3406 幾何処理によるB-spline補間(OS14 CAD,未来社会を支えるものづくりとひとづくり(設計・システムから))

概要

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The purpose of this study is to introduce a new method to fit a set of point by B-spline curves/surfaces by geometric algorithms. Standard B-spline curve/surface fitting algorithms first associate suitable parameter values for each input point, known as parameterization of data, and form a linear system with control points as unknowns. In this paper we propose a geometric algorithm to construct smooth B-spline curves/surfaces that fit a finite set of points. Our method takes an approach that the initial shape is updated step by step by moving the control points to reach the target shape. It relies on a surprisingly simple geometric algorithm which iteratively updates the input control points mesh in a global manner based on a local point-surface distance computation and an offsetting procedure without solving a linear system. The complexity of our algorithm is O(mn) where n is the number of vertices to be interpolated and m is the number of iterations. Therefore it is very fast compared to the conventional fitting methods, as m<<n.
一般社団法人日本機械学会の論文
2006-11-14