A robust intersection search applies branch and bound to pairs of subdivision surface patches. Certified bounding volumes reject disjoint pairs, and refinement reduces unresolved pairs. Limit evaluation, tangent data and controlled approximation bounds produce and correct local intersection arcs, then patch adjacency joins them. Bounds must enclose the limit, not merely the current mesh. Flat polygon intersections are approximations and can miss tiny components or tangencies unless the associated geometric and transversality conditions are verified.
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