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...
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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...
58 KB (7,173 words) - 01:04, 1 July 2025
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...
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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...
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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...
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Degeneracy (mathematics) (redirect from Degenerate regular polygon)
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...
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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...
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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...
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same length). Regular polygons may be either convex or star. In the limit, a sequence of regular polygons with an increasing number of sides approximates...
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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...
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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...
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available for some special polygons. Simpler algorithms are possible for monotone polygons, star-shaped polygons, convex polygons and triangles. The triangle...
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Polyhedron (redirect from Convex polyhedra)
of such a surface is not itself a convex polygon, O'Rourke requires it to be subdivided into smaller convex polygons, with flat dihedral angles between...
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Euclidean plane tilings by convex regular polygons have been widely used since antiquity. The first systematic mathematical treatment was that of Kepler...
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Examples of convex curves include the convex polygons, the boundaries of convex sets, and the graphs of convex functions. Important subclasses of convex curves...
37 KB (4,174 words) - 06:39, 27 September 2024
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...
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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...
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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...
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to convex polygon ratio.[definition needed] To use this method, every proposed district is circumscribed by the smallest possible convex polygon (its...
170 KB (18,726 words) - 20:56, 6 July 2025
Corollary: every rectilinear polygon has at least 4 convex corners. The number of knobs (sides connecting two convex corners) is four more than the...
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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...
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In Euclidean geometry, a tangential polygon, also known as a circumscribed polygon, is a convex polygon that contains an inscribed circle (also called...
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Internal and external angles (redirect from Angle sum of polygon)
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...
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Viviani's theorem (section Convex polygon)
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...
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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...
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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...
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Voronoi diagram (redirect from Voronoi polygon)
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...
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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...
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convex polygons (n-gons). A polygonal mesh may also be more generally composed of concave polygons, or even polygons with holes. The study of polygon...
26 KB (2,618 words) - 06:27, 12 June 2025