Search results
Results from the WOW.Com Content Network
The polygon is the convex hull of its edges. Additional properties of convex polygons include: The intersection of two convex polygons is a convex polygon. A convex polygon may be triangulated in linear time through a fan triangulation, consisting in adding diagonals from one vertex to all other vertices.
Non-convex: a line may be found which meets its boundary more than twice. Equivalently, there exists a line segment between two boundary points that passes outside the polygon. Simple: the boundary of the polygon does not cross itself. All convex polygons are simple. Concave: Non-convex and simple. There is at least one interior angle greater ...
In geometry, a convex curve is a plane curve that has a supporting line through each of its points. There are many other equivalent definitions of these curves, going back to Archimedes. Examples of convex curves include the convex polygons, the boundaries of convex sets, and the graphs of convex functions.
Cell is the intersection of all of these half-spaces, and hence it is a convex polygon. [6] When two cells in the Voronoi diagram share a boundary, it is a line segment , ray , or line, consisting of all the points in the plane that are equidistant to their two nearest sites.
Convex hull ( in blue and yellow) of a simple polygon (in blue) The convex hull of a simple polygon encloses the given polygon and is partitioned by it into regions, one of which is the polygon itself. The other regions, bounded by a polygonal chain of the polygon and a single convex hull edge, are called pockets.
Definitions based on the idea of a bounding surface rather than a solid are also common. [8] For instance, O'Rourke (1993) defines a polyhedron as a union of convex polygons (its faces), arranged in space so that the intersection of any two polygons is a shared vertex or edge or the empty set and so that their union is a manifold. [9]
The simplest way of measuring the home range is to construct the smallest possible convex polygon around the data but this tends to overestimate the range. The best known methods for constructing utilization distributions are the so-called bivariate Gaussian or normal distribution kernel density methods.
One might characterise the Greek definition as follows: A regular polygon is a planar figure with all edges equal and all corners equal. A regular polyhedron is a solid (convex) figure with all faces being congruent regular polygons, the same number arranged all alike around each vertex.