Complexity reduction for symbolic computation with rational B-splines

被引：0
|
作者：
Chen, Xianming [1 ]
Riesenfeld, Richard F. [1 ]
Cohen, Elaine [1 ]
机构：
[1] School of Computing, University of Utah, 50 S. Central Campus Dr., Salt Lake City, UT 84112, United States
来源：
International Journal of Shape Modeling | 2007年 / 13卷 / 01期
关键词：
Codes (symbols) - Computational complexity - Computational geometry - Logic programming;
D O I：
10.1142/S0218654307000932
中图分类号：
学科分类号：
摘要：
Symbolic computation of NURBS plays an important role in many areas of NURBS-based geometric computation and design. However, any nontrivial symbolic computation, especially when rational B-splines are involved, would typically result in B-splines with high degrees. In this paper we develop degree reduction strategies for NURBS symbolic computation on curves. The specific topics we consider include zero curvatures and critical curvatures of plane curves, various ruled surfaces related to space curves, and point/curve bisectors and curve/curve bisectors. © World Scientific Publishing Company.
引用
收藏
页码：25 / 49
相关论文
共 50 条
  • [21] Reverse engineering of complex geometry using rational B-splines
    Natl Chung Cheng Univ, Cha-Yi, Taiwan
    Int J Adv Manuf Technol, 8 (548-555):
  • [22] Algorithm 999: Computation of Multi-Degree B-Splines
    Speleers, Hendrik
    ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2019, 45 (04):
  • [23] MODIFYING THE SHAPE OF RATIONAL B-SPLINES .2. SURFACES
    PIEGL, L
    COMPUTER-AIDED DESIGN, 1989, 21 (09) : 538 - 546
  • [24] A TCHEBYCHEFFIAN EXTENSION OF MULTIDEGREE B-SPLINES: ALGORITHMIC COMPUTATION AND PROPERTIES
    Hiemstra, Rene R.
    Hughes, Thomas J. R.
    Mannis, Carla
    Speleers, Hendrik
    Toshniwal, Deepesh
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2020, 58 (02) : 1138 - 1163
  • [25] Multi-degree B-splines: Algorithmic computation and properties
    Toshniwal, Deepesh
    Speleers, Hendrik
    Hiemstra, Rene R.
    Manni, Carla
    Hughes, Thomas J. R.
    COMPUTER AIDED GEOMETRIC DESIGN, 2020, 76
  • [26] Data reduction of polygonal curves using B-splines
    Saux, E
    Daniel, M
    COMPUTER-AIDED DESIGN, 1999, 31 (08) : 507 - 515
  • [27] Principal components, B-splines, and fuzzy system reduction
    Yen, J
    Langari, R
    Wang, L
    INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 1996, 4 (06) : 561 - 572
  • [28] Data reduction of polygonal curves using B-splines
    Saux, E.
    Daniel, M.
    CAD Computer Aided Design, 1999, 31 (08): : 507 - 515
  • [29] Gear mesh excitation and non-uniform Rational B-Splines; [Verzahnungsanregung und nicht-uniforme rationale B-Splines]
    Beinstingel A.
    Heider M.
    Pinnekamp B.
    Marburg S.
    Forschung im Ingenieurwesen, 2022, 86 (3) : 331 - 336
  • [30] Complex B-splines
    Forster, B
    Blu, T
    Unser, M
    APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2006, 20 (02) : 261 - 282
12345