### 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 | |

Publication status | Published - 2002 Dec 1 |

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### Keywords

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

### ASJC Scopus subject areas

- Modelling and Simulation
- Applied Mathematics

### Cite this

*Journal of Mathematical Modelling and Algorithms*,

*1*(4), 283-300. https://doi.org/10.1023/A:1021603330228

**Optimal Hierarchies for Quadrilateral Surfaces.** / Chung, Kuo Liang; Yan, Wen Ming; Wu, Jung Gen.

Research output: Contribution to journal › Article

*Journal of Mathematical Modelling and Algorithms*, vol. 1, no. 4, pp. 283-300. https://doi.org/10.1023/A:1021603330228

}

TY - JOUR

T1 - Optimal Hierarchies for Quadrilateral Surfaces

AU - Chung, Kuo Liang

AU - Yan, Wen Ming

AU - Wu, Jung Gen

PY - 2002/12/1

Y1 - 2002/12/1

N2 - 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.

AB - 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.

KW - multiresolution representation

KW - near-Toeplitz tridiagonal systems

KW - quadrilateral surface

KW - stability analysis

UR - http://www.scopus.com/inward/record.url?scp=84888606481&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84888606481&partnerID=8YFLogxK

U2 - 10.1023/A:1021603330228

DO - 10.1023/A:1021603330228

M3 - Article

AN - SCOPUS:84888606481

VL - 1

SP - 283

EP - 300

JO - Journal of Mathematical Modelling and Algorithms

JF - Journal of Mathematical Modelling and Algorithms

SN - 1570-1166

IS - 4

ER -