Approximating isosurfaces by guaranteed‐quality triangular meshes

• 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
• DOI: 10.1111/cgf.14066

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.