Geometric Rounding and Feature Separation in Meshes

TL;DR

This paper introduces a practical geometric rounding algorithm for 3D meshes that preserves topology by ensuring feature separation before rounding, facilitating better integration of geometric and numerical algorithms.

Contribution

It presents a novel mesh modification strategy to achieve feature separation, enabling topology-preserving rounding of mesh vertices in 3D models.

Findings

The algorithm effectively preserves mesh topology during rounding.

Feature separation improves robustness and accuracy of geometric processing.

Implementation demonstrates practical applicability in CAD and computational geometry.

Abstract

Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical algorithms. We present a practical geometric rounding algorithm for 3D triangle meshes that preserves the topology of the mesh. The basis of the algorithm is a novel strategy: 1) modify the mesh to achieve a feature separation that prevents topology changes when the coordinates change by the rounding unit; and 2) round each vertex coordinate to the closest floating point number. Feature separation is also useful on its own, for example for satisfying minimum separation rules in CAD models. We demonstrate a robust, accurate implementation.