Constrained space curve interpolation with constraint planes

被引：2

作者：

Kong, VP ^{[1
]}

Ong, BH ^{[1
]}

机构：

[1] Univ Sains Malaysia, Sch Math Sci, George Town 11800, Malaysia

来源：

COMPUTER AIDED GEOMETRIC DESIGN | 2005年 / 22卷 / 06期

关键词：

constrained interpolation; rational cubic splines; G(2) space curve; constraint planes;

D O I：

10.1016/j.cagd.2005.02.002

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We consider the interpolation of a given set of ordered data points in R-3 by a smooth curve in the presence of a set of finite or infinite constraint planes, where the polyline joining consecutive data points does not intersect the constraint planes. A method is presented for the construction of the G 2 constrained piecewise rational cubic interpolant which is local. The geometric properties of the Bezier rational cubics are characterized and exploited in the derivation of conditions for the interpolant to avoid crossing the constraint planes. (c) 2005 Elsevier B.V. All rights reserved.

引用

页码：531 / 550

页数：20

共 12 条

[1] PRESERVING POSITIVITY USING PIECEWISE CUBIC INTERPOLATION
BUTT, S
BRODLIE, KW
[J]. COMPUTERS & GRAPHICS, 1993, 17 (01) : 55 - 64
[2] DOUGHERTY RL, 1989, MATH COMPUT, V52, P471, DOI 10.1090/S0025-5718-1989-0962209-1
[3] Goodman T. N. T., 1991, NURBS CURVE SURFACE, P59
[4] POSITIVE HERMITE INTERPOLATION BY QUADRATIC SPLINES
LAHTINEN, A
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1993, 24 (01) : 223 - 233
[5] McKerrow P.J., 1991, Introduction to Robotics
[6] Constrained interpolation with rational cubics
Meek, DS
Ong, BH
Walton, DJ
[J]. COMPUTER AIDED GEOMETRIC DESIGN, 2003, 20 (05) : 253 - 275
[7] Ong B. H., 1992, MATH METHODS COMPUTE, VII, P419
[8] OPFER G, 1988, NUMER MATH, V52, P17, DOI 10.1007/BF01401019
[9] POSITIVITY OF CUBIC POLYNOMIALS ON INTERVALS AND POSITIVE SPLINE INTERPOLATION
SCHMIDT, JW
HESS, W
[J]. BIT, 1988, 28 (02): : 340 - 352
[10] NON-NEGATIVE EXPONENTIAL SPLINES
WEVER, U
[J]. COMPUTER-AIDED DESIGN, 1988, 20 (01) : 11 - 16

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