Approximation of a Planar B-Spline Curve by Polygonal Trail with Special Characteristics
Last modified: 2017-03-16
When using the output data from CAD systems, the curve is often described in a so-called "spline" format. The regulation of a cutting, respectively other machine requires, that the input data are given in a form of a sequence of linear segments with prescribed maximal difference to the real curve, expressed in the "spline" format. Specifically, we are talking about replacing the given planar B-spline curve by polygonal trail with tops on this curve. We are doing this by a way when the distance between the individual linear segments of the trail and to those linear segments corresponding parallel tangent of the curve is less than or equal to the given positive ε. The requirement of a construction like this is motivated by the fact that during the cutting process by a laser, respectively a water beam, the polygonal trail is easier to track than the whole curve. A company MIR in Eskede, Sweden, which was the ordering party od this task, had chosen from a set of different types of planar B-spline curves the following three mostly used ones, the so-called clamped, opened and closed ones. The positive result of solving this task become used in a regulation system AMOS, which is a component of one laser-cutting machine in a company Skanpak, Czech Republic.
Planar B-spline curves; The types of planar B-spline curves; Approximation of B-spline curves by a polygonal trail; Cox – de Boor’s formula