computation, the convex hull of a simple polygon, triangulation, and Euclidean shortest paths. Other constructions in geometry related to simple polygons include...

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...

union of the interior and the boundary of the polygon. In particular, it is a simple polygon (not self-intersecting). Equivalently, a polygon is convex if...

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 the more general...

their convex hull is a convex polygon whose vertices are some of the points in the input set. Its most common representation is the list of its vertices...

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...

computational geometry, polygon triangulation is the partition of a polygonal area (simple polygon) P into a set of triangles, i.e., finding a set of triangles with...

relative convex hull or geodesic convex hull is an analogue of the convex hull for the points inside a simple polygon or a rectifiable simple closed curve...

forms a simple polygon, the orientation of the resulting polygon is directly related to the sign of the angle at any vertex of the convex hull of the polygon...

drastic change of the size of the output. Therefore, if the convex hull is required to be reported in traditional way as a polygon, the lower bound for the...

endpoints are convex corners. An antiknob is an edge whose two endpoints are concave corners. A rectilinear polygon that is also simple is also called...

around the convex hull. It is a trivial task when the convex polygon is specified in a traditional way for polygons, i.e., by the ordered sequence of its vertices...

the space. An ideal polyhedron is the convex hull of a finite set of ideal points. Its faces are ideal polygons, but its edges are defined by entire hyperbolic...

a set of points is a 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...

A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called vertices, are zero-dimensional...

removes a piece from a figure, its area decreases but its perimeter may not. The convex hull of a figure may be visualized as the shape formed by a rubber...

for convex hulls in physics engines. For two convex polygons P and Q in the plane with m and n vertices, their Minkowski sum is a convex polygon with...

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

e.g. 720° for a pentagram and 0° for an angular "eight". Regular polygon Convex hull Nonzero-rule List of self-intersecting polygons Coxeter, 1974. Rae...

intersection of 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...

geometries of every convex regular polytope in the first four dimensions (except the polygons {7} and above). As the sixth and largest regular convex 4-polytope...

always inhabit a single plane. This is not necessarily true of more complex polygons, however. The flat nature of triangles makes it simple to determine...

a simple case analysis: if four or more points are vertices of the convex hull, any four such points can be chosen. If on the other hand, the convex hull...

fundamental problems of this type are: Convex hull: Given a set of points, find the smallest convex polyhedron/polygon containing all the points. Line segment...

anthropomorphic polygons. Repeatedly finding and removing a mouth from a non-convex polygon will eventually turn it into the convex hull of the initial polygon. This...

theorem is a result in discrete geometry stating that a non-convex simple polygon can be made into a convex polygon by a finite sequence of flips. The...

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 Graham...

or convex skull problem is a problem of finding the convex polygon of the largest possible area that lies within a given non-convex simple polygon. It...

outer vertices of a compound can be connected to form a convex polyhedron called its convex hull. A compound is a faceting of its convex hull.[citation needed]...

of 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...