期刊文献+

α-非均匀B样条曲线的保单调插值 被引量:8

Monotonicity-Preserving Interpolation with Non-uniform α-B Spline
下载PDF
导出
摘要 针对α 均匀B样条曲线的局限性 ,引进α 非均匀B样条曲线 ,并相应地研究这种曲线保单调插值的可能性与算法 通过设置奇异混合函数 ,无需求解方程组或迭代计算 ,可方便地构造出一类带有形状控制参数的α 非均匀B样条插值曲线族 ;进一步 ,利用Bernstein多项式的正性条件 ,得到该形状参数α的取值范围 ,使得与该范围内每个形状参数相应的插值曲线都是保单调的 ,且得到的曲线为C2 (或G1)连续 Compared with uniform α -B spline it is very necessary to introduce non-uniform α -B spline and investigate the possibility as well as the algorithm for the monotonicity-preserving interpolation to this kind of curve In this paper, a family of non-uniform α -B spline interpolation curve with the shape control parameter α is constructed expediently by using singular blending function but dispensing with solving any system of equations or going at any iterative computation; then, the positive conditions of Bernstein polynomial can be used to obtain a range in which the shape parameter takes its value so as to make the corresponding interpolating curves monotonicity-preserving and C 2 (or G 1) continuity maintained Several numerical examples are given to illustrate the correctness and the validity of theoretical reasoning
出处 《计算机辅助设计与图形学学报》 EI CSCD 北大核心 2004年第10期1386-1391,1395,共7页 Journal of Computer-Aided Design & Computer Graphics
基金 国家自然科学基金 (60 3 73 0 3 3 60 3 3 3 0 10 ) 国家重点基础研究发展规划项目(2 0 0 2CB3 12 10 1)资助
关键词 保单调插值 α-非均匀B样条曲线 形状参数 BERNSTEIN多项式 monotonicity-preserving interpolation non-uniform α-B spline shape parameter Bernstein polynomial
  • 相关文献

参考文献12

  • 1Schweikert D. An interpolation curve using splines in tension[J]. Journal of Mathematics and Physics, 1966, 45: 312~317
  • 2Sp(a)th H. Exponential spline interpolation[J]. Computing, 1969, 4: 225~233
  • 3Pruess S. Properties of splines in tension[J]. Journal of Approximation Theory, 1976, 17: 86~96
  • 4Renka R. Interpolatory tension splines with automatic selection of tension factors[J]. SIAM Journal on Scientific and Statistical Computing, 1987, 8(2): 393~415
  • 5Fritsch F N, Carlson R E. Monotone piecewise cubic interpolation[J]. SIAM Journal on Numerical Analysis, 1980, 17(2): 238~246
  • 6Costantini P. On monotone and convex spline interpolation[J]. Mathematics of Computation, 1986, 46: 203~214
  • 7Ancher J C, Le Gruyer E. Two shape preserving Lagrange C2 interpolants[J]. Numerische Mathematik, 1993, 64: 1~11
  • 8Pruess S. Shape preserving C2 cubic spline interpolation[J]. IMA Journal of Numerical Analysis, 1993, 13: 493~507
  • 9Manni C, Sablonnière P. Monotone interpolation of order 3 by C2 cubic splines[J]. IMA Journal of Numerical Analysis, 1997, 17: 305~320
  • 10Delbourgo R, Gregory J A. C2 rational quadratic spline interpolation to monotonic data[J]. IMA Journal of Numerical Analysis, 1983, 3: 141~152

二级参考文献14

  • 1Farin G. NURB Curves and Surfaces. Boston: Peters AK, 1995.
  • 2Farin G. Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide. 2th ed., San Diego: Academic Press,1990.
  • 3Goodman TNT, Unsworth IC Manipulating shape and producing geometric continuity in β-spline curves. IEEE Computer Graphics and Applications, 1986,6:50--56.
  • 4Costantini P. On monotone and convex spline interpolation. Mathematics of Computation, 1986,46:203-214.
  • 5Ancher JC, Gruyer E. Two shape preserving lagrange C^2-interpolants. Numerische Mathematilc, 1993,64:1- 11.
  • 6Manni C, Sablonnière P. Monotone interpolation of order 3 by C^2 cubic splines. IMA Journal of Numerical Analysis, 1997,17(2):305-320.
  • 7Lavery JE. Univariate cubic Lv splines and shape-preserving, multiscale interpolation by univariate cubic L1 splines. Computer Aided Geometric Design, 2000,17(4):319-336.
  • 8Lavery, JE. Shape-Preserving, multiscale interpolation by univariate curvature-based cubic L1 splines in Cartesian and polar coordinates. Computer Aided Geometric Design, 2002,19(4):257-273.
  • 9Cai ZJ. Convergence, error estimation and some properties for four-point interpolation subdivision scheme. Computer Aided Geometric Design, 1995,12(5):459-468.
  • 10Kuijt F, Van Damme R. Monotonicity preserving interpolatory subdivision schemes. Journal of Computational and Applied Mathematics, 1999,101 (1-2):203-229.

共引文献16

同被引文献37

引证文献8

二级引证文献23

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部