In this paper, we study B-spline curve interproximation with different energy forms and parametrization techniques, and present an interproximation scheme for B-spline surfaces. It shows that the energy form has a muc...
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In this paper, we study B-spline curve interproximation with different energy forms and parametrization techniques, and present an interproximation scheme for B-spline surfaces. It shows that the energy form has a much bigger impact on the generated curve than the parametrization technique. With the same energy form, different parametrization techniques generate relatively small difference on the corresponding curves. With the same parametrization technique, however, different energy forms make significant difference on the shape and smoothness of the resulting curves. Furthermore, interproximating B-spline curves generated by minimizing approximated energy forms are far from being good approximations to the optimal curves. They tend to generate flatter regions and sharper turns than curves generated by minimizing the exact energy form. The interproximation scheme for surfaces is aimed at generating a smooth surface to interpolate a grid of data which could either be a point or a region. This is achieved by minimizing a strain energy based on squared principal curvatures for bicubic B-spline surfaces. The surface interproximation process is also studied with different energy forms and parametrization techniques. The test results of the surface interproximation process also show the same conclusion as the curve interproximation process. (C) 1997 Elsevier Science Ltd.
interproximation methods for surfaces can be used to construct a smooth surface interpolating some data points and passing through specified regions. In this paper we study the use of mixed splines, that is smoothing ...
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interproximation methods for surfaces can be used to construct a smooth surface interpolating some data points and passing through specified regions. In this paper we study the use of mixed splines, that is smoothing splines with additional interpolation constraints, to solve the interproximation problem for surfaces in the case of scattered data. The solution is obtained by solving a linear system whose structure can be improved by using "bell-shaped" thin plate splines. (C) 2001 Elsevier Science B.V. All rights reserved.
B-H-curves are used for modelling ferromagnetic materials in connection with electromagnetic field computations. They are needed for the numerical simulation of devices such as transformers or magnetic valves. Startin...
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B-H-curves are used for modelling ferromagnetic materials in connection with electromagnetic field computations. They are needed for the numerical simulation of devices such as transformers or magnetic valves. Starting from real-life measurement data, we present an approximation technique which is based on the use of spline functions and a data-dependent smoothing functional. It preserves physical properties, such as monotonicity, and is robust with respect to noise in the measurements. (c) 2005 Elsevier B.V. All rights reserved.
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