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In this paper, we discuss how to obtain the parametric surface of minimal area defined on a rectangular parameter domain among all the surfaces with prescribed entire or partial borders, i.e, the quasi-Plateau problem. An approximation method is presented based on the Multiresolution Analysis (MRA) using B-splines. Four algorithms are proposed according to different cases of the boundary conditions. The solution surfaces can be obtained by solving a system of linear equations of simple and sparse structure. Examples are provided to illustrate that the proposed method is effective and flexible.  相似文献
2.
In this paper, a linear 6-point binary approximating subdivision scheme with support [−6, 5] is fully investigated. It is shown that the scheme is simple and has elegant properties. We prove that the scheme can have high order continuity, polynomial reproduction and convexity preserving properties simultaneously. Furthermore, we explore the trade-offs among these properties. Examples are given to demonstrate the efficiency and flexibility of the scheme.  相似文献
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