Hierarchical Quad Meshing of 3D Scanned Surfaces

Abstract

In this paper we present a novel method to reconstruct watertight quad meshes on scanned 3D geometry. There exist many different approaches to acquire 3D information from real world objects and sceneries. Resulting point clouds depict scanned surfaces as sparse sets of positional information. A common downside is the lack of normals, connectivity or topological adjacency data which makes it difficult to actually recover a meaningful surface. The concept described in this paper is designed to reconstruct a surface mesh despite all this missing information. Even when facing varying sample density, our algorithm is still guaranteed to produce watertight manifold meshes featuring quad faces only. The topology can be set‐up to follow superimposed regular structures or align naturally to the point cloud's shape. Our proposed approach is based on an initial divide and conquer subsampling procedure: Surface samples are clustered in meaningful neighborhoods as leafs of a kd‐tree. A representative sample of the surface neighborhood is determined for each leaf using a spherical surface approximation. The hierarchical structure of the binary tree is utilized to construct a basic set of loose tiles and to interconnect them. As a final step, missing parts of the now coherent tile structure are filled up with an incremental algorithm for locally optimal gap closure. Disfigured or concave faces in the resulting mesh can be removed with a constrained smoothing operator.

At‐Most‐Hexa Meshes

“…The concepts proposed by Jakob et al [JTPSH15] and Schertler et al [STJ*17] use flow-fields to extract such quad meshes from oriented point clouds. Other works [ZLGH10,BL18] proposed techniques that do not require scanned or pre-computed normals for the point cloud to come up with a surface or, in the latter case, with a quad-mesh.…”