A method for improving the shape of a spatial C 2 cubic B-spline under tolerance constraints is p... more A method for improving the shape of a spatial C 2 cubic B-spline under tolerance constraints is proposed. This is achieved by specifying the sign of torsion and controlling the direction of the binormal and normal vectors of the curve, which leads to a nonlinear programming problem with a quadratic objective function, multilinear shape constraints, and quadratic tolerance ones. The numerical performance of the scheme is tested on an industrial data set.
Computational Methods for Algebraic Spline Surfaces, 2005
ABSTRACT In this paper we further the theoretical investigation, initiated in [1], on the shape e... more ABSTRACT In this paper we further the theoretical investigation, initiated in [1], on the shape effect of a single control point, measured in terms of the sign of Gaussian and mean curvatures of the underlying parametric surface. The so far obtained theoretical results are illustrated by experimenting with three typical NURBS surfaces, namely a cylinder, an ellipsoid and a torus.
A method for improving the shape of a spatial C 2 cubic B-spline under tolerance constraints is p... more A method for improving the shape of a spatial C 2 cubic B-spline under tolerance constraints is proposed. This is achieved by specifying the sign of torsion and controlling the direction of the binormal and normal vectors of the curve, which leads to a nonlinear programming problem with a quadratic objective function, multilinear shape constraints, and quadratic tolerance ones. The numerical performance of the scheme is tested on an industrial data set.
Computational Methods for Algebraic Spline Surfaces, 2005
ABSTRACT In this paper we further the theoretical investigation, initiated in [1], on the shape e... more ABSTRACT In this paper we further the theoretical investigation, initiated in [1], on the shape effect of a single control point, measured in terms of the sign of Gaussian and mean curvatures of the underlying parametric surface. The so far obtained theoretical results are illustrated by experimenting with three typical NURBS surfaces, namely a cylinder, an ellipsoid and a torus.
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Papers by panagiotis kaklis