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Some polygons of different kinds: open (excluding its boundary), boundary only (excluding interior), closed (including both boundary and interior), and self-intersecting. In geometry, a polygon (/ ˈ p ɒ l ɪ ɡ ɒ n /) is a plane figure made up of line segments connected to form a closed polygonal chain.
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 intersect itself and has no holes. That is, it is a piecewise-linear Jordan curve consisting of finitely many line segments.
In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is contained in the union of the interior and the boundary of the polygon. In particular, it is a simple polygon (not self-intersecting ). [1] Equivalently, a polygon is convex if every line that ...
A self-intersecting quadrilateral is called variously a cross-quadrilateral, crossed quadrilateral, butterfly quadrilateral or bow-tie quadrilateral. In a crossed quadrilateral, the four "interior" angles on either side of the crossing (two acute and two reflex , all on the left or all on the right as the figure is traced out) add up to 720°.
Some types of self-intersecting polygons are: the crossed quadrilateral, with four edges. the antiparallelogram, a crossed quadrilateral with alternate edges of equal length. the crossed rectangle, an antiparallelogram whose edges are two opposite sides and the two diagonals of a rectangle, hence having two edges parallel. Star polygons.
The density of a polygon is the number of times that the polygonal boundary winds around its center. For convex polygons, and more generally simple polygons (not self-intersecting), the density is 1, by the Jordan curve theorem . The density of a polygon can also be called its turning number; the sum of the turn angles of all the vertices ...
Internal and external angles. In geometry, an angle of a polygon is formed by two adjacent sides. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or non-convex, this angle is called an internal angle (or interior angle) if a point within the angle is in the interior of the polygon.
In computer graphics, a complex polygon is a polygon which has a boundary comprising discrete circuits, such as a polygon with a hole in it. [2] Self-intersecting polygons are also sometimes included among the complex polygons. [3] Vertices are only counted at the ends of edges, not where edges intersect in space.