Approximating isosurfaces by guaranteed‐quality triangular meshes

We describe a new method for approximating an implicit surface F by a piecewise‐flat triangulated surface whose triangles are as close as possible to equilateral. The main advantage is improved mesh quality which is guaranteed for smooth surfaces. The GradNormal algorithm generates a triangular mesh...

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Vydáno v:	Computer graphics forum Ročník 39; číslo 5; s. 29 - 40
Hlavní autoři:	Hass, J., Trnkova, M.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Oxford Blackwell Publishing Ltd 01.08.2020
Témata:	Algorithms Approximation Categories and Subject Descriptors (according to ACM CCS) Curve, surface, solid, and object representations I.3.5 [Computational Geometry and Object Modeling] Mesh generation Triangles
ISSN:	0167-7055, 1467-8659
On-line přístup:	Získat plný text
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Popis
Shrnutí:	We describe a new method for approximating an implicit surface F by a piecewise‐flat triangulated surface whose triangles are as close as possible to equilateral. The main advantage is improved mesh quality which is guaranteed for smooth surfaces. The GradNormal algorithm generates a triangular mesh that gives a piecewise‐differentiable approximation of F, with angles between 35.2 and 101.5 degrees. As the mesh size approaches 0, the mesh converges to F through surfaces that are isotopic to F.
Bibliografie:	Partially supported by NSF grants DMS1760485 and DMS1719582 The authors thank Benjamin Hass for assistance with the software implementation. Partially supported by NSF grants DMS‐1107452, 1107263, 1107367 “RNMS: Geometric structures and Representation Varieties” (the GEAR Network) ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0167-7055 1467-8659
DOI:	10.1111/cgf.14066