article

Multi-level partition of unity implicits

Authors:

Alexander Belyaev,

Hans-Peter SeidelAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 22, Issue 3

Pages 463 - 470

https://doi.org/10.1145/882262.882293

Published: 01 July 2003 Publication History

Abstract

We present a new shape representation, the multi-level partition of unity implicit surface, that allows us to construct surface models from very large sets of points. There are three key ingredients to our approach: 1) piecewise quadratic functions that capture the local shape of the surface, 2) weighting functions (the partitions of unity) that blend together these local shape functions, and 3) an octree subdivision method that adapts to variations in the complexity of the local shape.Our approach gives us considerable flexibility in the choice of local shape functions, and in particular we can accurately represent sharp features such as edges and corners by selecting appropriate shape functions. An error-controlled subdivision leads to an adaptive approximation whose time and memory consumption depends on the required accuracy. Due to the separation of local approximation and local blending, the representation is not global and can be created and evaluated rapidly. Because our surfaces are described using implicit functions, operations such as shape blending, offsets, deformations and CSG are simple to perform.

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Index Terms

Multi-level partition of unity implicits
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 22, Issue 3

July 2003

683 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/882262

Issue’s Table of Contents

Copyright © 2003 ACM.

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Publication History

Published: 01 July 2003

Published in TOG Volume 22, Issue 3

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https://doi.org/10.20965/ijat.2024.p0287
Fayolle PFriedrich M(2024)A Survey of Methods for Converting Unstructured Data to CSG ModelsComputer-Aided Design10.1016/j.cad.2023.103655168:COnline publication date: 1-Mar-2024
https://dl.acm.org/doi/10.1016/j.cad.2023.103655
Ma BLiu YHan ZKrause ABrunskill ECho KEngelhardt BSabato SScarlett J(2023)Learning signed distance functions from noisy 3D point clouds via noise to noise mappingProceedings of the 40th International Conference on Machine Learning10.5555/3618408.3619380(23338-23357)Online publication date: 23-Jul-2023
https://dl.acm.org/doi/10.5555/3618408.3619380
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