Spline on a generalized hyperbolic paraboloid

In this paper, we present an approach to produce a kind of spline, which is very close to G 2 -continuity. 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.