Interpolating and Approximating Moving Frames Using B-splines

The representation of moving geometry entities is an important issue in the fields of CAD/CAM and robotics motion design. We present a method to interpolate the moving frame homogeneously using B-splines. By analysing the matrix representation of the moving frames, a simplified optimization functional is derived and a recursive iteration method is presented for approximating orthogonal frames at any positions. The error caused by approximation and interpolation is given and shown to be controllable. Since the calculation of moving frames only related with linear equations of two or three unknowns, and the moving frames are approximated with lower degree of polynomial Bspline, the proposed approach can run very fast. The method is useful in motion design and the swept volume representation.

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