# Geometric rounding and feature separation in meshes

Victor Milenkovic, Elisha Sacks

Research output: Contribution to journalArticle

### Abstract

Geometric rounding of a 3D triangle mesh is the task of approximating the vertex coordinates by floating point numbers while preserving the topology. We present a practical geometric rounding algorithm based on 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. The geometric rounding algorithm allows computational geometry algorithms to interface with numerical algorithms. Mesh feature separation is also useful on its own, for example for enforcing minimum feature sizes in CAD models. We demonstrate a robust, efficient implementation.

Original language English (US) 12-18 7 CAD Computer Aided Design 108 https://doi.org/10.1016/j.cad.2018.10.003 Published - Mar 1 2019

### Fingerprint

Topology
Computational geometry
Computer aided design

### Keywords

• Geometric rounding
• Mesh simplification
• Robust computational geometry

### ASJC Scopus subject areas

• Computer Science Applications
• Computer Graphics and Computer-Aided Design
• Industrial and Manufacturing Engineering

### Cite this

In: CAD Computer Aided Design, Vol. 108, 01.03.2019, p. 12-18.

Research output: Contribution to journalArticle

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