Surface realization with the intersection segment functional. (English) Zbl 1191.52010

Hougardy, Stefan; Lutz, Frank H.; Zelke, Mariano

Exp. Math. 19, No. 1, 79-92 (2010).

The heuristic algorithm starts with random positions for the vertices in 3-space and then “moves vertices around” subject to minimizing the functional which is defined as the sum of the lengths of all intersection segments of triangles which are not adjacent. If the intersection segment functional becomes zero, a polyhedral embedding (called a realization) of the given triangulation is found.

Reviewer: Wolfgang Kühnel (Stuttgart)

MSC:

52B70	Polyhedral manifolds
57Q15	Triangulating manifolds
52-04	Software, source code, etc. for problems pertaining to convex and discrete geometry

Keywords:

polyhedral surface; triangulation; simplicial map; realizability; edge expansion; polyhedron; edge contraction; integer coordinates