23 relations: Circumscribed circle, Concave polygon, Convex hull, Convex polytope, Convex set, Degree (angle), Fan triangulation, Helly's theorem, Homothetic transformation, Hyperplane separation theorem, Interior (topology), Internal and external angles, Krein–Milman theorem, Line segment, List of self-intersecting polygons, Mean width, Morgan Kaufmann Publishers, Parallelogram, Polygon triangulation, Simple polygon, Tangential polygon, Time complexity, Triangle.
In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon.
A simple polygon that is not convex is called concave, non-convex or reentrant.
In mathematics, the convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X., p. 3.
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.
In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.
A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360 degrees.
A fan triangulation is a simple way to triangulate a polygon by choosing a vertex and drawing diagonals to all of the other vertices of the polygon.
Helly's theorem is a basic result in discrete geometry on the intersection of convex sets.
In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and a nonzero number λ called its ratio, which sends in other words it fixes S, and sends any M to another point N such that the segment SN is on the same line as SM, but scaled by a factor λ. In Euclidean geometry homotheties are the similarities that fix a point and either preserve (if) or reverse (if) the direction of all vectors.
In geometry, the hyperplane separation theorem is a theorem about disjoint convex sets in n-dimensional Euclidean space.
In mathematics, specifically in topology, the interior of a subset S of points of a topological space X consists of all points of S that do not belong to the boundary of S. A point that is in the interior of S is an interior point of S. The interior of S is the complement of the closure of the complement of S. In this sense interior and closure are dual notions.
In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint.
In the mathematical theory of functional analysis, the Krein–Milman theorem is a proposition about convex sets in topological vector spaces.
In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.
Self-intersecting polygons, crossed polygons, or self-crossing polygons are polygons some of whose edges cross each other.
In geometry, the mean width is a measure of the "size" of a body; see Hadwiger's theorem for more about the available measures of bodies.
Morgan Kaufmann Publishers is a Burlington, Massachusetts (San Francisco, California until 2008) based publisher specializing in computer science and engineering content.
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.
In computational geometry, polygon triangulation is the decomposition of a polygonal area (simple polygon) P into a set of triangles, Chapter 3: Polygon Triangulation: pp.45–61.
In geometry a simple polygon is a flat shape consisting of straight, non-intersecting line segments or "sides" that are joined pair-wise to form a closed path.
In Euclidean geometry, a tangential polygon, also known as a circumscribed polygon, is a convex polygon that contains an inscribed circle (also called an incircle).
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.
A triangle is a polygon with three edges and three vertices.