TOPOLOGICAL METHOD FOR LOOP DETECTION OF SURFACE INTERSECTION PROBLEMS

One method of detecting closed loops in surface intersections requires the computation of collinear normal vectors. Such collinear normal ve ctors form a subset of critical points of the plane vector field defin ed by the gradient of an oriented distance function from one surface t o the other. The Poincare index theorem detects the existence of a cri tical point in a region of the vector field, but fails when two critic al points having different signs of the index are in the same region. This paper presents a method for a conclusive test by extending the Po incare index theorem to three-dimensional vector fields. The idea of s olid angle is introduced to compute the rotation of vector fields in t hree dimensions. The Poincare index gives the total number of critical points enclosed by a three-dimensional boundary.