Application of uniform cubic B-splines to machine tools and robots numerical control: determination of vertices under various constraints

The mathematical formulation of B-splines uses the notion of vertices, also called control points, rather than that of pass-points. The use of uniform cubic B-splines for the numerical control of a machine tool or of a robot, for representing and manufacturing or manipulating pieces, previously required to translate the imposed pass-points of a given contour into the vertices of a B-spline curve. In this paper, the authors present three procedures allowing one, under some constraints, to convert rapidly the imposed pass-points into the corresponding vertices of a uniform cubic B-spline curve.<>