59:. This formalizes the notion that such a polygon allows segments to touch but not to cross. This generalizes the notion of the polygonal boundary of a topological disk: this boundary is the limit of a sequence of polygons, offset from it within the disk. However, this type of weakly simple polygon does not need to form the boundary of a region, as its "interior" can be empty. For example, referring to the same image, the polygonal chain ABCBA is a weakly simple polygon according to this definition: it may be viewed as the limit of "squeezing" of the polygon ABCFGHA.
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in the plane is bounded by finitely many line segments, then its boundary forms a weakly simple polygon. In the image, ABCDEFGHJKLM is a weakly simple polygon according to this definition, with the color blue marking the region for which it is the boundary. This type of weakly simple polygon can
49:: for each hole a "cut" is created to connect it to an external boundary. Referring to the image above, ABCM is an external boundary of a planar region with a hole FGHJ. The cut ED connects the hole with the exterior and is traversed twice in the resulting weakly simple polygonal representation.
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In an alternative and more general definition of weakly simple polygons, they are the limits of sequences of simple polygons. The polygons in the sequence should all have the same combinatorial type as each other, with convergence under the
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Dumitrescu, Adrian; Tóth, Csaba D. (2007). "Light orthogonal networks with constant geometric dilation". In Thomas, Wolfgang; Weil, Pascal (eds.).
24:, allowing the polygon sides to touch each other in limited ways. Different authors have defined weakly simple polygons in different ways:
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Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on
Discrete Algorithms, SODA 2015, San Diego, CA, USA, January 4-6, 2015
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Symposium on Theoretical Aspects of Computer Science, Aachen, Germany, February 22-24, 2007, Proceedings
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Chang, Hsien-Chih; Erickson, Jeff; Xu, Chao (2015). "Detecting weakly simple polygons". In Indyk, Piotr (ed.).
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47:polygonal regions with holes
124:10.1137/1.9781611973730.110
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20:is a generalization of a
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18:weakly simple polygon
389:Nonagon/Enneagon (9)
319:Tangential trapezoid
501:Megagon (1,000,000)
269:Isosceles trapezoid
471:Icositetragon (24)
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686:Types of polygons
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491:Myriagon (10,000)
476:Triacontagon (30)
440:Heptadecagon (17)
430:Pentadecagon (15)
425:Tetradecagon (14)
364:Quadrilateral (4)
234:Antiparallelogram
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486:Chiliagon (1000)
466:Icositrigon (23)
445:Octadecagon (18)
435:Hexadecagon (16)
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459:>20 sides
394:Decagon (10)
379:Heptagon (7)
369:Pentagon (5)
359:Triangle (3)
254:Equidiagonal
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655:Star-shaped
630:Rectilinear
600:Equilateral
595:Equiangular
559:Hendecagram
403:11–20 sides
384:Octagon (8)
374:Hexagon (6)
349:Monogon (1)
191:Equilateral
660:Tangential
564:Dodecagram
342:1–10 sides
333:By number
314:Tangential
294:Right kite
64:References
640:Reinhardt
549:Enneagram
539:Heptagram
529:Pentagram
496:65537-gon
354:Digon (2)
324:Trapezoid
289:Rectangle
239:Bicentric
201:Isosceles
178:Triangles
115:1407.3340
680:Category
615:Isotoxal
610:Isogonal
554:Decagram
544:Octagram
534:Hexagram
335:of sides
264:Harmonic
165:Polygons
38:open set
635:Regular
580:Concave
573:Classes
481:257-gon
304:Rhombus
244:Crossed
645:Simple
590:Cyclic
585:Convex
309:Square
249:Cyclic
211:Obtuse
206:Kepler
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620:Magic
216:Right
196:Ideal
186:Acute
110:arXiv
650:Skew
274:Kite
169:List
85:ISBN
120:doi
43:CAD
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