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 in Computational Geometry: Theory and Applications, 37:38-58, 2007 (pdf). Video available here.
We consider the problem of discovering a smooth unknown surface S
bounding an object O in R^3. 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 = {J.-D. Boissonnat and L. J. Guibas and S. Y. Oudot}, title = {Learning Smooth Objects by Probing}, booktitle = {Proc. 21st Annu. Sympos. on Computational Geometry}, pages = {198--207}, year = {2005} } |