PCO: Precision-Controllable Offset Surfaces with Sharp Features

Abstract

Surface offsetting is a crucial operation in digital geometry processing and computer-aided design, where an offset is defined as an iso-value surface of the distance field. A challenge emerges as even smooth surfaces can exhibit sharp features in their offsets due to the non-differentiable characteristics of the underlying distance field. Prevailing approaches to the offsetting problem involve approximating the distance field and then extracting the iso-surface. However, even with dual contouring (DC), there is a risk of degrading sharp feature points/lines due to the inaccurate discretization of the distance field. This issue is exacerbated when the input is a piecewise-linear triangle mesh. This study is inspired by the observation that a triangle-based distance field, unlike the complex distance field rooted at the entire surface, remains smooth across the entire 3D space except at the triangle itself. With a polygonal surface comprising n triangles, the final distance field for accommodating the offset surface is determined by minimizing these n triangle-based distance fields. In implementation, our approach starts by tetrahedralizing the space around the offset surface, enabling a tetrahedron-wise linear approximation for each triangle-based distance field. The final offset surface within a tetrahedral range can be traced by slicing the tetrahedron with planes. As illustrated in the teaser figure, a key advantage of our algorithm is its ability to precisely preserve sharp features. Furthermore, this paper addresses the problem of simplifying the offset surface's complexity while preserving sharp features, formulating it as a maximal-clique problem.