Creating good quality meshes from smooth implicit surfaces

TL;DR

This paper introduces a tessellation algorithm for converting smooth implicit surfaces into high-quality, nearly isotropic meshes, improving the approximation of surface properties for visualization and analysis.

Contribution

The proposed method efficiently generates well-structured meshes from multi-sided implicit surfaces, addressing limitations of existing algorithms in quality and computational overhead.

Findings

Produces high-quality, nearly isotropic meshes

Improves approximation of surface normals and curvatures

Reduces post-processing computational costs

Abstract

Visualization of implicit surfaces is an actively researched topic. While raytracing can produce high quality images, it is not well suited for creating a quick preview of the surface. Indirect algorithms (e.g. Marching Cubes) create an easily renderable triangle mesh, but the result is often not sufficiently well-structured for a good approximation of differential surface quantities (normals, curvatures, etc.). Post-processing methods usually have a considerable computational overhead, and high quality is not guaranteed. We propose a tessellation algorithm to create nearly isotropic meshes, using multi-sided implicit surfaces.