An algorithm and data structure for 3D object synthesis using surface patch intersections

Abstract

There are several successful systems that provide algorithms that allow for the intersection of polygonal objects or other primitive shapes to create more complex objects. Our intent is to provide similar algorithms for intersecting surface patches. There have been contributions to this concept at the display algorithm level, that is, computing the intersection at the time the frame is generated. In an animation environment, however, it becomes important to incorporate the intersection in the data generation routines, in order that those parts of the intersected object that never contribute to an image are not processed by the display algorithm. This only increases the complexity of the object unnecessarily, and subsequently puts an additional burden on the display algorithms. An algorithm is described which uses a modified Catmull recursive subdivision scheme to find the space curve which is the intersection of two bicubic patches. An associated data structure is discussed which incorporates this curve of intersection in the patch description in a way suitable for efficient display of the intersected object. Sample output of these intersections are shown which serve to illustrate the capabilities and limitations of the described procedures.