Yang, JinlinLiu, ShiboChai, ShuangmingLiu, LigangFu, Xiao-MingCampen, MarcelSpagnuolo, Michela2022-06-272022-06-2720221467-8659https://doi.org/10.1111/cgf.14604https://diglib.eg.org:443/handle/10.1111/cgf14604We 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.CCS Concepts: Computing methodologies --> Shape modelingComputing methodologiesShape modeling10.1111/cgf.1460479-8810 pages