Name
Abstract | ||
|---|---|---|
Given a nonsingular compact 2-manifold F without boundary, we present methods for establishing a family of surfaces which can approximate F so that each approximant is ambient isotopic to F. The current state of the art in surface reconstruction is that both theory and practice are limited to generating a piecewise linear (PL) approximation. The methods presented here offer broader theoretical guidance for a rich class of ambient isotopic approximations. They are also used to establish sufficient conditions for an interval solid to be ambient isotopic to the solid it is approximating.The methods are based on global theoretical considerations and are compared to existing local methods. Practical implications of these methods are also presented. For the global case, a differential surface analysis is performed to find a positive number ρ so that the offsets Fo(± ρ) of F at distances ± ρ are nonsingular. In doing so, a normal tubular neighborhood, F(ρ), of F is constructed. Then, each approximant of F lies inside F(ρ). Comparisons between these global and local constraints are given. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1145/781606.781634 | Symposium on Solid Modeling and Applications |
Keywords | Field | DocType |
local constraint,approximate f,differential surface analysis,inside f,surface reconstruction,global case,2-manifold f,ambient isotopic approximation,ambient isotopic,global theoretical consideration,interval solid,broader theoretical guidance,computational topology,surface analysis,piecewise linear,reverse engineering | Surface reconstruction,Mathematical optimization,Invertible matrix,Piecewise linear function,Ambient isotopy,Tubular neighborhood,Computational topology,Mathematics | Conference |
ISBN | Citations | PageRank |
1-58113-706-0 | 6 | 0.58 |
References | Authors | |
17 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Takis Sakkalis | 1 | 347 | 34.52 |
| Thomas J. Peters | 2 | 181 | 18.68 |