The mathematics of nonlinear programming
The mathematics of nonlinear programming
Interpolation with developable Be´zier patches
Computer Aided Geometric Design
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Computational Line Geometry
Surface fairing and featuring by mean curvature motions
Journal of Computational and Applied Mathematics - Special issue on proceedings of the international symposium on computational mathematics and applications
Bézier surfaces of minimal area: the Dirichlet approach
Computer Aided Geometric Design
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In the freeform surface design, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smooth closed curve. In this paper, tensor product Bézier surfaces interpolating the closed curves are determined and the result surface is a minimum of the functional defined by the L2 -integral norm of the Gaussian curvature. The Gaussian curvature of the surfaces is minimized by the method of solving nonlinear optimization problems. An improved approach is proposed: the Pseudo-Newtonian method. A simple application example is also given.