1612 # Return C{(alpha)}, see .points.nearestOn5
1613 a = (y * dy + x * dx) / self._hypot2
1614 d = (y * dx - x * dy) / self._hypot0
1615 return a, fabs(d)
1617 def _Error(self, n, *args, **kwds): # PYCHOK no cover
1618 t = unstr(_EdgeGH.__name__, self._s1, self._s2)
1619 t = _DOT_(t, _EdgeGH._intersect4.__name__)
1620 t = unstr(t, *args, **kwds)
1621 return ClipError(_case_, n, txt=t)
1623 @Property_RO
1624 def _hypot0(self):
1625 _, sx, _, sy = self._x_sx_y_sy
1626 return hypot(sx, sy) * _0_EPS
1628 @Property_RO
1629 def _hypot2(self):
1630 _, sx, _, sy = self._x_sx_y_sy
1631 return hypot2(sx, sy)
1633 def _intersect4(self, c1, c2, parallel=True): # MCCABE 14
1634 # Yield the intersection(s) of this and another edge.
1636 # @return: None, 1 or 2 intersections, each a 4-Tuple
1637 # (y, x, s_alpha, c_alpha) with intersection
1638 # coordinates x and y and both alphas.
1640 # @raise ClipError: Intersection unhandled.
1642 # @see: U{Intersection point of two line segments
1643 # <http://PaulBourke.net/geometry/pointlineplane/>}.
1644 c1_x, c1_y = c1.x, c1.y
1645 if not (_outside(c1_x, c2.x, *self._lr) or
1646 _outside(c1_y, c2.y, *self._bt)):
1647 x, sx, \
1648 y, sy = self._x_sx_y_sy
1650 cx = c2.x - c1_x
1651 cy = c2.y - c1_y
1652 d = cy * sx - cx * sy
1654 if fabs(d) > _0_EPS: # non-parallel edges
1655 dx = x - c1_x
1656 dy = y - c1_y
1657 ca = (sx * dy - sy * dx) / d
1658 if _0_EPS < ca < _EPS_1 or (self._xtend and
1659 _EPS_0 < ca < _1_EPS):
1660 sa = (cx * dy - cy * dx) / d
1661 if _0_EPS < sa < _EPS_1 or (self._xtend and
1662 _EPS_0 < sa < _1_EPS):
1663 yield (y + sa * sy), (x + sa * sx), sa, ca
1665 # unhandled, "degenerate" cases 1, 2 or 3
1666 elif self._raiser and not (sa < _EPS_0 or sa > _1_EPS): # PYCHOK no cover
1667 raise self._Error(1, c1, c2, sa=sa) # intersection at s1 or s2
1669 elif self._raiser and not (ca < _EPS_0 or ca > _1_EPS): # PYCHOK no cover
1670 # intersection at c1 or c2 or at c1 or c2 and s1 or s2
1671 sa = (cx * dy - cy * dx) / d
1672 e = 2 if sa < _EPS_0 or sa > _1_EPS else 3
1673 raise self._Error(e, c1, c2, ca=ca)
1675 elif parallel and (sx or sy) and (cx or cy): # PYCHOK no cover
1676 # non-null, parallel or colinear edges
1677 sa1, d1 = self._alpha2(c1_x - x, c1_y - y, sx, sy)
1678 sa2, d2 = self._alpha2(c2.x - x, c2.y - y, sx, sy)
1679 if max(d1, d2) < _0_EPS:
1680 if self._xtend and not _outside(sa1, sa2, _EPS_0, _1_EPS):
1681 if sa1 > sa2: # anti-parallel
1682 sa1, sa2 = sa2, sa1
1683 ca1, ca2 = _1_0, _0_0
1684 else: # parallel
1685 ca1, ca2 = _0_0, _1_0
1686 ca = fabs((sx / cx) if cx else (sy / cy))
1687 # = hypot(sx, sy) / hypot(cx, cy)
1688 if sa1 < 0: # s1 is between c1 and c2
1689 ca *= ca1 + sa1
1690 yield y, x, ca1, _alpha1(ca)
1691 else: # c1 is between s1 and s2
1692 yield (y + sa1 * sy), (x + sa1 * sx), sa1, ca1
1693 if sa2 > 1: # s2 is between c1 and c2
1694 ca *= sa2 - _1_0
1695 yield (y + sy), (x + sx), ca2, _alpha1(ca2 - ca)
1696 else: # c2 is between s1 and s2
1697 yield (y + sa2 * sy), (x + sa2 * sx), sa2, ca2
1698 elif self._raiser and not _outside(sa1, sa2, _0_0, _1_EPS):
1699 raise self._Error(4, c1, c2, d1=d1, d2=d2)
1702class _BooleanBase(object):
1703 # Shared C{Boolean[FHP|GH]} methods.
1705 def __add__(self, other):
1706 '''Sum: C{this + other} clips.
1707 '''
1708 return self._sum(_other(self, other), self.__add__) # PYCHOK OK
1710 def __and__(self, other):
1711 '''Intersection: C{this & other}.
1712 '''
1713 return self._boolean(other, False, False, self.__and__) # PYCHOK OK
1715 def __iadd__(self, other):
1716 '''In-place sum: C{this += other} clips.
1717 '''
1718 return self._inplace(self.__add__(other))
1720 def __iand__(self, other):
1721 '''In-place intersection: C{this &= other}.
1722 '''
1723 return self._inplace(self.__and__(other))
1725 def __ior__(self, other):
1726 '''In-place union: C{this |= other}.
1727 '''
1728 return self._inplace(self.__or__(other))
1730 def __or__(self, other):
1731 '''Union: C{this | other}.
1732 '''
1733 return self._boolean(other, True, True, self.__or__) # PYCHOK OK
1735 def __radd__(self, other):
1736 '''Reverse sum: C{other + this} clips.
1737 '''
1738 return _other(self, other)._sum(self, self.__radd__)
1740 def __rand__(self, other):
1741 '''Reverse intersection: C{other & this}
1742 '''
1743 return _other(self, other).__and__(self)
1745 def __ror__(self, other):
1746 '''Reverse union: C{other | this}
1747 '''
1748 return _other(self, other).__or__(self)
1750 def _boolean4(self, other, op):
1751 # Set up a new C{Boolean[FHP|GH]}.
1752 C = self.__class__
1753 kwds = C._kwds(self, op)
1754 a = C(self, **kwds)
1755 b = _other(self, other)
1756 return a, b, C, kwds
1758 def _inplace(self, r):
1759 # Replace this with a L{Boolean*} result.
1760 self._clips, r._clips = r._clips, None
1761# if self._raiser != r._raiser:
1762# self._raiser = r._raiser
1763# if self._xtend != r._xtend:
1764# self._xtend = r._xtend
1765# if self._eps != r._eps:
1766# self._eps = r._eps
1767 return self
1770class BooleanFHP(_CompositeFHP, _BooleanBase):
1771 '''I{Composite} class providing I{boolean} operations between two
1772 I{composites} using U{Forster-Hormann-Popa<https://www.ScienceDirect.com/
1773 science/article/pii/S259014861930007X>}'s C++ implementation, transcoded
1774 to pure Python.
1776 The supported operations between (composite) polygon A and B are:
1778 - C = A & B or A &= B, intersection of A and B
1780 - C = A + B or A += B, sum of A and B clips
1782 - C = A | B or A |= B, union of A and B
1784 - A == B or A != B, equivalent A and B clips
1786 - A.isequalTo(B, eps), equivalent within tolerance
1788 @see: Methods C{__eq__} and C{isequalTo}, function L{clipFHP4}
1789 and class L{BooleanGH}.
1790 '''
1791 _kind = _boolean_
1793 def __init__(self, lls, raiser=False, eps=EPS, **name):
1794 '''New L{BooleanFHP} operand for I{boolean} operation.
1796 @arg lls: The polygon points and clips (iterable of L{LatLonFHP}s,
1797 L{ClipFHP4Tuple}s or other C{LatLon}s).
1798 @kwarg raiser: If C{True}, throw L{ClipError} exceptions (C{bool}).
1799 @kwarg esp: Tolerance for eliminating null edges (C{degrees}, same
1800 units as the B{C{lls}} coordinates).
1801 @kwarg name: Optional C{B{name}=NN} (C{str}).
1802 '''
1803 _CompositeFHP.__init__(self, lls, raiser=raiser, eps=eps, **name)
1805 def __isub__(self, other):
1806 '''Not implemented.'''
1807 return _NotImplemented(self, other)
1809 def __rsub__(self, other):
1810 '''Not implemented.'''
1811 return _NotImplemented(self, other)
1813 def __sub__(self, other):
1814 '''Not implemented.'''
1815 return _NotImplemented(self, other)
1817 def _boolean(self, other, Union, unused, op):
1818 # One C{BooleanFHP} operation.
1819 p, q, C, kwds = self._boolean4(other, op)
1820 r = p._clip(q, Union=Union, **kwds)
1821 return C(r, **kwds)
1824class BooleanGH(_CompositeGH, _BooleanBase):
1825 '''I{Composite} class providing I{boolean} operations between two
1826 I{composites} using the U{Greiner-Hormann<http://www.Inf.USI.CH/
1827 hormann/papers/Greiner.1998.ECO.pdf>} algorithm and U{Correia
1828 <https://GitHub.com/helderco/univ-polyclip>}'s implementation,
1829 modified and extended.
1831 The supported operations between (composite) polygon A and B are:
1833 - C = A - B or A -= B, difference A less B
1835 - C = B - A or B -= A, difference B less B
1837 - C = A & B or A &= B, intersection of A and B
1839 - C = A + B or A += B, sum of A and B clips
1841 - C = A | B or A |= B, union of A and B
1843 - A == B or A != B, equivalent A and B clips
1845 - A.isequalTo(B, eps), equivalent within tolerance
1847 @note: To handle I{degenerate cases} like C{point-edge} and
1848 C{point-point} intersections, use class L{BooleanFHP}.
1850 @see: Methods C{__eq__} and C{isequalTo}, function L{clipGH4}
1851 and class L{BooleanFHP}.
1852 '''
1853 _kind = _boolean_
1855 def __init__(self, lls, raiser=True, xtend=False, eps=EPS, **name):
1856 '''New L{BooleanFHP} operand for I{boolean} operation.
1858 @arg lls: The polygon points and clips (iterable of L{LatLonGH}s,
1859 L{ClipGH4Tuple}s or other C{LatLon}s).
1860 @kwarg raiser: If C{True}, throw L{ClipError} exceptions (C{bool}).
1861 @kwarg xtend: If C{True}, extend edges of I{degenerate cases}, an
1862 attempt to handle the latter (C{bool}).
1863 @kwarg esp: Tolerance for eliminating null edges (C{degrees}, same
1864 units as the B{C{lls}} coordinates).
1865 @kwarg name: Optional C{B{name}=NN} (C{str}).
1866 '''
1867 _CompositeGH.__init__(self, lls, raiser=raiser, xtend=xtend, eps=eps, **name)
1869 def _boolean(self, other, s_entry, c_entry, op):
1870 # One C{BooleanGH} operation.
1871 s, c, C, kwds = self._boolean4(other, op)
1872 r = s._clip(c, s_entry, c_entry, **kwds)
1873 return C(r, **kwds)
1875 def __isub__(self, other):
1876 '''In-place difference: C{this -= other}.
1877 '''
1878 return self._inplace(self.__sub__(other))
1880 def __rsub__(self, other):
1881 ''' Reverse difference: C{other - this}
1882 '''
1883 return _other(self, other).__sub__(self)
1885 def __sub__(self, other):
1886 '''Difference: C{this - other}.
1887 '''
1888 return self._boolean(other, True, False, self.__sub__)
1891def _alpha1(alpha):
1892 # Return C{alpha} in C{[0..1]} range
1893 if _EPS_0 < alpha < _1_EPS:
1894 return max(_0_0, min(alpha, _1_0))
1895 t = _not_(Fmt.SQUARE(_ELLIPSIS_(0, 1)))
1896 raise ClipError(_alpha_, alpha, txt=t)
1899def _alpha4(a):
1900 # Return 4-tuple (alpha, -EPS < alpha < EPS,
1901 # 0 < alpha < 1,
1902 # not 0 < alpha < 1)
1903 return (a, False, True, False) if _0_EPS < a < _EPS_1 else (
1904 (a, False, False, True) if _0_EPS < fabs(a) else
1905 (a, True, False, False))
1908def _Cps(Cp, composites_points, where):
1909 # Yield composites and points as a C{Cp} composite.
1910 try:
1911 kwds = dict(kind=_points_, name__=where)
1912 for cp in composites_points:
1913 yield cp if isBoolean(cp) else Cp(cp, **kwds)
1914 except (AttributeError, ClipError, TypeError, ValueError) as x:
1915 raise _ValueError(points=cp, cause=x)
1918def _eps0(eps):
1919 # Adjust C{eps} or C{None}.
1920 return eps if eps and eps > EPS else 0
1923def isBoolean(obj):
1924 '''Check for C{Boolean} composites.
1926 @arg obj: The object (any C{type}).
1928 @return: C{True} if B{C{obj}} is L{BooleanFHP}, L{BooleanGH}
1929 or some other composite, C{False} otherwise.
1930 '''
1931 return isinstance(obj, _CompositeBase)
1934def _left_right_bottom_top_eps2(p1, p2):
1935 '''(INTERNAL) Return 2-tuple C{(left, right), (bottom, top)}, oversized.
1936 '''
1937 return (_min_max_eps2(p1.x, p2.x),
1938 _min_max_eps2(p1.y, p2.y))
1941def _low_high_eps2(lo, hi, eps):
1942 '''(INTERNAL) Return 2-tuple C{(lo, hi)}, oversized.
1943 '''
1944 lo *= (_1_0 + eps) if lo < 0 else (_1_0 - eps)
1945 hi *= (_1_0 - eps) if hi < 0 else (_1_0 + eps)
1946 return (lo or -eps), (hi or eps)
1949def _min_max_eps2(*xs):
1950 '''(INTERNAL) Return 2-tuple C{(min, max)}, oversized.
1951 '''
1952 lo, hi = min(xs), max(xs)
1953 lo *= _1_EPS if lo < 0 else _EPS_1
1954 hi *= _EPS_1 if hi < 0 else _1_EPS
1955 return (lo or _EPS_0), (hi or _0_EPS)
1958def _other(this, other):
1959 '''(INTERNAL) Check for compatible C{type}s.
1960 '''
1961 C = this.__class__
1962 if isinstance(other, C):
1963 return other
1964 raise _IsnotError(C.__name__, other=other)
1967def _outside(x1, x2, lo, hi):
1968 '''(INTERNAL) Is C{(x1, x2)} outside C{(lo, hi)}?
1969 '''
1970 return max(x1, x2) < lo or min(x1, x2) > hi
1973__all__ += _ALL_DOCS(_BooleanBase, _Clip,
1974 _CompositeBase, _CompositeFHP, _CompositeGH,
1975 _LatLonBool)
1977# **) MIT License
1978#
1979# Copyright (C) 2018-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1980#
1981# Permission is hereby granted, free of charge, to any person obtaining a
1982# copy of this software and associated documentation files (the "Software"),
1983# to deal in the Software without restriction, including without limitation
1984# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1985# and/or sell copies of the Software, and to permit persons to whom the
1986# Software is furnished to do so, subject to the following conditions:
1987#
1988# The above copyright notice and this permission notice shall be included
1989# in all copies or substantial portions of the Software.
1990#
1991# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1992# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1993# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1994# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1995# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1996# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1997# OTHER DEALINGS IN THE SOFTWARE.
1999# ***) GNU GPL 3
2000#
2001# Copyright (C) 2011-2012 Helder Correia <Helder.MC@Gmail.com>
2002#
2003# This program is free software: you can redistribute it and/or
2004# modify it under the terms of the GNU General Public License as
2005# published by the Free Software Foundation, either version 3 of
2006# the License, or any later version.
2007#
2008# This program is distributed in the hope that it will be useful,
2009# but WITHOUT ANY WARRANTY; without even the implied warranty of
2010# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
2011# GNU General Public License for more details.
2012#
2013# You should have received a copy of the GNU General Public License
2014# along with this program. If not, see <http://www.GNU.org/licenses/>.
2015#
2016# You should have received the README file along with this program.
2017# If not, see <https://GitHub.com/helderco/univ-polyclip>.