Modelling subdivision connectivity meshes using our global optimization approach: (a) the initial coarse mesh; (b) the subdivided mesh from (a); (c) the optimized mesh with feature point constraints and 1-ring neighborhood center constraints from (b); (d) the smooth shading of (c); (e) the optimized mesh with feature point constraints, 1-ring neighborhood center constraints, and co-planar constraints from (b).
กก
Abstract
This paper presents a
global optimization operator for arbitrary meshes. The global
optimization operator is composed of two main terms, one part is the
global Laplacian operator of the mesh which keeps the fairness and
another is the constraint condition which reserves the fidelity to the
mesh. The global optimization operator is formulated as a quadratic
optimization problem, which is easily solved by solving a sparse linear
system. Our global mesh optimization approach can be effectively used in
at least three applications: smoothing the noisy mesh, improving the
simplified mesh, and geometric modeling with subdivision-connectivity.
Many experimental results are presented to show the applicability and
flexibility of the approach.
กก
This work is an extension
of our previous work on mesh denoising using global Laplacian operator:
* Zhongping Ji, Ligang Liu, and Guojin Wang. A global Laplacian
smoothing approach with feature preservation. Proceedings of The 9th
International Conference on Computer Aided Design and Computer Graphics,
2005, HongKong, IEEE Computer Society, pp. 269-274, The Best Student
Paper Award. [PDF, 0.7M] [Talk
slides, 2M]
A
concurrent work on mesh optimization by using global Laplacian operator:
* A. Nealen, T. Igarashi, O. Sorkine, M. Alexa. Laplacian mesh
optimization. Proceedings of ACM GRAPHITE, 381-389, 2006. [download]
กก
This work is supported by
the National Natural Science Foundation of China (No. 60503067,
60333010), Zhejiang Provincial Natural Science Foundation of China (No.
Y105159), the Hong Kong Research Grant Council (Project No.
HKUST6295/04E), and the National Grand Fundamental Research 973 Program
of China (No. 2002CB312101).
กก
title = {Non-Iterative Approach for Global Mesh Optimization},
author = {Ligang Liu and Chiew-Lan Tai and Zhongping Ji and Guojin Wang}
journal = {Computer-Aided Design},
volume = {39},
number = {9},
pages = {772-782},
year = {2007}
}