Stresses and Liftings of Cell-Complexes

K. Rybnikov
1999 Discrete & Computational Geometry  
This paper introduces a general notion of stress on cell-complexes and reports on connections between stresses and liftings (generalization of C 0 1 -splines) of d-dimensional cell-complexes in R d . New sufficient conditions for the existence of a sharp lifting for a "flat" piecewise-linear realization of a manifold are given. Our approach also gives some new results on the equivalence between spherical complexes and convex and star polytopes. As an application, two algorithms are given that
more » ... termine whether a piecewise-linear realization of a d-manifold in R d admits a lifting to R d+1 which satisfies given constraints. We also demonstrate connections between stresses and Voronoi-Dirichlet diagrams and show that any weighted Voronoi-Dirichlet diagram without non-compact cells can be represented as a weighted Delaunay decomposition and vice versa.
doi:10.1007/pl00009434 fatcat:p6lp5j56r5ehbp5qtqxmevwx5e