Imposing angle boundary conditions on B-spline/NURBS surfaces. (May 2015)

• Record Type: Journal Article
• Authors: Michálková, Kristýna; Bastl, Bohumír
• Is Part Of: Computer aided design. Volume 62(2015)
• Page Start: 1
• Page End: 9
• Publication Date: 2015-05
• Subjects: NURBS surface -- B-spline surface -- Pelton turbine bucket; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2014.10.002
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: In this paper, we study the construction of a B-spline surface satisfying prescribed angle distribution (with respect to a chosen vector) of tangent planes along its boundary curve. This problem arises e.g. in a creation of a parametric geometric model of a Pelton turbine bucket, where specific angle distributions along a splitter and an outlet curve have to be fulfilled in order to control the flow of water into and out of the bucket. We prove that for a given B-spline curve c ( t ), t ∈ [ 0, 1 ], the exact solution exists only in very special cases (for a special form of an angle function f ( t ) ). Further, we formulate an algorithm for finding an approximate solution. We also derive a bound on its approximation error and give a numerical evidence that the approximation order of the proposed algorithm is four. Finally, the method is demonstrated on several examples. Highlights: We study the construction of a B-spline surface satisfying prescribed angle distribution of tangent planes along its boundary curve. We prove that for a given B-spline curve, the exact solution exists only in very special cases (for a special form of an angle function). We propose an algorithm for finding an approximate solution, derive a bound on its approximation error and study the approximation order of the proposed algorithm. Graphical abstract: