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.
Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
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
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 -