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

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...

set of continuously moving points. It should be distinguished from dynamic convex hull data structures, which handle points undergoing discrete changes...

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...

invocation yields a running time of Ω(n log n). Using (fully or semi-) dynamic convex hull data structures, the simplification performed by the algorithm can...

converted into the dynamic range searching problem by providing for addition and/or deletion of the points. The dynamic convex hull problem is to keep...

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...

is in convex position if all of the points are vertices of their convex hull. More generally, a family of convex sets is said to be in convex position...

easier to analyze. There is also a heap-like structure based on the dynamic convex hull data structure which achieves better performance for affine motion...

algorithm maintains a dynamic convex hull for the points on each side of a separating line, repeatedly finds a bitangent of these two hulls, and moves each...

convex preferences (that do not prefer extremes to in-between values) and convex budget sets and on producers with convex production sets; for convex...

any two points. The diameter is always attained by two points of the convex hull of the input. A trivial brute-force search can be used to find the diameter...

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...

Examples of convex curves include the convex polygons, the boundaries of convex sets, and the graphs of convex functions. Important subclasses of convex curves...

pointed pseudotriangulation is a pseudotriangulation of its convex hull: all convex hull edges may be added while preserving the angle-spanning property...

diameter. A kite with three 108° angles and one 36° angle forms the convex hull of the lute of Pythagoras, a fractal made of nested pentagrams. The four...

K {\displaystyle K} is a convex set. When it is not convex but merely a connected set, it can be replaced by its convex hull without changing its opaque...

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...

use. A convex hull is the smallest convex volume containing the object. If the object is the union of a finite set of points, its convex hull is a polytope...

guaranteed to exist a linear inequality that separates the optimum from the convex hull of the true feasible set. Finding such an inequality is the separation...

shown in red, and the red dashed lines indicate their convex hull, which is the smallest convex polyhedron that contains all of these points. The blue...

balanced hull of H {\displaystyle H} is equicontinuous. the convex hull of H {\displaystyle H} is equicontinuous. the convex balanced hull of H {\displaystyle...

length. A point-set triangulation is a polygon triangulation of the convex hull of a set of points. A Delaunay triangulation is another way to create...

triangulation of minimal total edge length. That is, an input polygon or the convex hull of an input point set must be subdivided into triangles that meet edge-to-edge...

of users, while the weighted max-min fairness utility results in a quasi-convex optimization problem with only a polynomial scaling with the number of users...

optimal solution (xmin, f(xmin)) to the "convexified problem", where convex hulls are taken of the graphs of the summand functions. Such an optimal solution...

The regular icosahedron (or simply icosahedron) is a convex polyhedron that can be constructed from pentagonal antiprism by attaching two pentagonal pyramids...

a polygonalization is to choose any point q {\displaystyle q} in the convex hull of P {\displaystyle P} (not necessarily one of the given points). Then...

\mathbb {R} ^{d}} lies in the convex hull of a set P {\displaystyle P} , then x {\displaystyle x} can be written as the convex combination of at most d +...