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Constructing fair curves and surfaces with a Sobolev gradient method. (English) Zbl 1069.65565

Summary: We have devised a new method for constructing discrete approximations to fair curves and surfaces by directly minimizing an arbitrarily selected fairness functional subject to geometric constraints. The nonlinear optimization problem is solved efficiently by a Sobolev gradient method. We first describe the method in general terms and then present results which demonstrate its effectiveness for constructing minimum variation curves which interpolate specified control points, tangent vectors, and/or curvature vectors.

MSC:

65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
65D17 Computer-aided design (modeling of curves and surfaces)
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