Dimension-independent modeling with simplicial complexes

Abstract

Dealing with simplicial decompositions which are dimension independent allows for the convergence of disparate viewpoints from computer graphics, solid and geometric modeling. In this framework it is possible to treat in a unified manner several geometric problems, such as solid modeling of articulated objects, simplicial approximation of curved manifolds, motion encoding and interference detection, free configuration space computation, and graphical representation of multidimensional data. In the paper the authora describe the winged scheme, a simple representation based on simplicial decompositions, which can be used for linear polyhedra of any dimension and which allows for "solid" approximation of curved manifolds when combined with curved maps (e.g., NURBS). Various operators and algorithms are discussed, including boundary evaluation, linear and screw extrusion, grid generation, simplicial maps, and set operations. A simple manipulation language is also introduced, and some nontrivial examples are discussed.