A new definition of Beta-Bezier curves which include classic Bezier curves as a special case is given. With the new definition, the functions of Beta-Bezier curves are easier to study. It shows that Beta-Bezier curves not only have all the basic properties of Bezier curves such as convex hull property, recursive subdivision, B-spline conversion and C2 interpolation, but also the capability of modifying the shape a Bezier curve segment or a C2-continuous, composite cubic Bezier curve without changing the control points of the curve. This is because in the cubic case a Beta-Bezier curve is actually also a Bezier curve. Hence, we have a curve design technique more general than Bezier curves. Since C2-continuous, composite cubic Bezier curves are equivalent to uniform B-spline curves, this means the new curve design technique is more general than uniform B-spline curves as well.
|Number of pages
|Computer-Aided Design and Applications
|Published - 2021
Bibliographical noteFunding Information:
This work is supported by NNSFC (Grant No. 61572020).
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- Beta-Bernstein basis function
- Beta-Bezier curve
- Bezier curve
- Shape parameter
ASJC Scopus subject areas
- Computational Mechanics
- Computer Graphics and Computer-Aided Design
- Computational Mathematics