System and method of hybrid forward differencing to render Bezie

Details System and method of hybrid forward differencing to render Bezie System and method of hybrid forward differencing to render Bezie

1992-07-02

1994-11-22

Nguyen, Phu K.

G06F 1562

Patent

active

053676173

ABSTRACT:
A high speed and memory efficient system and method for rendering Bezier curves. The system utilizes a hybrid forward differencing function representing the Bezier curve defined by the Bezier control points and renders the curve with a small number of straight line segments. The system renders the curve in a manner that results in the same Bezier control points that are calculated using recursive subdivision techniques and rejects line segment approximations that would not be derived from recursive subdivision. The system can start at either end of a Bezier curve and will render the same approximation. The method is readily implemented on a computer and is applicable to Bezier curves of any order.

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Sheue-Ling Chang et al., "Rendering Cubic Curves and Surfaces with Integer Adaptive Forward Differencing," Computer Graphics 23:157-166, 1989.
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Sheue-Ling Lien et al., "Adaptive Forward Differencing for Rendering Curves and Surfaces," Computer Graphics 21:111-118, 1987.
Michael Shantz and Sheue-Ling Chang, "Rendering Trimmed NURBS with Adaptive Forward Differencing," Computer Graphics 22:189-196, 1988.
Bob Wallis, "Tutorial on Forward Differencing," pp. 594-603, Graphics Gems, ed. Andrew Glassner, Academic Press, 1990.

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