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In geometry, a star-shaped polygon is a polygonal region in the plane that is a star domain, that is, a polygon that contains a point from which the entire polygon boundary is visible. Formally, a polygon P is star-shaped if there exists a point z such that for each point p of P the segment z p ¯ {\displaystyle {\overline {zp}}} lies ...
A regular star polygon is a self-intersecting, equilateral, and equiangular polygon. A regular star polygon is denoted by its Schläfli symbol { p / q }, where p (the number of vertices) and q (the density ) are relatively prime (they share no factors) and where q ≥ 2.
A star domain (equivalently, a star-convex or star-shaped set) is not necessarily convex in the ordinary sense. An annulus is not a star domain.. In geometry, a set in the Euclidean space is called a star domain (or star-convex set, star-shaped set [1] or radially convex set) if there exists an such that for all , the line segment from to lies in .
Regular convex and star polygons with 3 to 12 vertices labelled with their Schläfli symbols. Stellating a regular polygon symmetrically creates a regular star polygon or polygonal compound. These polygons are characterised by the number of times m that the polygonal boundary winds around the centre of the figure. Like all regular polygons ...
This is the smallest star polygon that can be drawn in two forms, as irreducible fractions. The two heptagrams are sometimes called the heptagram (for {7/2}) and the great heptagram (for {7/3}). The previous one, the regular hexagram {6/2}, is a compound of two triangles. The smallest star polygon is the {5/2} pentagram.
A p-gonal regular polygon is represented by Schläfli symbol {p}. Many sources only consider convex polygons, but star polygons, like the pentagram, when considered, can also be regular. They use the same vertices as the convex forms, but connect in an alternate connectivity which passes around the circle more than once to be completed.
For the same choice of a pivot point for the sorting algorithm, connecting all of the other points in their sorted order around this point rather than performing the remaining steps of the Graham scan produces a star-shaped polygon, a polygonalization of the input. [4]
Two classes of shape-based visual identification that are not done through geon representations, are those involved in: a) distinguishing between similar faces, and b) classifications that don’t have definite boundaries, such as that of bushes or a crumpled garment. Typically, such identifications are not viewpoint-invariant.