Tracing surface intersections

Abstract We consider the problem of tracing the intersection of surfaces given either implicitly or parametrically. We give a numerical tracing procedure in which a third-order Taylor approximant is constructed for taking steps of variable length, and the points so found are improved by Newton iteration. We show how this construction relates to local parametrizations of the curve at singularities, and discuss our experience with the method. For plane curves, given implicitly, we show how desingularization techniques can be incorporated to trace correctly through all types of singularities. An implementation of this method is also discussed.

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