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Journal of Inforamtion Science and Engineering, Vol.8 No.1, pp.121-130 (March 1992)
Automatic Generation of Shape Preserving Curves
by a Dynamic Tangent Algorithm*

Jenn-Hua Lee
Department of Computer Engineering and Science
Yuan-Ze Institute of Technology,
135 Yuan-Tung Road, Nei-Li, Taoyuan Shian,
Taiwan, 32026, R.O.C.

For automaic generation of shape preserving curves, Fletcher and McAllister have proposed a natural bias approach. Moreover, Lee and Yang have proposed a direct algorithm for shape preserving interpolation. Both of these methods have their respective merits. And without losing generality, one line's intersection routine should be executed to compute the tangent vecrors of each interpolating curve segment to stay in the shape preserving ranges. In this paper, a dynamic tangent algorithm based upon the Bezier formulation is proposed. As far as automatic shape preserving interpolation is concerned, this new algorithm combines the merits of both the natural bias approach and the direct algorithm. Also, it is more efficient than previous approaches. The basic idea is to perform the line's intersection algorithm to directly compute the interior Bezier points only when it is necessary. Several examples will by given to demonstrate the capability of this new method.

Keywords: computer graphics, curve interpolation, computer-aided design, shape parameters

Received September 10, 1991; revised Novermber 28, 1991.
Communicated by Ferng-Ching Lin.
* A preliminary version has been presented in the 1991 Workshop on CVGIP, Tainan, Taiwan, R.O.C.