A local coordinate system on a surface Export

@inproceedings{citeulike:6031685, abstract = {Coordinate systems associated to a finite set of sample points have been extensively studied, especially in the context of interpolation of multivariate scattered data. Notably, Sibson proposed the so-called natural neighbor coordinates that are defined from the Voronoi diagram of the sample points. A drawback of those coordinate systems is that their definition domain is restricted to the convex hull of the sample points. This make them difficult to use when the sample points belong to a surface. To overcome this difficulty, we propose a new system of coordinates. Given a closed surface, i.e. a manifold of, the coordinate system is defined everywhere on the surface, is continuous, and is local even if the sampling density is finite. Moreover, it is inherently 1-dimensional while the previous systems are dimensional. No assumption is made about the ordering, the connectivity or topology of the sample points nor of the surface. We illustrate our results with an application to interpolation over a surface.}, address = {New York, NY, USA}, author = {Boissonnat, Jean D. and Flototto, Julia}, booktitle = {SMA '02: Proceedings of the seventh ACM symposium on Solid modeling and applications}, citeulike-article-id = {6031685}, citeulike-linkout-0 = {http://portal.acm.org/citation.cfm?id=566282.566302}, citeulike-linkout-1 = {http://dx.doi.org/10.1145/566282.566302}, doi = {10.1145/566282.566302}, isbn = {1-58113-506-8}, keywords = {phd}, location = {Saarbr\"{u}cken, Germany}, pages = {116--126}, posted-at = {2009-10-29 10:09:28}, priority = {2}, publisher = {ACM}, title = {A local coordinate system on a surface}, url = {http://dx.doi.org/10.1145/566282.566302}, year = {2002} }

TY - CONF ID - citeulike:6031685 L3 - citeulike-article-id:6031685 N2 - Coordinate systems associated to a finite set of sample points have been extensively studied, especially in the context of interpolation of multivariate scattered data. Notably, Sibson proposed the so-called natural neighbor coordinates that are defined from the Voronoi diagram of the sample points. A drawback of those coordinate systems is that their definition domain is restricted to the convex hull of the sample points. This make them difficult to use when the sample points belong to a surface. To overcome this difficulty, we propose a new system of coordinates. Given a closed surface, i.e. a manifold of, the coordinate system is defined everywhere on the surface, is continuous, and is local even if the sampling density is finite. Moreover, it is inherently 1-dimensional while the previous systems are dimensional. No assumption is made about the ordering, the connectivity or topology of the sample points nor of the surface. We illustrate our results with an application to interpolation over a surface. CY - Saarbr\"{u}cken, Germany SN - 1-58113-506-8 AD - New York, NY, USA EP - 126 TI - A local coordinate system on a surface PB - ACM T2 - SMA '02: Proceedings of the seventh ACM symposium on Solid modeling and applications SP - 116 KW - phd AU - Boissonnat, Jean AU - Flototto, Julia PY - 2002/// UR - http://dx.doi.org/10.1145/566282.566302 ER -