Shaping a Tubular B-Spline Surface

The tubular B-spline surface is closed at one end by a movable closing point. This closing point influences two upper rows of control points in the control net, which can be seen by switching it on. The wavy shape is generated by the transformation of the third row of control points in the control net. After "reset", the position of the closing point is fixed—choose one of the other two options for further manipulation.


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The computation of the control points of a B-spline surface from given boundary conditions is presented here in a specific case, where these are given: a single interpolation point at one end of the tube-shaped surface, zero first partial derivatives, and zero twist vectors. The surface patches are cubic in the longitudinal and quadratic in the cross direction. The computational algorithm can be applied to tangential fitting of B-spline surfaces and to filling holes.
G. E. Farin, Curves and Surfaces for Computer Aided Geometric Design, Boston: Academic Press, 1988.
M. Szilvási-Nagy, "Tubular NURB Surfaces with Boundary Control," Mathematica Pannonica, 6, 1995 pp. 217–228.
M. Szilvási-Nagy, "Shaping and Fairing of Tubular B-Spline Surfaces," Computer Aided Geometric Design, 14(8), 1997 pp. 699–706.
M. Szilvási-Nagy, "Closing Pipes by Extension of B-Spline Surfaces," KoG 3, 1998 pp. 13–19.


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US Common Core State Standards, Mathematics