Geometric rounding and feature separation in meshes

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.