Aspects of Algorithms for Manifold Intersection
The implementation of intersection algorithms is in most cases tailored to the use of specific methods for geometry representation and to the specific needs in a given application. As the computers grow more and more powerful, the ability to solve complex intersection problems are improved. Thus better understanding of intersection algorithms independent of the dimension of the objects being intersected and the dimension of the space in which the objects lie, will simplify the development of new intersection algorithms. To contribute to this we will in this chapter address some topics that are central when new intersection algorithms are to be developed. The first of these is a generic structure for intersection algorithms, then the handling of intersection tolerances is addressed followed by strategies for identifying intersections. The final topic addressed is conditions that ensure that no internal loops exist in the intersection of smooth manifolds.
KeywordsTangent Bundle Smooth Manifold Disjoint Subset Intersection Problem NURBS Curve
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