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Read  full  paper  at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53577#.VMnaLyzQrzE Author(s)    Vincent Delos , Denis Teissandier Affiliation(s) University of Bordeaux, CNRS, National Center for French Research, I2M, UMR 5295, Talence, France . ABSTRACT Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis problem described in [1]. Our approach is based on the use of linear programming and is solvable in polynomial time. The algorithm we developed can be implemented and parallelized in a very easy way. KEYWORDS Computational Geometry , Polytope , Minkowski Sum , Linear Programming , Convex Hull Cite this paper Delos, V. and Teissandier, D. (2015) Minkowski Sum of Polytopes Defined by Their Vertices. Journal of Applied Mathematics and Physics , 3 , 62-67. doi...

Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=48300#.VESxm1fHRK0 Author(s)   Amin Alqudah Affiliation(s) Computer Engineering Department, Hijjawi Faculty for Engineering Technology, Yarmouk University, Irbid, Jordan . ABSTRACT Surface reconstruction is a problem in the field of computational geometry that is concerned with recreating a surface from scattered data points sampled from an unknown surface. To date, the primary application of surface reconstruction algorithms has been in computer graphics, where physical models are digitized in three dimensions with laser range scanners or mechanical digitizing probes (Bernardini   et al ., 1999   [1] ). Surface reconstruction algorithms are used to conv...