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A polynomial time algorithm for Minkowski reconstruction
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Source Annual Symposium on Computational Geometry archive
Proceedings of the eleventh annual symposium on Computational geometry table of contents
Vancouver, British Columbia, Canada
Pages: 1 - 9  
Year of Publication: 1995
ISBN:0-89791-724-3
Authors
Peter Gritzmann  Universität Trier, Fb IV, Mathematik, D-54286 Trier, Germany
Alexander Hufnagel  Universität Trier, Fb IV, Mathematik, D-54286 Trier, Germany
Sponsors
SIGACT: ACM Special Interest Group on Algorithms and Computation Theory
SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques
Publisher
ACM  New York, NY, USA
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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.

 
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M.E. Dyer, P. Gritzmann, and A. Hufnagel, On the complexity of computing mixed volumes, Manuscript, 1994.
 
3
M.R. Garey and D.S. Johnson, Computers and intractability, Freeman, San Francisco, 1979.
 
4
P. Gritzmann and A. Hnfnagel, On the algorithmic complexity of Minkowski's reconstruction theorem, Manuscript, 1994.
 
5
P. Gritzmann and V. Klee, On the complexity of some basic problems in computational convexity: Ii. Volume and mixed voh~mes, Polytopes: Abstract, Convex and Computational (Boston) (T. Bisztriczky, P. McMullen, R. Schneider, and A. I. Weiss, eds.), Kluwer, 1994, pp. 373-466.
 
6
H. Groemer, On an inequality of Minkowski for mixed volumes, Geom. Dedicata 33 (1990), 117-122.
 
7
~, Stability of geometric inequalities, Handbook of Convex Geometry Vol. A (Amsterdam) (P.M. Gruber and J.M. Wills, eds.), North-Holland, 1993, pp. 125-150.
 
8
M. Gr~Stschel, L. Lov&sz, and A. Schrijver, Geometric algorithms and combinatorial optimization, Springer, Berlin, 1988.
 
9
B.K.P. Horn, Extended Gaussian images, Proceedings of the IEEE 72 (1984), 1671-1686.
 
10
 
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A. Hufnagel, Algorithmic problems in Brunn-Minkowski theory, Dissertation, Trier, 1995.
 
12
J. Lawrence, Polytope volume computation, Math. Comput. 57 (1991), 259-271.
 
13
J.J. Little, An iterative method for reconstructing convex polyhedra from extended Gaussian images, Proceedings of the AAAI, National Conference on Artificial Intelligence (Washington D.C.), 1983, pp. 247-250.
14
 
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H. Minkowski, Allgemeine Lehrs~tze ~ber konvexe Polyeder, Nachr. Ges. Wiss. G~ttingen (1897), 198-219.
 
16
~___, Volumen und Oberflgche, Math. Ann. 57 (1903), 447-495.
 
17
J.R. Sangwine-Yager, Mixed volumes, Handbook of Convex Geometry, Vol. A (Amsterdam) (P.M. Gruber and J.M. Wills, eds.), North-Holland, 1993, pp. 43-72.
 
18
R. Schneider, Convex bodies: The Brunn-Minkowski theory, Encyclopedia of Mathematics and its Applications, Vol. 44, Cambridge University Press, 1993.

Collaborative Colleagues:
Peter Gritzmann: colleagues
Alexander Hufnagel: colleagues