The bisector of a point and a plane parametric curve
The bisector of a point \(p\) and a smooth plane curve \(c\) is defined as the locus traced by all points that remain equidistant with respect to \(p\) and \(c\). The problem of computing such bisectors arises for example within the context of planning paths of maximum clearance in robotics, or computing Voronoi diagrams for areas with curved boundaries. The present paper, which appears to be a condensed version of a longer technical report, gives a systematic analysis of such point/curve bisectors. More precisely, the contents are as follows: After the presentation of some basic results on point/curve bisectors, it is shown how to represent the (untrimmed) bisector, which is a superset of the true bisector, as a so-called variable-distance offset. Then, a trimming procedure is developed, which is able to compute the true bisector by computing its self-intersections and throwing away the (finite number of) recognized superfluous segments. Moreover, for simple curves, e.g. conics, it is possible to write down the trim points a priori. The paper is in my eyes well-organized; a total of 14 figures illustrates the authors' results.
scientific article; zbMATH DE number 571724
scientific article