𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A rational quartic Bézier representation for conics

✍ Scribed by Lian Fang

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
254 KB
Volume
19
Category
Article
ISSN
0167-8396

No coin nor oath required. For personal study only.

✦ Synopsis

This paper presents a special representation for conic sections in the form of a rational quartic Bézier curve which has the same weight for all control points but the middle one. This representation allows a conic section to be joined with other conics in the same form or other integral B-spline curves in a way that the joined curve still possesses C 1 continuity in the homogeneous space, which is not possible if rational quadratic representation is adopted. This also allows the creation of skinned surfaces from section curves containing conic sections to possess better parametrization and curvature property.

📜 SIMILAR VOLUMES

Real-time CNC interpolators for Bézier c
Real-time CNC interpolators for Bézier conics
✍ Rida T. Farouki; Carla Manni; Alessandra Sestini 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 136 KB

Arbitrary conic segments can be specified in the rational Bézier form, r(ξ ) for ξ ∈ [0, 1], by control points p 0 , p 1 , p 2 and a scalar weight w 1 . An expression for the cumulative arc length function s(ξ ), amenable to accurate and efficient evaluation, is required in formulating real-time CNC

Bézier representation for quadric surfac
Bézier representation for quadric surface patches
✍ Suresh Lodha; Joe Warren 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 586 KB

Quadric surfaces such as cylinders and spheres play an important role in CAD. This paper describes a new method for creating triangular surface patches on a quadric surface. The surface patches are defined using a restricted type of quadratic B~zier control polyhedron. The control polyhedron and the