Anisotropy and Cross Fields
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Date
2024
Authors
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Journal ISSN
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Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
We consider a cross field, possibly with singular points of valence 3 or 5, in which all streamlines are finite, and either end on the boundary or form cycles. We show that we can always assign lengths to the two cross field directions to produce an anisotropic orthogonal frame field. There is a one-dimensional family of such length functions, and we optimize within this family so that the two lengths are everywhere as similar as possible. This gives a numerical bound on the minimal anisotropy of any quad mesh exactly following the input cross field. We also show how to remove some limit cycles.
Description
CCS Concepts: Computing methodologies → Mesh geometry models; Shape analysis
@article{10.1111:cgf.15132,
journal = {Computer Graphics Forum},
title = {{Anisotropy and Cross Fields}},
author = {Simons, Lance and Amenta, Nina},
year = {2024},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.15132}
}