Abstract.
This paper introduces a general notion of stress on cell-complexes and reports on connections between stresses and liftings (generalization of C 1 0 -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 determine 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.
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Received April 24, 1997, and in revised form July 31, 1998.
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Rybnikov, K. Stresses and Liftings of Cell-Complexes. Discrete Comput Geom 21, 481–517 (1999). https://doi.org/10.1007/PL00009434
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DOI: https://doi.org/10.1007/PL00009434