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The authors propose that recursive subdivision techniques be used for some of these tasks and for some special subclasses. Specifically, they advocate the use of interval computation methods that treat the parametric range as an interval. These techniques can be extended to evaluating piecewise continuously differentiable functions over intervals. Also presented is a general schema for designing algorithms using interval evaluation of functions. The power of this methodology is illustrated through the design of algorithms for commonly required processing tasks on geometric objects.