## Abstract

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 C^{2} interpolation, but also the capability of modifying the shape a Bezier curve segment or a C^{2}-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 C^{2}-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.

Original language | English |
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Pages (from-to) | 1265-1278 |

Number of pages | 14 |

Journal | Computer-Aided Design and Applications |

Volume | 18 |

Issue number | 6 |

DOIs | |

State | Published - 2021 |

### Bibliographical note

Funding Information:This work is supported by NNSFC (Grant No. 61572020).

Publisher Copyright:

© 2021 CAD Solutions, LLC.

## Keywords

- 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