Dominance for Containment Problems

In a containment problem, the goal is to preprocess a set of geometric objects so that, given a geometric query object, we can report all the objects containing the query object. We consider the containment problem where input objects are homothetic triangles and the query objects considered are line segments, circles, and trapezoids with bases parallel to either axis. We show that this problem can be solved using the 3-d query dominance problem. The solutions presented can also be extended for higher dimensions.