Precise High‐order Meshing of 2D Domains with Rational Bézier Curves. (6th October 2022) - Yang, Jinlin; Liu, Shibo; Chai, Shuangming; Liu, Ligang; Fu, Xiao‐Ming
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.