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Variational Normal Meshes
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@MISC{And_variationalnormal,
author = {Ilja Friedel And and Andrei Khodakovsky},
title = {Variational Normal Meshes},
year = {}
}
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Abstract
this article, we propose a novel method to approximate a given mesh with a normal mesh. Instead of building an associated parameterization on the fly, we assume a globally smooth parameterization at the beginning and cast the problem as one of perturbing this parameterization. Controlling the magnitude of this perturbation gives us explicit control over the range between fully constrained (only scalar coefficients) and unconstrained (3-vector coefficients) approximations. With the unconstrained problem giving the lowest approximation error, we can thus characterize the error cost of normal meshes as a function of the number of nonnormal offsets---we find a significant gain for little (error) cost. Because the normal mesh construction creates a geometry driven approximation, we can replace the difficult geometric distance minimization problem with a much simpler least squares problem. This variational approach reduces magnitude and structure (aliasing) of the error further. Our method separates the parameterization construction into an initial setup followed only by subsequent perturbations, giving us an algorithm which is far simpler to implement, more robust, and significantly faster
Keyphrases
variational normal mesh normal mesh 3-vector coefficient parameterization construction scalar coefficient geometry driven approximation approximation error difficult geometric distance minimization problem significant gain unconstrained problem variational approach reduces square problem nonnormal offset smooth parameterization subsequent perturbation error cost much simpler normal mesh construction initial setup novel method
