Multi-Level Partition of Unity Algebraic Point Set Surfaces

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-sq...

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Bibliographic Details
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
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Summary: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.
ISSN:1000-9000
1860-4749
DOI:10.1007/s11390-011-9429-2