When we are trying to shape a surface X by 3-axis milling, we encounter a list of problems: First we have to decide if locally the milling tool Σ is able to move along the surface such that its envelope during the motion is the given surface. This is a question involving the curvatures of X and Σ. Second, we want to avoid that while milling in one part of X, Σ intersects another, already finish...