Concepts inExact minkowski sums of convex polyhedra
Convex polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space R. Some authors use the terms "convex polytope" and "convex polyhedron" interchangeably, while others prefer to draw a distinction between the notions of a polyhedron and a polytope. In addition, some texts require a polytope to be a bounded set, while others (including this article) allow polytopes to be unbounded.
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General position
In algebraic geometry, general position is a notion of genericity for a set of points, or other geometric objects. It means the general case situation, as opposed to some more special or coincidental cases that are possible. Its precise meaning differs in different settings. For example, generically, two lines in the plane intersect in a single point (they are not parallel or coincident).
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Minkowski addition
In geometry, the Minkowski sum (also known as dilation) of two sets A and B in Euclidean space is the result of adding every element of A to every element of B, i.e. the set
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Computational geometry
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry.
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Convex hull
In mathematics, the convex hull or convex envelope for a set X of points in the Euclidean plane or Euclidean space is the minimal convex set containing X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape formed by a rubber band stretched around X. Formally, the convex hull may be defined as the intersection of all convex sets containing X, the intersection of all halfspaces containing X, or the set of all convex combinations of points in X.
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Degeneracy (mathematics)
In mathematics, a degenerate case is a limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. A degenerate case thus has special features, which depart from the properties that are generic in the wider class, and which would be lost under an appropriate small perturbation. A point is a degenerate circle, namely one with radius 0. A circle is a degenerate form of an ellipse, namely one with eccentricity 0.
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Vertex (geometry)
In geometry, a vertex (plural vertices) is a special kind of point that describes the corners or intersections of geometric shapes.
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