## Abstract

A class of polynomial curve schemes is introduced that may have widespread application to CAGD (computer-aided geometric design), and which contains many well-known curve schemes, including Bézier curves, Lagrange polynomials, B-spline curve (segments), and Catmull-Rom spline (segments). The curves in this class can be characterized by a simple recursion formula. They are also shown to have many properties desirable for CAGD; in particular they are affine invariant, have the convex hull property, and possess a recursive evaluation algorithm. Further, these curves have shape parameters which may be used as a design tool for introducing such geometric effects as tautness, bias, or interpolation. The link between probability theory and this class of curves is also discussed.

Original language | English (US) |
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Pages (from-to) | 65-96 |

Number of pages | 32 |

Journal | Constructive Approximation |

Volume | 6 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1990 |

Externally published | Yes |

## Keywords

- AMS classification: 41A10
- B-spline
- Bézier curve
- Computer-aided geometric design
- Lagrange polynomial
- Probability distribution
- Recursion
- Recursive evaluation algorithm
- Urn model