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

Autor(en): Mandad, Manish
Campen, Marcel 
Stichwörter: 3D; APPROXIMATION; Bezier simplex; Bezier triangle; BOUNDARY; Computer Science; Computer Science, Software Engineering; curvilinear mesh; FINITE-ELEMENT SOLUTION; GENERATION; isogeometric analysis; MESHES; P-VERSION; QUALITY
Erscheinungsdatum: 2020
Herausgeber: ASSOC COMPUTING MACHINERY
Journal: ACM TRANSACTIONS ON GRAPHICS
Volumen: 39
Ausgabe: 4
Zusammenfassung: 
We present a mesh generation algorithm for the curvilinear triangulation of planar domains with piecewise polynomial boundary. The resulting mesh consists of regular, injective higher-order triangular elements and precisely conforms with the domain's curved boundary. No smoothness requirements are imposed on the boundary. Prescribed piecewise polynomial curves in the interior, like material interfaces or feature curves, can be taken into account for precise interpolation by the resulting mesh's edges as well. In its core, the algorithm is based on a novel explicit construction of guaranteed injective Bezier triangles with certain edge curves and edge parametrizations prescribed. Due to the use of only rational arithmetic, the algorithm can optionally be performed using exact number types in practice, so as to provide robustness guarantees.
ISSN: 07300301
DOI: 10.1145/3386569.3392372

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