J.-D. Boissonnat, L. J. Guibas, S. Y. Oudot. Learning Smooth Objects by Probing. Proc. 21st Annual Sympos. on Comput. Geom., pp. 198-207, 2005.
Full version appeared in Computational Geometry: Theory and Applications, 37:38-58, 2007 (pdf).
We consider the problem of discovering a smooth unknown surface S bounding an object O in R3. 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 propose a probing strategy for generating a sequence of surface samples on S from which a triangulated surface can be generated which approximates S within any desired accuracy. We bound the number of probes and the number of elementary moves of the probing device. Our solution is an extension of previous work on Delaunay refinement techniques for surface meshing. The approximating surface we generate enjoys the many nice properties of the meshes obtained by those techniques, e.g. exact topological type, normal approximation, etc.
@inproceedings{bgo-lsop-05, author = {Jean-Daniel Boissonnat and Leonidas J. Guibas and Steve Oudot}, title = {Learning smooth objects by probing}, booktitle = {SCG '05: Proceedings of the twenty-first annual symposium on Computational geometry}, year = {2005}, isbn = {1-58113-991-8}, pages = {198--207}, location = {Pisa, Italy}, publisher = {ACM Press}, address = {New York, NY, USA}, } |