Work

Constrained Delaunay Tetrahedrization: A Robust and Practical Approach

Year: 2023

Type: article

Abstract: We present a numerically robust algorithm for computing the constrained Delaunay tetrahedrization (CDT) of a piecewise-linear complex, which has a 100% success rate on the 4408 valid models in the Thingi10k dataset. We build on the underlying theory of the well-known tetgen software, but use a floating-point implementation based on indirect geometric predicates to implicitly represent Steiner points: this new approach dramatically simplifies the implementation, removing the need for ad-hoc tolerances in geometric operations. Our approach leads to a robust and parameter-free implementation, with an empirically manageable number of added Steiner points. Furthermore, our algorithm addresses a major gap in tetgen's theory which may lead to algorithmic failure on valid models, even when assuming perfect precision in the calculations. Our output tetrahedrization conforms with the input geometry without approximations. We can further round our output to floating-point coordinates for downstream applications, which almost always results in valid floating-point meshes unless the input triangulation is very close to being degenerate.

Source: ACM Transactions on Graphics

DOI: 10.1145/3618352

Authors: Lorenzo Diazzi, Daniele Panozzo, Amir Vaxman, Marco Attene

Institutions: Istituto di Matematica Applicata e Tecnologie Informatiche, National Research Council, New York University, University of Edinburgh

Language: English

Topic: Computational Geometry and Mesh Generation

Subfield: Computer Graphics and Computer-Aided Design

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze

Funder: National Science Foundation

Awards: CHS: Small: Collaborative Research: Robust High Order Meshing and Analysis for Design Pipeline Automation, Elements:Software:Open-Source Robust Geometry Toolkit for Black-Box Finite Element Analysis