TY - JOUR

T1 - Optimal Hierarchies for Quadrilateral Surfaces

AU - Chung, Kuo Liang

AU - Yan, Wen Ming

AU - Wu, Jung Gen

N1 - Funding Information:
The authors appreciate the anonymous referees and the Editor-in-Chief Prof., M. Rayward-Smith, for their valuable comments that lead to the improved version of this paper. K.-L.C. was supported by NSC89-2213-E011-061; W.-M.Y. was supported by NSC87-2119-M002-006; and J.-G.W. was supported by NSC89-2614-H-003-001-F020.

PY - 2002

Y1 - 2002

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

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U2 - 10.1023/A:1021603330228

DO - 10.1023/A:1021603330228

M3 - Article

AN - SCOPUS:84888606481

SN - 1570-1166

VL - 1

SP - 283

EP - 300

JO - Journal of Mathematical Modelling and Algorithms

JF - Journal of Mathematical Modelling and Algorithms

IS - 4

ER -