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 |
Fingerprint
Keywords
- multiresolution representation
- near-Toeplitz tridiagonal systems
- quadrilateral surface
- stability analysis
ASJC Scopus subject areas
- Modelling and Simulation
- Applied Mathematics
Cite this
Optimal Hierarchies for Quadrilateral Surfaces. / Chung, Kuo Liang; Yan, Wen Ming; Wu, Jung Gen.
In: Journal of Mathematical Modelling and Algorithms, Vol. 1, No. 4, 01.12.2002, p. 283-300.Research output: Contribution to journal › Article
}
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 -