Research on underwater robots is attracting increased attention around the world. Various kinds of underwater robots have been developed, using an assortment of shapes, sizes, weights, and propulsion methods. In this paper, we propose a novel underwater robot, employing a spherical hull and equipped with multiple vectored water-jet-based thrusters. The overall design of the robot is first intro...

We consider the problems of finding two optimal triangulations of convex polygon: MaxMin area and MinMax area. These are the triangulations that maximize the area of the smallest area triangle in a triangulation, and respectively minimize the area of the largest area triangle in a triangulation, over all possible triangulations. The problem was originally solved by Klincsek by dynamic programmi...

We present a self-adjusting point location structure for convex subdivisions. Let n be the number of vertices in a convex subdivision S. Our structure for S uses O(n) space and processes any online query sequence σ in O(n+ OPT) time, where OPT is the minimum time required by any linear decision tree for answering point location queries in S to process σ. The O(n + OPT) time bound includes the p...

We consider a different L-Minkowski combination of compact sets in R than the one introduced by Firey and we prove an L-BrunnMinkowski inequality, p ∈ [0, 1], for a general class of measures called convex measures that includes log-concave measures, under unconditional assumptions. As a consequence, we derive concavity properties of the function t 7→ μ(t 1 pA), p ∈ (0, 1], for unconditional con...

Rappaport D., A convex hull algorithm for discs, and applications, Computational Geometry: Theory and Applications 1 (1992) 171-187. We show that the convex hull of a set of discs can be determined in @(n log n) time. The algorithm is straightforward and simple to implement. We then show that the convex hull can be used to efficiently solve various problems for a set of discs. This includes O(n...