Kinematic approximation algorithm with ruled surface

摘要

The present invention relates to a method for producing at least one surface on a workpiece by means of a material removal tool and a corresponding material removal device. It is an object of the present invention to provide a method for producing an arbitrary surface on a workpiece in such a way that the surface is produced quickly and inexpensively. An error between any surface to be generated and a generated control surface should be small. The invention is characterized in that, starting from any surface to be produced, a movement path of the material removal tool is controlled to produce a control surface approximating the arbitrary surface, the movement path being provided in the form of a curve on a dual unit sphere, a point on the Curve corresponds to a location and orientation of the material removal tool. The curve can be generated from linear lines that are transformed by mathematical transformations into points on the dual unit sphere. Interpolation of these points is performed by means of a dual-ball spline interpolation algorithm to generate the curve. This can now be transformed back into the control surface to be produced or can be used directly for controlling the movement path of the material removal tool. Likewise, direct-curve curves of the control surface can be determined by means of the dual-sphere-spline interpolation algorithm.