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of a concave polygon fail to divide the plane into two half-planes one of which entirely contains the polygon. None of these three statements holds for a convex polygon.
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Some lines containing interior points of a concave polygon intersect its boundary at more than two points. Some
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of the concave polygon's vertices, and that of its edges, contains points that are exterior to the polygon.
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At least one interior angle does not contain all other vertices in its edges and interior.
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for finding a decomposition into as few convex polygons as possible is described by
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266:"Definition and properties of concave polygons with interactive animation"
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of a concave polygon lie partly or wholly outside the polygon. Some
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286:(1985), "Optimal convex decompositions", in Toussaint, G.T. (ed.),
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can never be concave, but there exist concave polygons with
205:, Hauppauge, NY: Barron's Educational Series, p. 66,
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112:a concave polygon into a set of convex polygons. A
225:Mason, J.I. (1946), "On the angles of a polygon",
58:. A concave polygon will always have at least one
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233:(291), The Mathematical Association: 237β238,
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81:As with any simple polygon, the sum of the
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173:Computer Graphics: Theory Into Practice
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101: β 2) degrees (Β°), where
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27:Simple polygon which is not convex
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135:> 3. An example of a concave
34:An example of a concave polygon.
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170:McConnell, Jeffrey J. (2006),
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118:Chazelle & Dobkin (1985)
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295:, Elsevier, pp. 63β133
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114:polynomial-time algorithm
108:It is always possible to
227:The Mathematical Gazette
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105:is the number of sides.
85:of a concave polygon is
201:Leff, Lawrence (2008),
289:Computational Geometry
203:Let's Review: Geometry
35:
60:reflex interior angle
33:
559:Nonagon/Enneagon (9)
489:Tangential trapezoid
97:, equivalently 180Γ(
671:Megagon (1,000,000)
439:Isosceles trapezoid
855:Weisstein, Eric W.
641:Icositetragon (24)
36:
18:Re-entrant polygon
882:Types of polygons
858:"Concave polygon"
843:
842:
684:
683:
661:Myriagon (10,000)
646:Triacontagon (30)
610:Heptadecagon (17)
600:Pentadecagon (15)
595:Tetradecagon (14)
534:Quadrilateral (4)
404:Antiparallelogram
280:Chazelle, Bernard
212:978-0-7641-4069-3
16:(Redirected from
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656:Chiliagon (1000)
636:Icositrigon (23)
615:Octadecagon (18)
605:Hexadecagon (16)
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284:Dobkin, David P.
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93: β 2)
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580:Hendecagon (11)
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469:Right trapezoid
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83:internal angles
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585:Dodecagon (12)
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131:sides for any
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40:simple polygon
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835:Weakly simple
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775:Infinite skew
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690:Star polygons
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676:Apeirogon (β)
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620:Icosagon (20)
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454:Parallelogram
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449:Orthodiagonal
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429:Ex-tangential
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749:
629:>20 sides
564:Decagon (10)
549:Heptagon (7)
539:Pentagon (5)
529:Triangle (3)
424:Equidiagonal
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42:that is not
37:
825:Star-shaped
800:Rectilinear
770:Equilateral
765:Equiangular
729:Hendecagram
573:11β20 sides
554:Octagon (8)
544:Hexagon (6)
519:Monogon (1)
361:Equilateral
151:convex hull
830:Tangential
734:Dodecagram
512:1β10 sides
503:By number
484:Tangential
464:Right kite
176:, p.
52:non-convex
46:is called
863:MathWorld
810:Reinhardt
719:Enneagram
709:Heptagram
699:Pentagram
666:65537-gon
524:Digon (2)
494:Trapezoid
459:Rectangle
409:Bicentric
371:Isosceles
348:Triangles
110:partition
76:sidelines
72:diagonals
56:reentrant
876:Category
785:Isotoxal
780:Isogonal
724:Decagram
714:Octagram
704:Hexagram
505:of sides
434:Harmonic
335:Polygons
125:triangle
805:Regular
750:Concave
743:Classes
651:257-gon
474:Rhombus
414:Crossed
247:3611229
139:is the
95:radians
66:Polygon
48:concave
815:Simple
760:Cyclic
755:Convex
479:Square
419:Cyclic
381:Obtuse
376:Kepler
245:
209:
184:
44:convex
790:Magic
386:Right
366:Ideal
356:Acute
293:(PDF)
243:JSTOR
157:Notes
820:Skew
444:Kite
339:List
207:ISBN
182:ISBN
149:The
141:dart
235:doi
178:130
54:or
878::
860:.
282:;
255:^
241:,
231:30
229:,
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143:.
123:A
120:.
89:Γ(
50:,
38:A
866:.
341:)
337:(
327:e
320:t
313:v
297:.
268:.
250:.
237::
191:.
133:n
129:n
103:n
99:n
91:n
87:Ο
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
