The Minkowski sum of simplices in 3-dimensional space: An analytical description
作者： Jean-Paul Bourrières
DOI: 10.1016/J.COMGEO.2014.04.002
关键词:
摘要: We provide an analytical description of the Minkowski sum simplices in View MathML source. The convex polytope is determined by coordinates facets' vertices, may be degenerate or not. pre-established allows a rapid implementation using popular applications, here achieved Matlab®.
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sci-hub.se 参考文章(19)
Margaret M. BAYER, Carl W. LEE, Combinatorial Aspects of Convex Polytopes Handbook of Convex Geometry#R##N#Part A. pp. 485- 534 ,(1993) , 10.1016/B978-0-444-89596-7.50019-5
Jürgen Richter-Gebert, Günter M. Ziegler, Martin Henk, Basic properties of convex polytopes Handbook of discrete and computational geometry. pp. 243- 270 ,(1997) , 10.1201/9781420035315.CH16
Peter Gritzmann, Bernd Sturmfels, Minkowski addition of polytopes: computational complexity and applications to Gro¨bner bases SIAM Journal on Discrete Mathematics. ,vol. 6, pp. 246- 269 ,(1993) , 10.1137/0406019
Efi Fogel, Dan Halperin, Exact and efficient construction of Minkowski sums of convex polyhedra with applications Computer-aided Design. ,vol. 39, pp. 929- 940 ,(2007) , 10.1016/J.CAD.2007.05.017
D. Pallaschke, J. Rosenmüller, Cephoids: Minkowski sums of de Gua simplexes Optimization. ,vol. 59, pp. 515- 540 ,(2010) , 10.1080/02331930801951280
Jun-ichi Imura, Optimal control of sampled-data piecewise affine systems Automatica. ,vol. 40, pp. 661- 669 ,(2004) , 10.1016/J.AUTOMATICA.2003.11.012
Denis Teissandier, Vincent Delos, Algorithm to calculate the Minkowski sums of 3-polytopes based on normal fans Computer-aided Design. ,vol. 43, pp. 1567- 1576 ,(2011) , 10.1016/J.CAD.2011.06.016
John Riordan, The number of faces of simplicial polytopes Journal of Combinatorial Theory, Series A. ,vol. 1, pp. 82- 95 ,(1966) , 10.1016/S0021-9800(66)80006-6
D. Pallaschke, J. Rosenmüller, Computing the Minkowski Sum of Prisms Journal of Global Optimization. ,vol. 35, pp. 321- 341 ,(2006) , 10.1007/S10898-005-3841-5
P. McMullen, The numbers of faces of simplicial polytopes Israel Journal of Mathematics. ,vol. 9, pp. 559- 570 ,(1971) , 10.1007/BF02771471