Approximating Boundary-Triangulated Objects with Balls

We compute a set of balls that approximates a given 3D object, and we derive small additive bounds for the overhead in balls with respect to the minimal solution with the same quality. The algorithm has been implemented and tested using the CGAL library [7].

[1]  Bernard Chazelle,et al.  Triangulating a non-convex polytype , 1989, SCG '89.

[2]  Franz Aurenhammer,et al.  Improved Algorithms for Discs and Balls Using Power Diagrams , 1988, J. Algorithms.

[3]  Carol O'Sullivan,et al.  Adaptive medial-axis approximation for sphere-tree construction , 2004, TOGS.

[4]  Philip M. Hubbard,et al.  Approximating polyhedra with spheres for time-critical collision detection , 1996, TOGS.

[5]  Dan Halperin,et al.  Exact and efficient construction of Minkowski sums of convex polyhedra with applications , 2006, Comput. Aided Des..

[6]  Hyeong In Choi,et al.  The Medial Axis Transform , 2002, Handbook of Computer Aided Geometric Design.

[7]  Sunghee Choi,et al.  The power crust, unions of balls, and the medial axis transform , 2001, Comput. Geom..

[8]  Komei Fukuda,et al.  From the zonotope construction to the Minkowski addition of convex polytopes , 2004, J. Symb. Comput..

[9]  Dinesh Manocha,et al.  Collision and Proximity Queries , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[10]  Leif Kobbelt,et al.  Ellipsoid decomposition of 3D-models , 2002, Proceedings. First International Symposium on 3D Data Processing Visualization and Transmission.

[11]  Marshall W. Bern,et al.  Surface Reconstruction by Voronoi Filtering , 1998, SCG '98.

[12]  John Dingliana,et al.  Collisions and perception , 2001, TOGS.

[13]  Richard L. Grimsdale,et al.  Collision Detection for Animation using Sphere‐Trees , 1995, Comput. Graph. Forum.

[14]  David S. Johnson,et al.  Approximation algorithms for combinatorial problems , 1973, STOC.

[15]  Bernard Chazelle,et al.  Triangulating a nonconvex polytope , 1990, Discret. Comput. Geom..

[16]  Raimund Seidel,et al.  On the difficulty of triangulating three-dimensional Nonconvex Polyhedra , 1992, Discret. Comput. Geom..