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.
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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
} }
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