Editing Simple polygon (section)

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{{Short description|Shape bounded by non-intersecting line segments}}
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[[File:Two simple polygons and a self-intersecting polygon.png|thumb|Two simple polygons (green and blue) and a self-intersecting polygon (red, in the lower right, not simple)]]
In [[geometry]], a '''simple polygon''' is a [[polygon]] that does not [[Intersection (Euclidean geometry)|intersect]] itself and has no holes. That is, it is a [[Piecewise linear curve|piecewise-linear]] [[Jordan curve]] consisting of finitely many [[line segment]]s. These polygons include as special cases the [[convex polygon]]s, [[star-shaped polygon]]s, and [[monotone polygon]]s.

The sum of [[external angle]]s of a simple polygon is <math>2\pi</math>. Every simple polygon with <math>n</math> sides can be [[polygon triangulation|triangulated]] by <math>n-3</math> of its diagonals, and by the [[art gallery theorem]] its interior is visible from some <math>\lfloor n/3\rfloor</math> of its vertices.

Simple polygons are commonly seen as the input to [[computational geometry]] problems, including [[point in polygon]] testing, [[area]] computation, the [[convex hull of a simple polygon]], triangulation, and [[Euclidean shortest path]]s.

Other constructions in geometry related to simple polygons include [[Schwarz–Christoffel mapping]], used to find [[conformal map]]s involving simple polygons, [[polygonalization]] of point sets, [[constructive solid geometry]] formulas for polygons, and [[visibility graph]]s of polygons.