ON THE DETERMINATION OF STARTING POINTS FOR PARAMETRIC SURFACE INTERSECTIONS

Two numerical algorithms for computing starting points on the curve of intersection between two parametric surfaces are presented. The probl em of determining intersection curves between two surfaces is analytic ally formulated by parametrizing inequality constraints into equality constraints and augmenting the constraint function. The first method u ses an iterative optimization formulation and an iterative conjugate g radient algorithm to minimize a function comprising the vector of coor dinates and a weighted constraint term. The second method uses the Moo re-Penrose pseudo inverse of the constraint function to determine a st arting point. Numerical examples are presented to validate both method s. Both methods require an initial point on one of the surfaces. Numer ical examples illustrating the validity of the presented methods are d iscussed. The local versus the global views of the intersection proble m in terms of iterative and recursive subdivision methods are addresse d. Difficulties in determining more than one point are also illustrate d using examples. The two algorithms are compared by studying their co mputational complexity. The Moore-Penrose inverse method has showed su perior efficiency in the computational complexity, number of iteration s needed, and time for conversion to a starting point. It is also show n that the Moore-Penrose inverse converges to a starting point in case s where the iterative optimization method does not. Copyright (C) 1996 Elsevier Science Ltd