Optimal Hierarchies for Quadrilateral Surfaces

Kuo Liang Chung, Wen Ming Yan, Jung Gen Wu

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)283-300
Number of pages18
JournalJournal of Mathematical Modelling and Algorithms
Issue number4
Publication statusPublished - 2002


  • multiresolution representation
  • near-Toeplitz tridiagonal systems
  • quadrilateral surface
  • stability analysis

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics


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