Optimal Hierarchies for Quadrilateral Surfaces

Kuo Liang Chung; Wen Ming Yan; Jung Gen Wu

doi:10.1023/A:1021603330228

Optimal Hierarchies for Quadrilateral Surfaces

Kuo Liang Chung, Wen Ming Yan, Jung Gen Wu

Department of Computer Science and Information Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

Multiresolution representation of quadrilateral surface approximation (MRQSA) is a useful representation for progressive graphics transmission in networks. Based on two requirements: (1) minimum mean square error and (2) fixed reduction ratio between levels, this paper first transforms the MRQSA problem into the problem of solving a sequence of near-Toeplitz tridiagonal linear systems. Employing the matrix perturbation technique, the MRQSA problem can be solved using about 24mn floating-point operations, i.e. linear time, if we are given a polygonal surface with (2m-1)×(2n-1) points. A numerical stability analysis is also given. To the best of our knowledge, this is the first time that such a linear algebra approach has been used for solving the MRQSA problem. Some experimental results are carried out to demonstrate the applicability of the proposed method.

Original language	English
Pages (from-to)	283-300
Number of pages	18
Journal	Journal of Mathematical Modelling and Algorithms
Volume	1
Issue number	4
DOIs	https://doi.org/10.1023/A:1021603330228
Publication status	Published - 2002 Dec 1

Keywords

multiresolution representation
near-Toeplitz tridiagonal systems
quadrilateral surface
stability analysis

ASJC Scopus subject areas

Modelling and Simulation
Applied Mathematics

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