Point-tangent/point-normal B-spline curve interpolation by geometric algorithms

Authors:
Shu-ichi Gofuku;Shigefumi Tamura;Takashi Maekawa
Affiliations:
Yokohama National University, Department of Mechanical Engineering, Digital Engineering Laboratory, Japan;Yokohama National University, Department of Mechanical Engineering, Digital Engineering Laboratory, Japan;Yokohama National University, Department of Mechanical Engineering, Digital Engineering Laboratory, Japan
Venue:
Computer-Aided Design
Year:
2009

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Abstract

We introduce a novel method to interpolate a set of data points as well as unit tangent vectors or unit normal vectors at the data points by means of a B-spline curve interpolation technique using geometric algorithms. The advantages of our algorithm are that it has a compact representation, it does not require the magnitudes of the tangent vectors or normal vectors, and it has C^2 continuity. We compare our method with the conventional curve interpolation methods, namely, the standard point interpolation method, the method introduced by Piegl and Tiller, which interpolates points as well as the first derivatives at every point, and the piecewise cubic Hermite interpolation method. Examples are provided to demonstrate the effectiveness of the proposed algorithms.