High-Precision Continuous Contact Motion for Planar Freeform Geometric Curves

This paper presents an efficient algorithm for generating a continuous precise contact motion between planar geometric models bounded by piecewise polynomial ^C1-continuous parametric B-spline curves. A system of algebraic constraint equations is formulated and then efficiently solved for the two/three-contact configuration between two planar B-spline curves. The result is essentially the same as the generation of configuration space obstacle for a moving curve (with translation and rotation) against a stationary curve. The two-contact motion can be characterized as the intersection curve in the boundary of the configuration space obstacle. The topology of the reconstructed solution is guaranteed to be correct up to a prescribed tolerance and we demonstrate the effectiveness of the proposed approach using several test examples of continuous contact motion among planar freeform smooth geometric models.