高速離散的フーリエ変換を用いたB-spline曲面あてはめ

DOI Web Site 被引用文献1件 参考文献24件

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タイトル別名
  • B-spline Surface Fitting using Fast Discrete Fourier Transform
  • コウソク リサンテキ フーリエ ヘンカン オ モチイタ B spline キョクメンアテハメ

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In the field of RE (Reverse Engineering), several researches of the method for applying the data measured by 3-D measurement machine to B-spline CAD surface have been conducted. The control points of a B-spline surface which should be fitted to the measured points can be obtained by solving a set of SLE (Simultaneous Linear Equations). The problem of this method is a computation cost which increases at an accelerated rate as the number of patches on the B-spline surface increases. We have proposed a new method, Fourier transform method, for obtaining the control points from the B-spline surface. However, there are two problems with this new approach; these are that the number of patches could not be freely specified and that the ringing at the surface edges must be suppressed. In this paper, we solve the first problem by subsampling the measured points at a decimated rate corresponding to the number of patches and calculating the B-spline surface which passes the decimated points. Both the subsampling and the determination of the control points on the B-spline surface can be processed at high speed because they are calculated in frequency space. The second problem is resolved by a preprocess consisting of shearing and point symmetric extension, and a postprocess which is the inverse transform of the preprocess. From the experimental investigations by using 3-D measurement machine, it was clarified that our proposed method where the number of patches could be specified and the ringing could be eliminated, enables high-speed processing compared with the conventional method of SLE.

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