Link Distance

	Link Distance In computational geometry, the link distance between two points in a polygon is the minimum number of line segments of any polygonal chain within the polygon that has the two points as its endpoints. The link diameter of the polygon is the maximum link distance of any two of its points. A polygon is a convex polygon if and only if its link diameter is one. Every star-shaped polygon has link diameter at most two: every two points may be connected by a polygonal chain that bends once, inside the kernel of the polygon. However, this property does not characterize star-shaped polygons, as there also exist polygons with holes In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon' ... in which the link diameter is two. References . Computational geometry Distance {{geometry-stub ... [...More Info...] [...Related Items...] OR:* [Wikipedia] [Google] [Baidu] [Amazon]
picture info	Polygon In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon's '' vertices'' or ''corners''. An ''n''-gon is a polygon with ''n'' sides; for example, a triangle is a 3-gon. A simple polygon is one which does not intersect itself. More precisely, the only allowed intersections among the line segments that make up the polygon are the shared endpoints of consecutive segments in the polygonal chain. A simple polygon is the boundary of a region of the plane that is called a ''solid polygon''. The interior of a solid polygon is its ''body'', also known as a ''polygonal region'' or ''polygonal area''. In contexts where one is concerned only with simple and solid polygons, a ''polygon'' may refer only to a simple polygon or to a solid polygon. A polygonal chain may cross over itself, creating star polyg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon]
	Polygonal Chain In geometry, a polygonal chain is a connected series of line segments. More formally, a polygonal chain is a curve specified by a sequence of points (A_1, A_2, \dots, A_n) called its vertices. The curve itself consists of the line segments connecting the consecutive vertices. Variations Simple A simple polygonal chain is one in which only consecutive segments intersect and only at their endpoints. Closed A closed polygonal chain is one in which the first vertex coincides with the last one, or, alternatively, the first and the last vertices are also connected by a line segment. A simple closed polygonal chain in the plane is the boundary of a simple polygon. Often the term "polygon" is used in the meaning of "closed polygonal chain", but in some cases it is important to draw a distinction between a polygonal area and a polygonal chain. A space closed polygonal chain is also known as a skew "polygon". Monotone A polygonal chain is called ''monotone'' if there is a strai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon]
picture info	Convex Polygon 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). Equivalently, a polygon is convex if every line that does not contain any edge intersects the polygon in at most two points. Strictly convex polygon A convex polygon is ''strictly'' convex if no line contains more than two vertices of the polygon. In a convex polygon, all interior angles are less than ''or equal'' to 180 degrees, while in a strictly convex polygon all interior angles are strictly less than 180 degrees. Properties The following properties of a simple polygon are all equivalent to convexity: Every internal angle is less than or equal to 180 degrees. Every point on every line segment between two points inside or on the boundary of the polygon remains inside or on the bou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon]
	Star-shaped Polygon 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 is star-shaped if there exists a point such that for each point of the segment lies entirely within . The set of all points with this property (that is, the set of points from which all of is visible) is called the kernel of . If a star-shaped polygon is convex, the link distance between any two of its points (the minimum number of sequential line segments sufficient to connect those points) is 1, and so the polygon's link diameter (the maximum link distance over all pairs of points) is 1. If a star-shaped polygon is not convex, the link distance between a point in the kernel and any other point in the polygon is 1, while the link distance between any two points that are in the polygon but outside the kernel is either 1 or 2; in this case the maximum link distance is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon]
picture info	Polygon With Holes In geometry, a polygon with holes is an area-connected planar polygon with one external boundary and one or more interior boundaries (holes). Polygons with holes can be dissected into multiple polygons by adding new edges, so they are not frequently needed. An ordinary polygon can be called simply-connected, while a polygon-with-holes is ''multiply-connected''. An ''H''-holed-polygon is ''H''-''connected''. Degenerate holes Degenerate cases may be considered, but a well-formed holed-polygon must have no contact between exterior and interior boundaries, or between interior boundaries. Nondegenerate holes should have 3 or more sides, excluding internal point boundaries (monogons) and single edge boundaries (digons). Boundary orientation Area fill algorithms in computational lists the external boundary vertices can be listed in counter-clockwise order, and interior boundaries clockwise. This allows the interior area to be defined as ''left'' of each edge. Conversion to ordinar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon]