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...

geometry 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...

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

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...

equivalent to being closed. For any convex set C ⊆ R n {\displaystyle C\subseteq \mathbb {R} ^{n}} the relative interior is equivalently defined as relint...

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...

on convex sets, published by Johann Radon in 1921, states that: Any set of d + 2 points in Rd can be partitioned into two sets whose convex hulls intersect...

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...

bound on the distance between any point in the Minkowski sum and its convex hull. This upper bound is sharpened by the Shapley–Folkman–Starr theorem (alternatively...

to the convex hull of a point set in a Euclidean space. The tight span is also sometimes known as the injective envelope or hyperconvex hull of M. It...

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...

problems in mathematical programming can be formulated as problems on convex sets or convex bodies. Six kinds of problems are particularly important:: Sec.2 ...

bounding box of a point set is the same as the minimum bounding box of its convex hull, a fact which may be used heuristically to speed up computation. In the...

maxima set problem, has been studied as a variant of the convex hull and orthogonal convex hull problems. It is equivalent to finding the Pareto frontier...

described to date: the prime polysphericons, the convex hulls of the two disc rollers (TDR convex hulls), the polycons and the Platonicons. Each developable...

hyperplane or maximum-margin hyperplane is a hyperplane which separates two convex hulls of points and is equidistant from the two. Hyperplane separation theorem—Let...

function's convex hull. Let I ⊂ R {\displaystyle I\subset \mathbb {R} } be an interval, and f : I → R {\displaystyle f:I\to \mathbb {R} } a convex function;...

triangle faces of the prism relative to each other, breaking each square face into two triangles separated by a non-convex edge. Some twist angles produce...

closure of the conic hull. Let X {\displaystyle X} be a normed vector space. If C ⊆ X {\displaystyle C\subseteq X} is a convex finite-dimensional set...

displays the convex hull in 2D for the vector y = ( 3 , 1 ) {\displaystyle \mathbf {y} =(3,\,1)} . Notice that the center of the convex hull, which is an...

advisor Franco P. Preparata for her thesis "Parallel Algorithms for Convex Hulls and Proximity Problems". She joined the Department of Computer Science...

connects alternate vertices. A vertex arrangement is often described by the convex hull polytope which contains it. For example, the regular pentagram can be...

subset of a vector space, the convex hull or affine hull of a subset of a vector space or the lower semicontinuous hull f ¯ {\displaystyle {\overline...

such that the convex hull of A1 intersects the convex hull of A2. Suppose that p is a point in the intersection of these two convex hulls. We claim that...

the relative interior of P. According to this definition, the set of faces of a polytope includes the polytope itself and the empty set. For convex polytopes...

Soddy's hexlet Sphericon Stereographic projection Stereometry Ball Convex Convex hull Coxeter group Euclidean distance Homothetic center Hyperplane Lattice...

convex hull of a regular polygon with an odd number of vertices. A less regular example is the cone in R3 whose base is the "house": the convex hull of...

pseudotriangles and 3 n − 3 {\displaystyle 3n-3} bitangent lines. The convex hull of any pseudotriangle is a triangle. A non-planar triangle is a triangle...

proportional to n {\displaystyle n} . One way to see this is to triangulate the convex hull of the given point set S {\displaystyle S} , and choose the smallest...