An acyclicity theorem for cell complexes in d dimension Authors
Received: 29 December 1988 DOI:
Cite this article as: Edelsbrunner, H. Combinatorica (1990) 10: 251. doi:10.1007/BF02122779 Abstract
C be a cell complex in d-dimensional Euclidean space whose faces are obtained by orthogonal projection of the faces of a convex polytope in d+ 1 dimensions. For example, the Delaunay triangulation of a finite point set is such a cell complex. This paper shows that the in_front/behind relation defined for the faces of C with respect to any fixed viewpoint x is acyclic. This result has applications to hidden line/surface removal and other problems in computational geometry. AMS subject classification (1980) 52 A 45 05 B 45 05 B 30
Research reported in this paper was supported by the National Science Foundation under grant CCR-8714565
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F. Aurenhammer: Power diagrams: properties, algorithms, and applications, SIAM J. Comput., 16 (1987), 78–96.
B. Chazelle: How to search in history, Inform. Control, 64 (1985), 77–99.
B. Delaunay: Sur la sphére vide, Izv. Akad. Nauk SSSR, Otdelenie Matematicheskii i Estestvennyka Nauk, 7 (1934), 793–800.
H. Edelsbrunner: Algorithms in Combinatorial Geometry, Springer-Verlag, Heidelberg, Germany, 1987.
H. Edelsbrunner, D. G. Kirkpatrick, and R. Seidel: On the shape of a set of points in the plane, IEEE Trans. Inform. Theory, IT-29 (1983), 551–559.
L. De Floriani, B. Falcidieno, C. Pienovi, and G. Nagy: On sorting triangles in a Delaunay tessellation, Techn. Rept., Istituto per la Matematica Applicata, Consiglio Nazionale delle Richerche, Genove, Italy, 1988.
J. D. Foley, and A. van Dam: Fundamentals of Interactive Computer Graphics, Addison-Wesley, Reading, Massachusetts, 1982.
H. Fuchs, Z. M. Kedem, and B. Naylor: On visible surface generation by a priori structures, Comput. Graphics, 14 (1980), 124–133.
G. Voronoi: Sur quelques propriétés des formes quadratiques parfaites, J. Reine Angew. Math., 133 (1907), 212–287.