An algorithm to build convex hulls for 3‐D objects

Abstract In this paper, a new algorithm based on the Quickhull algorithm is proposed to find convex hulls for 3‐D objects using neighbor trees. The neighbor tree is the data structure by which all visible facets to the selected furthest outer point can be found. The neighboring sequence of ridges on the outer boundary of all visible facets also can be found directly from the neighbor tree. This new algorithm is twice as efficient as Barber's algorithm.

[1]  Kenneth L. Clarkson,et al.  Algorithms for diametral pairs and convex hulls that are optimal, randomized, and incremental , 1988, SCG '88.

[2]  Maher M. Atwah,et al.  An Associative Implementation Of Classical Convex Hull Algorithms , 1996 .

[3]  Michael Ian Shamos,et al.  Convex Hulls: Basic Algorithms , 1985 .

[4]  Ronald L. Graham,et al.  An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set , 1972, Inf. Process. Lett..

[5]  Ray A. Jarvis,et al.  On the Identification of the Convex Hull of a Finite Set of Points in the Plane , 1973, Inf. Process. Lett..

[6]  Computing the three-dimensional convex hull , 1997 .

[7]  Herbert Edelsbrunner Constructing Convex Hulls , 1987 .

[8]  Selim G. Akl,et al.  An Associative Implementation of Graham's Convex Hull Algorithm , 1995, Parallel and Distributed Computing and Systems.

[9]  Kenneth R. Anderson,et al.  A Reevaluation of an Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set , 1978, Inf. Process. Lett..

[10]  Michael Kallay,et al.  The Complexity of Incremental Convex Hull Algorithms in Rd , 1984, Inf. Process. Lett..

[11]  Johnnie W. Baker,et al.  An associative static and dynamic convex hull algorithm , 2002, Proceedings 16th International Parallel and Distributed Processing Symposium.

[12]  Raimund Seidel,et al.  Linear programming and convex hulls made easy , 1990, SCG '90.

[13]  A. Bykat,et al.  Convex Hull of a Finite Set of Points in Two Dimensions , 1978, Inf. Process. Lett..

[14]  Günter Ewald,et al.  Geometry: an introduction , 1971 .

[15]  Joseph O'Rourke,et al.  Computational Geometry in C. , 1995 .

[16]  Andrew M. Day The implementation of an algorithm to find the convex hull of a set of three-dimensional points , 1990, TOGS.

[17]  Hanif D. Sherali,et al.  Convex hull representations of models for computing collisions between multiple bodies , 2001, Eur. J. Oper. Res..

[18]  F. P. Preparata,et al.  Convex hulls of finite sets of points in two and three dimensions , 1977, CACM.

[19]  Selim G. Akl,et al.  A Fast Convex Hull Algorithm , 1978, Inf. Process. Lett..

[20]  Ketan Mulmuley,et al.  Computational geometry - an introduction through randomized algorithms , 1993 .

[21]  Donald R. Chand,et al.  An Algorithm for Convex Polytopes , 1970, JACM.

[22]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[23]  William F. Eddy,et al.  A New Convex Hull Algorithm for Planar Sets , 1977, TOMS.

[24]  Jack Koplowitz,et al.  A More Efficient Convex Hull Algorithm , 1978, Inf. Process. Lett..

[25]  Herbert Edelsbrunner,et al.  Algorithms in Combinatorial Geometry , 1987, EATCS Monographs in Theoretical Computer Science.

[26]  David P. Dobkin,et al.  The quickhull algorithm for convex hulls , 1996, TOMS.

[27]  Kokichi Sugihara Three-dimensional convex hull as a fruitful source of diagrams , 2000, Theor. Comput. Sci..

[28]  Olivier D. Faugeras,et al.  Relative 3D positioning and 3D convex hull computation from a weakly calibrated stereo pair , 1995, Image Vis. Comput..

[29]  Kokichi Sugihara,et al.  Robust Gift Wrapping for the Three-Dimensional Convex Hull , 1994, J. Comput. Syst. Sci..