Concepts inApproximate convex decomposition of 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.
more from Wikipedia
Polyhedron
In elementary geometry a polyhedron (plural polyhedra or polyhedrons) is a geometric solid in three dimensions with flat faces and straight edges. The word polyhedron comes from the Classical Greek ¿¿¿¿¿¿¿¿¿, as poly- (stem of ¿¿¿¿¿, "many") + -hedron (form of ¿¿¿¿, "base", "seat", or "face"). A polyhedron is a 3-dimensional example of the more general polytope in any number of dimensions.
more from Wikipedia
Decomposition
Decomposition (or rotting) is the process by which organic substances are broken down into simpler forms of matter. The process is essential for recycling the finite matter that occupies physical space in the biome. Bodies of living organisms begin to decompose shortly after death. Although no two organisms decompose in the same way, they all undergo the same sequential stages of decomposition.
more from Wikipedia
Convex set
In Euclidean space, an object is convex if for every pair of points within the object, every point on the straight line segment that joins them is also within the object. For example, a solid cube is convex, but anything that is hollow or has a dent in it, for example, a crescent shape, is not convex. The notion can be generalized to other spaces as described below.
more from Wikipedia
Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R ¿ for example, the surface of a ball. On the other hand, there are surfaces, such as the Klein bottle, that cannot be embedded in three-dimensional Euclidean space without introducing singularities or self-intersections.
more from Wikipedia
Solid
Solid is one of the three classical states of matter. It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a gas does. The atoms in a solid are tightly bound to each other, either in a regular geometric lattice or irregularly.
more from Wikipedia
Partition of a set
In mathematics, a partition of a set X is a division of X into non-overlapping and non-empty "parts" or "blocks" or "cells" that cover all of X. More formally, these "cells" are both collectively exhaustive and mutually exclusive with respect to the set being partitioned.
more from Wikipedia