✦ LIBER ✦

Singularities of rational Bézier curves

✍ Scribed by J. Monterde

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 113 KB
Volume: 18
Category: Article
ISSN: 0167-8396
DOI: 10.1016/s0167-8396(01)00072-3

No coin nor oath required. For personal study only.

✦ Synopsis

We prove that if an nth degree rational Bézier curve has a singular point, then it belongs to the two (n -1)th degree rational Bézier curves defined in the (n -1)th step of the de Casteljau algorithm. Moreover, both curves are tangent at the singular point. A procedure to construct Bézier curves with singularities of any order is given.

📜 SIMILAR VOLUMES

Derivatives of rational Bézier curves

✍ M.S. Floater 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 731 KB

Algorithms for rational Bézier curves

✍ Gerald Farin 📂 Article 📅 1983 🏛 Elsevier Science 🌐 English ⚖ 420 KB

Linear precision of rational Bézier curv

Linear precision of rational Bézier curves

✍ Gerald Farin; Donghak Jung 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 86 KB

Variational design of smooth rational Bé

Variational design of smooth rational Bézier curves

✍ Hans Hagen; Georges-Pierre Bonneau 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 335 KB

Tighter convex hulls for rational Bézier

Tighter convex hulls for rational Bézier curves

✍ Gerald Farin 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 140 KB

Higher Order Derivatives of a Rational B

Higher Order Derivatives of a Rational Bézier Curve

✍ Guo-Zhao Wang; Guo-Jin Wang 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 212 KB

In this paper, a convenient and effective recurrence formula for the higher order derivatives of a rational degree \(n\) Bézier curve is derived. The \(\operatorname{sth}(s=1,2, \ldots)\)-order derivatives of this curve can be represented as a fraction whose numerator is a vector expression of degre