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B-spline Curve Approximation Based on Adaptive Selection of Dominant Points  

Lee J.H. (한국전자통신연구원)
Park H.J. (조선대학교 산업공학과)
Publication Information
Korean Journal of Computational Design and Engineering / v.11, no.1, 2006 , pp. 1-10 More about this Journal
Abstract
This paper addresses B-spline curve approximation of a set of ordered points to a specified toterance. The important issue in this problem is to reduce the number of control points while keeping the desired accuracy in the resulting B-spline curve. In this paper we propose a new method for error-bounded B-spline curve approximation based on adaptive selection of dominant points. The method first selects from the given points initial dominant points that govern the overall shape of the point set. It then computes a knot vector using the dominant points and performs B-spline curve fitting to all the given points. If the fitted B-spline curve cannot approximate the points within the tolerance, the method selects more points as dominant points and repeats the curve fitting process. The knots are determined in each step by averaging the parameters of the dominant points. The resulting curve is a piecewise B-spline curve of order (degree+1) p with $C^{(p-2)}$ continuity at each knot. The shape index of a point set is introduced to facilitate the dominant point selection during the iterative curve fitting process. Compared with previous methods for error-bounded B-spline curve approximation, the proposed method requires much less control points to approximate the given point set with the desired shape fidelity. Some experimental results demonstrate its usefulness and quality.
Keywords
B-spline curve approximation; Error-bound; Data reduction; Dominant point selection; Shape index;
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