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Smoothness of C-Bezier Curves
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Abstract
This paper presents G1 and G2 continuity conditions of c-Bezier curves. It shows that the collinear condition for G1 continuity of Bezier curves is generally no longer necessary for c-Bezier curves. Such a relaxation of constraints on control points is beneficial from the structure of c-Bezier curves. By using vector weights, each control point has two extra free design parameters, which offer the probability of obtaining G1 and G2 continuity by only adjusting the weights if the control points are properly distributed. The enlargement of control point distribution region greatly simplifies the design procedure to and enhances the shape control on constructing composite curves.
American Society of Mechanical Engineers
Title: Smoothness of C-Bezier Curves
Description:
Abstract
This paper presents G1 and G2 continuity conditions of c-Bezier curves.
It shows that the collinear condition for G1 continuity of Bezier curves is generally no longer necessary for c-Bezier curves.
Such a relaxation of constraints on control points is beneficial from the structure of c-Bezier curves.
By using vector weights, each control point has two extra free design parameters, which offer the probability of obtaining G1 and G2 continuity by only adjusting the weights if the control points are properly distributed.
The enlargement of control point distribution region greatly simplifies the design procedure to and enhances the shape control on constructing composite curves.
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