A Dimension-Independent Representation for Multiresolution Nonmanifold Meshes

[+] Author and Article Information
Leila De Floriani

Department of Computer Science, University of Maryland, College Park, Maryland 20742 and Departimento di Informatica e Scienze dell' Informazione University of Genova, Genova, Italy 16146

Annie Hui

Department of Computer Science, University of Maryland, College Park, Maryland 20742

J. Comput. Inf. Sci. Eng 6(4), 397-404 (Aug 29, 2006) (8 pages) doi:10.1115/1.2364207 History: Received September 30, 2005; Revised August 29, 2006

We consider the problem of representing and manipulating nonmanifold objects of any dimension and at multiple resolutions. We present a modeling scheme based on (1) a multiresolution representation, called the vertex-based nonmanifold multitessellation, (2) a compact and dimension-independent data structure, called the Simplified Incidence Graph (SIG), and (3) an atomic mesh update operator, called vertex-pair contraction/vertex expansion. We propose efficient algorithms for performing the vertex-pair contraction on a simplicial mesh encoded as a SIG, and an effective representation for encoding this multiresolution model based on a compact encoding of vertex-pair contractions and vertex expansions.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Examples of a vertex-pair contraction and of a vertex expansion

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Figure 2

An example of two vertex-pair contractions performed consecutively and the tree describing them

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Figure 3

Two 3D examples of the relations stored in a SIG at a vertex and at an edge

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Figure 4

A comparion between the SIG and the IG

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Figure 5

Examples of the effect of map λ and the effect of map μ

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Figure 6

The three possible cases that can occur for a triangle f in the reduced complex

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Figure 7

Example of the generation of code cd during vertex-pair contraction

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Figure 8

Meshes that describe the handgun model at variable resolutions



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