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 either...

Algorithms that construct convex hulls of various objects have a broad range of applications in mathematics and computer science. In computational geometry...

subset A of Euclidean space is called the convex hull of A. It is the smallest convex set containing A. A convex function is a real-valued function defined...

Carathéodory's theorem is a theorem in convex geometry. It states that if a point x {\displaystyle x} lies in the convex hull C o n v ( P ) {\displaystyle \mathrm...

locally convex space, the convex hull and the disked hull of a totally bounded set is totally bounded. In a complete locally convex space, the convex hull and...

learning resources about Convex combination Affine hull Carathéodory's theorem (convex hull) Simplex Barycentric coordinate system Convex space Rockafellar,...

"balanced"), in which case it is called a disk. The disked hull or the absolute convex hull of a set is the intersection of all disks containing that set...

the convex hull of its edges. Additional properties of convex polygons include: The intersection of two convex polygons is a convex polygon. A convex polygon...

every convex set is orthogonally convex but not vice versa. For the same reason, the orthogonal convex hull itself is a subset of the convex hull of the...

The dynamic convex hull problem is a class of dynamic problems in computational geometry. The problem consists in the maintenance, i.e., keeping track...

and computational geometry, the relative convex hull or geodesic convex hull is an analogue of the convex hull for the points inside a simple polygon or...

spheres determines a specific volume known as the convex hull of the packing, defined as the smallest convex set that includes all the spheres. There are many...

A kinetic convex hull data structure is a kinetic data structure that maintains the convex hull of a set of continuously moving points. It should be distinguished...

The convex polyhedra are a well defined class of polyhedra with several equivalent standard definitions. Every convex polyhedron is the convex hull of...

The polynomially convex hull contains the holomorphically convex hull. The domain G {\displaystyle G} is called holomorphically convex if for every compact...

C} is the convex hull of its extremal rays. For a vector space V {\displaystyle V} , every linear subspace of V {\displaystyle V} is a convex cone. In...

In discrete geometry and computational geometry, the convex hull of a simple polygon is the polygon of minimum perimeter that contains a given simple...

convex set of points in space. Other important definitions are: as the intersection of half-spaces (half-space representation) and as the convex hull...

Delone triangulation of a set of points in the plane subdivides their convex hull into triangles whose circumcircles do not contain any of the points;...

Local convex hull (LoCoH) is a method for estimating size of the home range of an animal or a group of animals (e.g. a pack of wolves, a pride of lions...

to the closed convex hull of its extreme points. This theorem generalizes to infinite-dimensional spaces and to arbitrary compact convex sets the following...

problems, including point in polygon testing, area computation, the convex hull of a simple polygon, triangulation, and Euclidean shortest paths. Other...

generalization of the concept of the convex hull, i.e. every convex hull is an alpha-shape but not every alpha shape is a convex hull. For each real number α, define...

geometric object that was discovered by Paul Schatz in 1929. It is the convex hull of a skeletal frame made by placing two linked congruent circles in perpendicular...

Olshevsky nicknamed it the yog-sothoth (after the Cthulhu Mythos deity). Its convex hull is a nonuniform truncated dodecahedron. Let ξ = − 3 2 − 1 2 1 + 4 ϕ ≈...

Closed hulls In a locally convex space, convex hulls of bounded sets are bounded. This is not true for TVSs in general. The closed convex hull of a set...

Quickhull is a method of computing the convex hull of a finite set of points in n-dimensional space. It uses a divide and conquer approach similar to...

Graham's scan is a method of finding the convex hull of a finite set of points in the plane with time complexity O(n log n). It is named after Ronald...

geometry, the gift wrapping algorithm is an algorithm for computing the convex hull of a given set of points. In the two-dimensional case the algorithm is...

when c lies in the interior of the convex hull of S, and otherwise (when c lies on the boundary of the convex hull of S) A is unbounded. A subset F of...