Spline on a generalized hyperbolic paraboloid

✍ Scribed by Fengfu Peng; Juanjuan Chen

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 274 KB
• Volume: 235
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2010.10.046

✦ Synopsis

In this paper, we present an approach to produce a kind of spline, which is very close to G 2continuity. For a control polygon, we can construct a polyhedron. A generalized hyperbolic paraboloid with a Bernstein-Bézier algebraic form is obtained by the barycentric coordinate system, in which parametrical forms can be represented with two parameters. Having constrained the two parameters with a functional relation for the generalized hyperbolic paraboloid, a variety of arcs could be constructed with the nature of fitting the tangent direction at the endpoints and a little curvature for the whole arc, which can be attached into a spline curve of G 2 -continuity. Further, using the method of simple averages, we present a new symmetry spline to a control polygon, which can improve the approximating effect for a control polygon.