  Plotting solution sets for particular equations may be complicated by the
existence of turning points. Here we describe an algorithm which not only
overcomes such problematic points, but does so in the most general of settings.
Applications of the algorithm are highlighted through two examples: the first
provides verification, while the second demonstrates a non-trivial application.
The latter is followed by a thorough run-time analysis. While both examples
deal with bivariate equations, it is discussed how the algorithm may be
generalized for space curves in $\R^{3}$.
