Multi-Level Partition of Unity Algebraic Point Set Surfaces

• Published in: Journal of computer science and technology 2011-03, Vol.26 (2), p.229-238
• Main Author: Xiao, Chun-Xia
• Format: Article
• Language: English
• Subjects: Algebra; Algorithms; Analysis; Approximation; Artificial Intelligence; Computer Science; Construction; Data Structures and Information Theory; Geometry; Information Systems Applications (incl.Internet); Mathematical analysis; Mathematical models; Partitions; Projection; R&D; Reconstruction; Research & development; Software Engineering; Spheres; Studies; Theory of Computation; Topological manifolds; Unity
• ISSN: 1000-9000; 1860-4749
• DOI: 10.1007/s11390-011-9429-2

We present a multi-level partition of unity algebraic set surfaces (MPU-APSS) for surface reconstruction which can be represented by either a projection or in an implicit form. An algebraic point set surface (APSS) defines a smooth surface from a set of unorganized points using local moving least-squares (MLS) fitting of algebraic spheres. However, due to the local nature, APSS does not work well for geometry editing and modeling. Instead, our method builds an implicit approximation function for the scattered point set based on the partition of unity approach. By using an octree subdivision strategy, we first adaptively construct local algebraic spheres for the point set, and then apply weighting functions to blend together these local shape functions. Finally, we compute an error-controlled approximation of the signed distance function from the surface. In addition, we present an efficient projection operator which makes our representation suitable for point set filtering and dynamic point resampling. We demonstrate the effectiveness of our unified approach for both surface reconstruction and geometry modeling such as surface completion.