Searching for Point Locations using Lines
arXiv:2106.10149
Abstract
Versions of the following problem appear in several topics such as Gamma Knife radiosurgery, studying objects with the X-ray transform, the 3SUM problem, and the -linear degeneracy testing. Suppose there are points on a plane whose specific locations are unknown. We are given all the lines that go through the points with a given slope. We show that the minimum number of slopes needed, in general, to find all the point locations is and we provide an algorithm to do so.
13 pages, 7 figures