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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Bibliographic Details
Published in:Computer graphics forum Vol. 39; no. 5; pp. 29 - 40
Main Authors: Hass, J., Trnkova, M.
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.08.2020
Subjects:
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
Online Access:Get full text
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Summary: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.
Bibliography: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)
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.14066