Search results
Results From The WOW.Com Content Network
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 ¯ lies entirely within P. [1]
In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not to have been formally defined, certain notable ones can arise through truncation operations on regular simple or star polygons.
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 .
Pattern or Texture is the aggregation of large numbers of similar symbols into a composite symbol, such as a forest represented by a random scattering of tree icons. In addition to the visual variables that make up the sub-symbols, there are variables for controlling the pattern as a whole:
As well as star-shaped polygonalizations, every non-collinear set of points has a polygonalization that is a monotone polygon. This means that, with respect to some straight line (which may be taken as the x {\displaystyle x} -axis) every perpendicular line to the reference line intersects the polygon in a single interval, or not at all.
Deeper truncations of the square can produce isogonal (vertex-transitive) intermediate star polygon forms with equal spaced vertices and two edge lengths. A truncated square is an octagon, t{4}={8}. A quasitruncated square, inverted as {4/3}, is an octagram, t{4/3}={8/3}.
An isotoxal polygon has two vertices and one edge. There are isotoxal decagram forms, which alternates vertices at two radii. Each form has a freedom of one angle. The first is a variation of a double-wound of a pentagon {5}, and last is a variation of a double-wound of a pentagram {5/2}.
The star unfolding should be distinguished from another way of cutting a convex polyhedron into a simple polygon net, the source unfolding.The source unfolding cuts the polyhedron at points that have multiple equally short geodesics to the given base point , and forms a polygon with at its center, preserving geodesics from .