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This paper presents an approach to nding an approximate implicit equation and an approximate inversion map of a planar rational parametric curve or a rational parametric surface. High accuracy of the approximation is achieved with a relatively small numberof low-degree curve segments or surface patches. By using monoid curves and surfaces, the method eliminates the undesirable singularities and phantom" branches, normally associated with implicit representation. The monoids are expressed indoi:10.1006/gmip.1999.0497 fatcat:zyrvkpv4ine4nfqbgkt53y3n7y