A defect-correction algorithm for minimizing the volume of a simple polyhedron which circumscribes a sphere

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A defect-correction algorithm for minimizing the volume of a simple polyhedron which circumscribes a sphere

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Annual Symposium on Computational Geometry archive
Proceedings of the second annual symposium on Computational geometry table of contents

Yorktown Heights, New York, United States

Pages: 159 - 168

Year of Publication: 1986

ISBN:0-89791-194-6

Author

A H Schoen

Dept. of Computer Science, Southern Illinois University, Carbondale, IL

Sponsors

SIGACT: ACM Special Interest Group on Algorithms and Computation Theory
SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

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ACM New York, NY, USA

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Downloads (6 Weeks): 3, Downloads (12 Months): 11, Citation Count: 0

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	Berman, J. D. and Hanes, K. {1970}: Volumes of polyhedra inscribed in the unit sphere in E$, Mathematische Annalen vol. 188 (1970), pp. 78-84.
	2	B~hmer, K. and Stetter, H. J. {1984}: Defect Correction Methods, Theory and Applications, Springer Verlag (1984).
	3	Goldberg, M. {1935}: The isoperimetric problem for polyhedra, Tohoku Mathematics Journal vol. 40 (1935), pp. 226-236.
	4	Goodman, J. E. and Pollack, R. {1986}: There are asymptotically far fewer polytopes than we thought, Bull. Amer. Math. Soc. vol. 14, No. i (1986).
	5	Gr~nbaum, B. {1967}: Oonvex polytopes, Interscience-Wiley, London (1967).
	6	Klee, V. {1972}: Viewer's Manual to accompany the film Shapes of the Future - Some Unsolved Problems in Geometry, Part II: Three Dimensions, distributed by Modern Learning Aids (1972).
	7	Lhuilier, S. {1782}: De melatione mutua oapacitatis et terminorum figurarum etc., Varsaviae (1782).
	8	Lindel~f, L. {1869, 1899}' Propri&t&s g&n&rales des polySdres etc., St. Petersburg, Bull. Acad. Sc. vol. XIV (1869), pp. 258-269. Recherches sur les poly~dres mamima, Helsingfors, Acta Soc. Sc. Fenn. vol. XXIV, No. 8 (1899).
	9	Melnyk, T. W., Knop, 0., and Smith, W. R. {1977}: Extremal arrangements of points and unit charges on a sphere: equilibrium configurations revisited, Can. J. Chem. 55, 10 (1977).
	10	Minkowski, H. {1897}: Allgemeine LehrsHtze ~ber die oonvexen PolyedeT, G6ttingen, Nach. Ges. Wiss. Math. phys. (1897), pp. 198-219.
	11	Steinitz, E. {1922, 1927, 1928}' Polyeder und Raumeinteilungen, Encyk. der Math. Wiss., Berlin, Band III-12, Heft 9 (1922), pp. 38-43, 94-101. ~ber i8operimetrisohe Probleme bei Konvezen PoZyedern, J. Math., Berlin, vol. 158 (1927), pp. 129-153, vol. 159 (1928), pp. 133-143.
	12	Wolter, J. D., Woo, T. C., and Volz R. A. {1985}' Optimal algorithms for symmetry detection in two and three dimensions, The Visua{ Computer vol 1, Springer-Verlag (1985).