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 geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined...

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...

length, or at least one angle is 180°. Thus a degenerate convex polygon of n sides looks like a polygon with fewer sides. In the case of triangles, this definition...

A simple polygon that is not convex is called concave, non-convex or reentrant. A concave polygon will always have at least one reflex interior angle—that...

These polygons include as special cases the convex polygons, star-shaped polygons, and monotone polygons. The sum of external angles of a simple polygon is...

algorithms have been proposed to triangulate a polygon. It is trivial to triangulate any convex polygon in linear time into a fan triangulation, by adding...

polygon's boundary, is described later in a separate subsection. If not all points are on the same line, then their convex hull is a convex polygon whose...

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...

same length). Regular polygons may be either convex, star or skew. In the limit, a sequence of regular polygons with an increasing number of sides approximates...

fundamental domain for Γ is given by a convex polygon for the hyperbolic metric on H. These can be defined by Dirichlet polygons and have an even number of sides...

then it is a regular polygon. If the number of sides is at least four, an equilateral polygon does not need to be a convex polygon: it could be concave...

Euclidean plane tilings by convex regular polygons have been widely used since antiquity. The first systematic mathematical treatment was that of Kepler...

flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is a polyhedron that bounds a convex set. Every convex polyhedron...

convex may refer to: Strictly convex function, a function having the line between any two points above its graph Strictly convex polygon, a polygon enclosing...

non-convex sets. A set that is not convex is called a non-convex set. A polygon that is not a convex polygon is sometimes called a concave polygon, and...

available for some special polygons. Simpler algorithms are possible for monotone polygons, star-shaped polygons, convex polygons and triangles. The triangle...

joins points Convex polygon, a polygon which encloses a convex set of points Convex polytope, a polytope with a convex set of points Convex metric space...

convex polygon, all the diagonals are inside the polygon, but for re-entrant polygons, some diagonals are outside of the polygon. Any n-sided polygon...

computational geometry, the convex hull of a simple polygon is the polygon of minimum perimeter that contains a given simple polygon. It is a special case of...

generate all antipodal pairs of points on a convex polygon and to compute the diameter of a convex polygon in O ( n ) {\displaystyle O(n)} time. Godfried...

accurately approximated by Reuleaux polygons. They have been applied in coinage shapes. If P {\displaystyle P} is a convex polygon with an odd number of sides...

of an equiangular polygon does not depend on the location of the point. A necessary and sufficient condition for a convex polygon to have a constant...

to convex polygon ratio.[definition needed] To use this method, every proposed district is circumscribed by the smallest possible convex polygon (its...

all of these n − 1 {\displaystyle n-1} half-spaces, and hence it is a convex polygon. When two cells in the Voronoi diagram share a boundary, it is a line...

given convex polygon, one with maximal area can be found in linear time; its vertices may be chosen as three of the vertices of the given polygon. A circular...

In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular...

shape defined by a convex polygonal chain with two rays attached to its ends, and a convex polygon. Special cases of an unbounded convex polytope are a slab...

angle of a polygon is formed by two adjacent sides. For a simple polygon (non-self-intersecting), regardless of whether it is convex or non-convex, this angle...

vertex is called "convex" if the internal angle of the polygon (i.e., the angle formed by the two edges at the vertex with the polygon inside the angle)...