Parametrization and smooth approximation of surface triangulations (1997)
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| Venue: | Computer Aided Geometric Design |
| Citations: | 225 - 15 self |
BibTeX
@ARTICLE{Floater97parametrizationand,
author = {Michael S. Floater},
title = {Parametrization and smooth approximation of surface triangulations},
journal = {Computer Aided Geometric Design},
year = {1997},
volume = {14},
pages = {231--250}
}
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Abstract
Abstract. A method based on graph theory is investigated for creating global parametrizations for surface triangulations for the purpose of smooth surface fitting. The parametrizations, which are planar triangulations, are the solutions of linear systems based on convex combinations. A particular parametrization, called shape-preserving, is found to lead to visually smooth surface approximations. A standard approach to fitting a smooth parametric curve c(t) through a given sequence of points xi = (xi,yi,zi) ∈ IR 3, i = 1,...,N is to first make a parametrization, a corresponding increasing sequence of parameter values ti. By finding smooth functions x,y,z: [t1,tN] → IR for which x(ti) = xi, y(ti) = yi, z(ti) = zi, an interpolatory curve
