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Polyhedral Approximation of 3 D Objects
| Content Provider | Semantic Scholar |
|---|---|
| Author | Schreiber, T. |
| Abstract | 1 everywhere except for the data sites where it is only C 0. 3. it has local support. 4. it has linear precision. We have investigated the folowing: instead of considering a discrete set of data sites, check what happens if all data sites are along a given closed boundary curve, and also let the number of data sites go to infinity. The interpolant now becomes transfinite-finite sums in Sibson's interpolant become convolution integrals for the transfinite case. The limits for these integrals have to be computed using the continuous Voronoi diagram of the boundary, a strucure closely related to its medial axis. For the special case of a circular boundary, we obtain parametric surfaces that are close to minimal. If we replace the planar circular domain by a sperical cap, we are able to reproduce Enneper's minimal surface exactly, but we only have a numerical "proof" for this. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.dagstuhl.de/fileadmin/files/Reports/96/9622.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
