Abstract
An approach has been proposed for the interpolation of bi-parameter curves, which are defined as the intersection of a parametric surface and an implicit surface. This paper relates the arc-length derivatives to time derivatives of parameters along the bi-parameter curve. The results are then used to derive the parametric interpolation. The bi-parametric curve interpolation is developed based on the parametric interpolation. The proposed interpolation can guarantee that interpolated points always stay on the parametric surface. An improvement interpolation is presented to alleviate point deviation from the implicit surface. Simulations of bi-parameter curve interpolation have been carried out to verify the effectiveness of the proposed algorithm. The proposed approach has applications in real time tool path interpolation for the machining of parametric surfaces.
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