Article

Harmonic volumetric mapping for solid modeling applications

Authors:

Hong QinAuthors Info & Claims

SPM '07: Proceedings of the 2007 ACM symposium on Solid and physical modeling

Pages 109 - 120

https://doi.org/10.1145/1236246.1236263

Published: 04 June 2007 Publication History

Abstract

Harmonic volumetric mapping for two solid objects establishes a one-to-one smooth correspondence between them. It finds its applications in shape registration and analysis, shape retrieval, information reuse, and material/texture transplant. In sharp contrast to harmonic surface mapping techniques, little research has been conducted for designing volumetric mapping algorithms due to its technical challenges. In this paper, we develop an automatic and effective algorithm for computing harmonic volumetric mapping between two models of the same topology. Given a boundary mapping between two models, the volumetric (interior) mapping is derived by solving a linear system constructed from a boundary method called the fundamental solution method. The mapping is represented as a set of points with different weights in the vicinity of the solid boundary. In a nutshell, our algorithm is a true meshless method (with no need of specific connectivity) and the behavior of the interior region is directly determined by the boundary. These two properties help improve the computational efficiency and robustness. Therefore, our algorithm can be applied to massive volume data sets with various geometric primitives and topological types. We demonstrate the utility and efficacy of our algorithm in shape registration, information reuse, deformation sequence analysis, tetrahedral remeshing and solid texture synthesis.

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cover image ACM Other conferences

SPM '07: Proceedings of the 2007 ACM symposium on Solid and physical modeling

June 2007

455 pages

ISBN:9781595936660

DOI:10.1145/1236246

Program Chairs:
Bruno Levy
INRIA
,
Dinesh Manocha
University of North Carolina

Copyright © 2007 ACM.

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Published: 04 June 2007

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SPM07: Symposium on Solid and Physical Modeling

June 4 - 6, 2007

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https://dl.acm.org/doi/10.1145/3592410
Wang XMa W(2021)Smooth Analysis-Suitable Parameterization Based on a Weighted and Modified Liao FunctionalComputer-Aided Design10.1016/j.cad.2021.103079140:COnline publication date: 1-Nov-2021
https://dl.acm.org/doi/10.1016/j.cad.2021.103079
Naitsat ANaitzat GZeevi Y(2021)On Inversion-Free Mapping and Distortion MinimizationJournal of Mathematical Imaging and Vision10.1007/s10851-021-01038-y63:8(974-1009)Online publication date: 6-Jun-2021
https://dl.acm.org/doi/10.1007/s10851-021-01038-y
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