A New Approach for Designing Rational Bézier Surfaces from a Given Geodesic ?
نویسندگان
چکیده
This paper proposes an approach to design the surface pencil with specified parametric representations from a given geodesic. The surface was considered as a combination of the marching-scale functions and the Frenet trihedron frame, for which some necessary and sufficient conditions must be met. This paper simplifies those conditions, and represents the surface by combination of control points and basis functions, which are more practical for applications. The paper provides the formulae to construct the rational Bézier surface pencil, and the algorithm to compute the control points of cubic rational Bézier surfaces. The method is useful in practical applications of the garment and shoe industry and so on.
منابع مشابه
Approximating rational triangular Bézier surfaces by polynomial triangular Bézier surfaces
An attractive method for approximating rational triangular Bézier surfaces by polynomial triangular Bézier surfaces is introduced. The main result is that the arbitrary given order derived vectors of a polynomial triangular surface converge uniformly to those of the approximated rational triangular Bézier surface as the elevated degree tends to infinity. The polynomial triangular surface is con...
متن کاملDesign of Rational Bézier Developable Surface Pencil Through A Common Isogeodesic
This paper studies the problem of designing a rational Bézier developable surface pencil with a common isogeodesic, and provides an algorithm for the representation of complicated geometric models in industrial applications which need to satisfy that the shape surface can be developed and a given curve is geodesic. By employing the local Frenet orthonormal frame, the explicit expression of the ...
متن کاملConversion of biquadratic rational Bézier surfaces into patches of particular Dupin cyclides: the torus and the double sphere
Toruses and double spheres are particular cases of Dupin cyclides. In this paper, we study the conversion of rational biquadratic Bézier surfaces into Dupin cyclide patches. We give the conditions that the Bézier surface should satisfy to be convertible, and present a new conversion algorithm to construct the torus or double sphere patch corresponding to a given Bézier surface, some conversion ...
متن کاملAn Approach for Designing a Developable Surface with a Common Geodesic Curve
This paper presents an approach for designing a developable surface possessing a given curve as the geodesic of it. We analyze the necessary and sufficient conditions when the resulting developable surface is a cylinder, cone or tangent surface. Also, we solve the problem of requiring the surfaces of revolution which are developable surfaces. Finally, we illustrate the convenience and efficienc...
متن کاملBézier patches on almost toric surfaces
The paper is devoted to the parametrization extension problem: given a loop composed of 3 (resp. 4) rational Bézier curves on a rational surface X, find a triangular (resp. tensor product) Bézier patch on X of optimal degree bounded by these curves. The constructive solution to the formulated problem is presented in details for cases where X is a sphere or a hyperbolic paraboloid. Then X is an ...
متن کامل