Bezier Guarding: Precise Higher-Order Meshing of Curved 2D Domains

摘要

We present a mesh generation algorithm for the curvilinear triangulation ofplanar domains with piecewise polynomial boundary. The resulting meshconsists of regular, injective higher-order triangular elements and preciselyconforms with the domain’s curved boundary. No smoothness requirementsare imposed on the boundary. Prescribed piecewise polynomial curves inthe interior, like material interfaces or feature curves, can be taken intoaccount for precise interpolation by the resulting mesh’s edges as well. In itscore, the algorithm is based on a novel explicit construction of guaranteedinjective Bézier triangles with certain edge curves and edge parametrizationsprescribed. Due to the use of only rational arithmetic, the algorithm canoptionally be performed using exact number types in practice, so as toprovide robustness guarantees.