COMMON TANGENTS TO PLANAR PARAMETRIC CURVES - A GEOMETRIC SOLUTION

The task of determining common tangent lines to a pair (or more) of parametric curves has important applications in draughting systems, enveloping polygon computation, bin-packing and compaction problems, and a host of other areas. In the paper, an efficient and robust algorithm to detect all common tangent lines between a pair of planar parametric curves has been presented. The algorithm uses a geometric search on the curves, and, by quickly rejecting large portions that are not likely to have a common tangent, it rapidly zeros in on the solution. The algorithm has been implemented on an IBM-compatible PC, and it works fast enough for realtime interactive use.