Today, in robot applications continuous paths often result from CAD or other planning tools. We present here an approach to the question that has been discussed for a long time, i.e. how to approximate a given path by a second one in such a way that the latter lies in a tube of given radius ε around the first. The approximation should be a (normally cubic) spline with a small number of breakpoints. The strategy is based on algorithms used in “computer aided geometric design” and is applied to examples from industrial and surgical robotics.