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Multi-level Partition of Unity Implicits

Ohtake, Yutake ; Belyaev, Alexander ; Alexa, Marc ; Turk, Greg ; Seidel, Hans-Peter (2003)
Multi-level Partition of Unity Implicits.
In: ACM Transactions on Graphics, 22 (3)
Article, Bibliographie

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.

Item Type: Article
Erschienen: 2003
Creators: Ohtake, Yutake ; Belyaev, Alexander ; Alexa, Marc ; Turk, Greg ; Seidel, Hans-Peter
Type of entry: Bibliographie
Title: Multi-level Partition of Unity Implicits
Language: English
Date: 2003
Journal or Publication Title: ACM Transactions on Graphics
Volume of the journal: 22
Issue Number: 3
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.

Uncontrolled Keywords: Computational geometry, Object modeling, Object representation, Adaptive distance field approximation, Implicit modeling
Divisions: 20 Department of Computer Science
20 Department of Computer Science > Interactive Graphics Systems
Date Deposited: 16 Apr 2018 09:04
Last Modified: 16 Apr 2018 09:04
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