



Abstract: 

An omegawedge is the closed set of points contained between two rays that are emanating from a single point (the apex), and are separated by an angle omega < pi. Given a convex polygon P, we place the omegawedge such that P is inside the wedge and both rays are tangent to P. The omegacloud of P is the curve traced by the apex of the omegawedge as it rotates around P while maintaining tangency to both rays. We investigate reconstructing a polygon P from its omegacloud. Previous work on reconstructing P from probes with the omegawedge required knowledge of the points of tangency between P and the two rays of the omegawedge in addition to the location of the apex. Here we consider the setting where the maximal omegacloud alone is given. We determine the conditions under which it uniquely defines P: We show that if neither of these two conditions hold, then P can be not unique. We show that, when the uniqueness conditions hold, the polygon P can be reconstructed in O(n) time with O(1) working space in addition to the input, where n is the number of arcs in the input omegacloud. 



Biography: 

Elena Arseneva, previously known as Elena Khramtcova, obtained her specialist degree (considered equal to BSc+MSc) at Mathematics and Mechanics Faculty of SaintPetersburg State University, Russia. After that she obtained her PhD at Universita della Svizzera italiana under supervision of Prof. Evanthia Papadopoulou in the area of computational geometry with the main focus in generalized Voronoi diagrams. After completing her PhD studies, she has done a postdoc in the Algorithms Research Group at Université libre de Bruxelles (ULB) hosted by Prof. Stefan Langerman, and funded by the SNF Early PostDoc Mobility program. Currently she is about to start as an Assistant Professor back at SaintPeretsburg State University, where she will be a part of BSc program in Mathematics and TCS. 



