Polyhedral subdivision methods for free-form surfaces

One of the central issues in computer-aided geometric design is the representation of free-form surfaces which are needed for many purposes in engineering and science. Several limitations are imposed on most available surface systems: the rectangularity of the network describing a surface and the manipulation of surfaces without regard to the volume enclosed are examples. Polyhedral subdivision methods suggest themselves as a solution to these problems. Their use, however, is not widespread for several reasons such as the lack of boundary control, and interpolation and interrogation capabilities. In this paper the original work on subdivision methods is extended to overcome these problems. Two methods are described, one for controlling the boundary curves of such surfaces, and another for interpolating points on irregular networks. A general surface/surface intersection algorithm is also provided: seven decisions need to be made in order to specify a particular implementation. The algorithm is also suitable for intersecting other classes of surfaces amongst which are the popular Bézier and B-spline surfaces.