Determining visibility between extended objects

Two query problems for visibility are considered. The first one is to find the visibility set of two query objects A and B of the same type as the objects of the given scene. The visibility set is characterized by those line segments connecting points on A and B which do not intersect scene objects between A and B. We show that scenes consisting of disjoint line segments in the plane can be processed into a data structure of about linear size so that the visibility set can be found in sublinear time per component of the representation chosen for the visibility set. The construction can also be applied to scenes of disjoint triangles in space. The disadvantage of possibly many components can be diminished by pre-clipping against the viewing hull of A and B. The query version of the clipping problem can also be solved in about linear space and sublinear query time. The result of the first problem is used for an efficient solution of the second problem which is to calculate the visibility sets between query object A and all scene objects visible from A