Learning smooth objects by probing

This video considers the problem of discovering the boundary S of an unknown smooth object O. The discovery process consists of moving a point probing device in the free space around O so that it repeatedly comes in contact with S. We present a probing strategy for generating a sequence of sample points of S, from which a PL-approximation of S can be constructed, within any desired accuracy. This strategy can be applied in any dimension, although its output is guaranteed only for objects embedded in the plane or in 3-space. For pedagogical purpose, the video focuses on the planar case.

[1]  Mariette Yvinec,et al.  Probing a scene of non convex polyhedra , 1989, SCG '89.

[2]  Mariette Yvinec,et al.  Non Convex Contour Reconstruction , 1990, J. Symb. Comput..

[3]  Alfred M. Bruckstein,et al.  Blind approximation of planar convex sets , 1994, IEEE Trans. Robotics Autom..

[4]  T. J. Richardson,et al.  Approximation of Planar Convex Sets from Hyperplane Probes , 1997, Discret. Comput. Geom..

[5]  Leonidas J. Guibas,et al.  Learning Surfaces by Probing , 2004 .

[6]  Richard Cole,et al.  Shape from Probing , 1987, J. Algorithms.

[7]  Steven Skiena,et al.  Geometric Reconstruction Problems , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[8]  Günter Rote,et al.  The convergence rate of the sandwich algorithm for approximating convex functions , 1992, Computing.