Computation of singularities and intersections of offsets of planar curves
The paper presents a new method for the computation of the singularities of a normal offset of a planar polynomial curve, as well as for the calculation of the intersections of two (specific) normal offsets of such curves. Offsets of the above-mentioned type are described not only by polynomials, but also by square roots of polynomials, which make it necessary to use sophisticated methods. The procedure developed in the paper is mainly based on the reduction of the original problem into the solution of systems of polynomial equations (in a higher-dimensional space) through the introduction of suitable auxiliary variables. Furthermore, the computation uses rounded interval arithmetic and is therefore quite robust. The paper also includes an extensive survey of the existing literature on the topic, a short appendix on the basics of interval arithmetic, and some numerical examples in order to illustrate the developed techniques.
scientific article; zbMATH DE number 516613
scientific article