December 2012
Intermediate to advanced
631 pages
13h 10m
English
Content preview from Graphics Gems III (IBM Version)
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V.10
UNDERSTANDING SIMPLOIDS
Doug Moore, Rice University, Houston, Texas
Publisher Summary
This chapter presents algorithms for splitting a simploid into a collection of simplices and splitting a simplex into a pair of simploids on opposite sides of a plane. A simploid is a polytope isomorphic to a product of simplices, that is, the vertices of a product of simplices can be moved around a bit, and the result is still a simploid if all the faces remain flat, and the incidence of vertices, edges, and faces does not change. In three dimensions, there are three kinds of simploids: the (3)-simploids, the (2, 1)-simploids, and the (1,1,1) simploids. Although a simploid is not necessarily a product, the structure is the same. Thus, algorithms ...
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