Alpha wrapping with an offset

Abstract

Given an input 3D geometry such as a triangle soup or a point set, we address the problem of generating a watertight and orientable surface triangle mesh that strictly encloses the input. The output mesh is obtained by greedily refining and carving a 3D Delaunay triangulation on an offset surface of the input, while carving with empty balls of radius alpha. The proposed algorithm is controlled via two user-defined parameters: alpha and offset. Alpha controls the size of cavities or holes that cannot be traversed during carving, while offset controls the distance between the vertices of the output mesh and the input. Our algorithm is guaranteed to terminate and to yield a valid and strictly enclosing mesh, even for defect-laden inputs. Genericity is achieved using an abstract interface probing the input, enabling any geometry to be used, provided a few basic geometric queries can be answered. We benchmark the algorithm on large public datasets such as Thingi10k, and compare it to state-of-the-art approaches in terms of robustness, approximation, output complexity, speed, and peak memory consumption. Our implementation is available through the CGAL library.