Dominance for Enclosure Problems

Given a set of homothetic triangles (i.e., closed under scaling and translating operations) in the plane, we study the problem of computing the triangles enclosing a query object. The query objects considered are points, line segments, trapezoids, and ellipses. We show that the problem can be solved using the 3-d dominance reporting problem. The result can also be extended to higher dimensions.