Abstract
A curve design method has been proposed which, in addition to enjoying the good features of cubic splines, possesses interested shape design features too. Two families of shape parameters have been introduced in such a way that one family of parameters is associated with intervals and the other with points. These parameters provide a variety of shape controls like point and interval tension. This is an interpolatory curve scheme, which utilizes a piece-wise rational cubic function in its description. The proposed method enjoy ideal geometric properties and geometric continuity of order two is also achieved.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Barnhill, R.E., Brown, J.H., and Klucewicz, I.M. (1978), A New Twist in Computer-Aided Geometric Design, Computer Graphics and Image Processing 8. 78–91.
Barsky, B.A. (1984), Exponential and Polynomial Methods for applying Tension to an Interpolating Spline Curve, Computer Vision, Graphics, and Image Processing 27, 1–18.
Boehm, W., Farin, G., and Kahmann, J. (1984), A Survey of Curve and Surface Methods in CAGD, Computer Aided Geometric Design, 1, 1–60.
Dierckx, P. and Tytgat, B. (1989), Generating the Bézier points of β-spline curve, Comp. Aided Geom. Design 6, 279–291.
Farin, G.E. (1996), Curves and Surfaces for CAGD, Academic Press, New York.
Faux, I.E., and Pratt, M.J. (1979), Computational Geometry for Design and Manufacture, Ellis Horwood, Chichester.
Foley, T.A. (1987), Weighted Bicubic Spline Interpolation to rapidly varying Data, ACM Trans. Graph. 6, 1–18.
Foley, T.A. (1987), Interpolation with Interval and Point Tension Controls using Cubic Weighted v-Splines, ACM Trans. Math. Soft. 13, 68–96.
Fritsch, F.N. (1986), The Wilson-Fowler Spline is a v-spline, Computer Aided Geometric Design 3, 155–162.
Gregory, J.A. and Sarfraz, M. (1990), A Rational cubic Spline with Tension, Computer Aided Geometric Design, North-Holland, Elsevier, Vol. 7, 1–13.
Mortenson, M.E. (1985), Geometric Modeling, Wiley, New York.
Nielson, G.M. (1974), Some Piecewise Polynomial Alternatives to Splines under Tension, in: R.E. Barnhill and R.F. Riesenfeld, eds., Computer Aided Geometric Design, Academic Press, New York, 209–235.
Nielson, G.M. (1986), Rectangular v-splines, IEEE Computer Graphics 6, 35–40.
Salkauskas, K. (1984), C 1 Splines for Interpolation of Rapidly Varying Data, Rocky Mtn. J. Math. 14, 239–250.
Sarfraz, M. (1994), A C2 Rational Cubic Spline which has Linear Denominator and Shape Control, Annales Univ. Sci. Budapest, Vol. 37, 53–62.
Sarfraz, M. (1993), Designing of Curves and Surfaces using Rational Cubics, Computers and Graphics, Elsevier Science, Vol. 17(5), 529–538.
Sarfraz, M. (1992), Interpolatory Rational Cubic Spline with Biased, Point and Interval Tension, Computers and Graphics, Elsevier Science, Vol. 16(4), 427–430.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sarfraz, M., Balah, M. (2003). A Curve Design Method with Shape Control. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44842-X_68
Download citation
DOI: https://doi.org/10.1007/3-540-44842-X_68
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40156-8
Online ISBN: 978-3-540-44842-6
eBook Packages: Springer Book Archive