Search results
Results from the WOW.Com Content Network
Convex hull (aka convex envelope) - the smallest convex set that contains a given set of points in Euclidean space. Convex lens - a lens in which one or two sides is curved or bowed outwards. Light passing through the lens is converged (or focused) to a spot behind the lens.
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. Helly's theorem: For every collection of at least three convex polygons: if all intersections of all but one polygon are nonempty ...
If every internal angle of a simple polygon is less than a straight angle (π radians or 180°), then the polygon is called convex. In contrast, an external angle (also called a turning angle or exterior angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side. [1]: pp. 261–264
All convex polygons are simple. Concave: Non-convex and simple. There is at least one interior angle greater than 180°. Star-shaped: the whole interior is visible from at least one point, without crossing any edge. The polygon must be simple, and may be convex or concave. All convex polygons are star-shaped. Self-intersecting: the boundary of ...
In geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain. These segments are called its edges or sides, and the points where two of the edges meet are the polygon's vertices (singular: vertex) or corners.
A non-convex regular polygon is a regular star polygon. The most common example is the pentagram, which has the same vertices as a pentagon, but connects alternating vertices. For an n-sided star polygon, the Schläfli symbol is modified to indicate the density or "starriness" m of the polygon, as {n/m}.
A polygon that is already convex has no pockets. [1] One can form a hierarchical description of any given polygon by constructing its hull and its pockets in this way and then recursively forming a hierarchy of the same type for each pocket. [1] This structure, called a convex differences tree, can be constructed efficiently. [2]
The boundary of any convex polygon forms a convex curve (one that is a piecewise linear curve and not strictly convex). A polygon that is inscribed in any strictly convex curve, with its vertices in order along the curve, must be a convex polygon. [43]