Abstract
A Nef polyhedron is any set in ℝd which can be obtained by applying a finite number of Boolean set operations cpl and ∩ to finitely many (open) linear halfspaces. After resuming some fundamentals, it is shown in which sense several kinds of well-known polyhedra are special cases of Nef polyhedra. Then a number of representations of Nef polyhedra are presented and discussed, and algorithms for converting them into each other are given.
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References
Bajaj, C. L., Edelsbrunner, H., Kaufman, A. E., Naylor, B. F., Rossignac, J. R.: Representations of geometry for computer graphics. Course Notes 29, ACM SIGGRAPH 96, 1996.
Bieri, H.: Boolean and topological operations for Nef polyhedra. In: CSG 94 Set-theoretic solid modelling—techniques and applications (Woodwark, J., ed.), pp. 35–53. Information Geometers 1994.
Bieri, H.: Nef polyhedra: a brief introduction. In: Geometric modelling—Dagstuhl 1993 (Hagen, H., Farin, G., Noltemeier, H., eds.), pp. 43–60. Wien New York: Springer, 1995.
Bieri, H.: Two basic operations for Nef polyhedra. In: CSG 96 Set-theoretic solid modelling—techniques and applications (Woodwark, J., ed.), pp. 337–356. Information Geometers, 1996.
Bieri, H., Mayor, D.: A ternary tree representation of generalized digital images. In: Virtual worlds and multimedia (Magnenat-Thalmann, N., Thalmann, D., eds.), pp. 23–35. New York: John Wiley, 1993.
Bieri, H., Nef, W.: Elmentary set-operations with d-dimensional polyhedra. In: Computational geometry and its applications (Noltemeier, H., ed.), pp. 97–112. Berlin Heidelberg New York Tokyo: Springer, 1998 (Lecture Notes in Computer Science 333).
Brønsted, A.: An introduction to convex polytopes. Berlin Heidelberg New York: Springer, 1983.
Edelsbrunner, H.: Algorithms in combinatorial geometry. Berlin Heidelberg New York Tokyo: Springer, 1987.
Ferrucci, V.: Dimension-independent solid modeling, PhD Thesis VII-95-4, Dipartimento di Informatica e Sistemistica, Univesità “La Sapienza”, Rome, Italy, 1995.
Gomes, J., Hoffmann, C. M., Shapiro, V., Velho, L.: Modeling in computer graphics. Course Notes 40, ACM SIGGRAPH 93, 1993.
Hartwig, A.: Algebraic 3-d modeling. A. K. Peters, 1996.
Hoffmann, C. M.: Geometric and solid modeling—an introduction. Morgan Kaufmann, 1989.
Mäntylä, M.: An introduction to solid modeling. Computer Science Press, 1988.
Nef, W.: Beiträge zur Theorie der Polyeder—mit Anwendungen in der Computergraphik (Contributions to the theory of polyhedra—with applications in computer graphics). Herbert Lang, 1978.
Paoluzzi, A., Pascucci, V., Vicentino, M.: Geometric programming: a programming approach to geometric design. ACM Trans. Graph. 14, 266–306 (1995).
Pascucci, V., Ferrucci, V., Paoluzzi, A.: Dimension-independent convex-cell based HPC: representation scheme and implementation issues. In: Third symposium on solid modeling and applications. (Hoffmann, C. M., Rossignac, J. R., eds.), pp. 163–174. ACM Press 1995.
Requicha, A. A. G.: Representations for rigid solids: theory, methods, and systems. ACM Comp. Surv. 12, 437–464 (1980).
Rossignac, J. R.: Through the cracks of the solid modeling mile-stone. Eurographics’ 91 State of the Art Report on Solid Modeling. In: From object modelling to advanced visualization (Coquillart, S., Strasser, W., Stucki, P., eds.), pp. 1–75. Berlin Heidelberg New York Tokyo: Springer, 1994.
Shapiro, V., Vossler, D. L.: What is a parametric family of solids? In: Third Symposium on Solid Modeling and Applications (Hoffmann, C. M., Rossignac, J. R., eds.), pp. 43–54. ACM Press, 1995.
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Dedicated to Walter Nef on the occasion of his eightieth birthday
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Bieri, H. (1998). Representation Conversions for Nef Polyhedra. In: Farin, G., Bieri, H., Brunnett, G., De Rose, T. (eds) Geometric Modelling. Computing Supplement, vol 13. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6444-0_3
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DOI: https://doi.org/10.1007/978-3-7091-6444-0_3
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