Localized intersections computation for solid modelling with straight homogenous generalized cylinders

This paper reports progress in the development of a solid modelling system combining straight homogeneous generalized cylinders through set operations. Two basic components of this system are the modules which compute the set operations between primitives and display the resulting solids using ray tracing. These two modules are also very computationally intensive as they involve a large number of surface-surface and ray-surface intersections computations. We introduce a novel hierarchical representation for straight homogeneous cylinders called Box Tree. The Box Tree is analogous to a Quadtree in parameter space. It is an exact boundary representation which describes the surface of the associated generalized cylinder by a hierarchy of enclosing boxes. We use the Box Tree to efficiently compute the set operations and ray tracing algorithms by localizing the search for intersections to the regions where they may occur. We discuss complexity issues and illustrate the performances of our modelling system on a variety of examples.