Precise High-order Meshing of 2D Domains with Rational Bézier Curves
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Date
2022
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
We propose a novel method to generate a high-order triangular mesh for an input 2D domain with two key characteristics: (1) the mesh precisely conforms to a set of input piecewise rational domain curves, and (2) the geometric map on each curved triangle is injective. Central to the algorithm is a new sufficient condition for placing control points of a rational Bézier triangle to guarantee that the conformance and injectivity constraints are theoretically satisfied. Taking advantage of this condition, we provide an explicit construct that robustly creates higher-order 2D meshes satisfying the two characteristics. We demonstrate the robustness and effectiveness of our algorithm over a data set containing 2200 examples.
Description
CCS Concepts: Computing methodologies --> Shape modeling
@article{10.1111:cgf.14604,
journal = {Computer Graphics Forum},
title = {{Precise High-order Meshing of 2D Domains with Rational Bézier Curves}},
author = {Yang, Jinlin and Liu, Shibo and Chai, Shuangming and Liu, Ligang and Fu, Xiao-Ming},
year = {2022},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.14604}
}