Convex polygon information

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...

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...

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...

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...

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...

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...

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

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

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...

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

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...

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...

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

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...

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...

subset forming a convex polygon, namely that the smallest number of points for which any general position arrangement contains a convex subset of n {\displaystyle...

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...

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

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

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...

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. One...

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...

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...

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...

simple convex polygons (n-gons), since this simplifies rendering, but may also be more generally composed of concave polygons, or even polygons with holes...