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.

Feature‐Preserving Offset Mesh Generation from Topology‐Adapted Octrees

“…Remeshing is completely independent of the octree constructed in Section 4 and can be applied to other methods that generate offset meshes. Alpha wrapping [PRH*22] is such a method: it aims to construct a manifold englobing volume around an input and for this generates an offset mesh with a user‐defined precision. Although the method guarantees the absence of intersections with the input mesh, it does not recover sharp features in the output offset surface.…”

“…It also yields high‐quality reconstructions of challenging geometric features such as thin tunnels. Finally, it is independent of the octree and can also be applied as a post‐processing step to other offset mesh generation methods such as [PRH*22] or [CK10b].…”

Surface-guided computing to analyze subcellular morphology and membrane-associated signals in 3D

“…In practice, segmentation algorithms continue to improve and postprocessing techniques can be used to create improved surface meshes. Moreover we can leverage surface meshing algorithms that are more sophisticated than marching cubes, such as dual contouring 86 and shrink-wrapping 87 , to guarantee watertight mesh creation. For timelapse acquisitions, as we showed in Fig.…”