Ray Tracing of Parametric Surfaces Based on Adaptive Simplicial Complexes

On Isomorphism of Simplicial Complexes and Their Related Algebras

Improving B ezier Clipping and Chebyshev Boxing for Ray Tracing Parametric Surfaces

Ray tracing is a well known rendering technique for producing high quality photorealistic pictures. Parametric surfaces are being used extensively in geometric modeling and require fast and robust methods for computing the intersetions of rays with these surfaces. In this paper, we review two recent intersections methods and discuss their problems. Combining and optimizing the advantages of bot...

Cohen-Macaulay-ness in codimension for simplicial complexes and expansion functor

In this paper we show that expansion of a Buchsbaum simplicial complex is $CM_t$, for an optimal integer $tgeq 1$. Also, by imposing extra assumptions on a $CM_t$ simplicial complex, we provethat it can be obtained from a Buchsbaum complex.

Vertex Decomposable Simplicial Complexes Associated to Path Graphs

Introduction Vertex decomposability of a simplicial complex is a combinatorial topological concept which is related to the algebraic properties of the Stanley-Reisner ring of the simplicial complex. This notion was first defined by Provan and Billera in 1980 for k-decomposable pure complexes which is known as vertex decomposable when . Later Bjorner and Wachs extended this concept to non-pure ...

Simplicial diffeomorphisms

In this paper we will present a theory for simplicial diffeomorphims, that is, diffeomorphims that preserve the incidence relations of a simplicial complex. Simplicial diffeomorphisms can be regarded as curvilinear barycentric coordinates. Using the combination of piecewise linear functions on complexes with simplicial diffeomorphisms, we also propose a new representation of curves and surfaces...