(The Eurographics Association and John Wiley & Sons Ltd., 2022) Yang, Jinlin; Liu, Shibo; Chai, Shuangming; Liu, Ligang; Fu, Xiao-Ming; Campen, Marcel; Spagnuolo, Michela
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.