Computer Graphics & Control of Bezier Curve Shapes by Midpoint Slope Handle 


Vol. 7,  No. 9, pp. 3019-3028, Sep.  2000
10.3745/KIPSTE.2000.7.9.3019


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  Abstract

One of the most frequently used spline scheme in CAD and graphics package is Bezier curve. Although simple and easy to implement, it supports diverse kinds of curves and surfaces. In view of the design convenience, the main advantage of the Bezier curves is that they observe user-specified slope conditions at both endpoints while maintaining smoothness. This paper expands the advantage by deriving equations for generalized Bezier curves, and applying the equation to observe additional slope condition at midpoint. This is possible by decomposing and analyzing the user-specified midpoint slope, and reflecting the result back into the Bezier basis matrix in parametric form. Consequently, users can control the curve shapes not only by the endpoint slope handles but also at the midpoint slope handle, which helps them to be able to apply more accurate control over the conventional Bezier curve shapes.

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[IEEE Style]

W. S. Jou, H. S. Jang, T. S. Lim, "Computer Graphics & Control of Bezier Curve Shapes by Midpoint Slope Handle," The Transactions of the Korea Information Processing Society (1994 ~ 2000), vol. 7, no. 9, pp. 3019-3028, 2000. DOI: 10.3745/KIPSTE.2000.7.9.3019.

[ACM Style]

Wou Seok Jou, Hyuk Soo Jang, and Tae Shik Lim. 2000. Computer Graphics & Control of Bezier Curve Shapes by Midpoint Slope Handle. The Transactions of the Korea Information Processing Society (1994 ~ 2000), 7, 9, (2000), 3019-3028. DOI: 10.3745/KIPSTE.2000.7.9.3019.

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