document: Using duality to implicitize and find cusps and inflection points of Bezier curves A planar algebraic curve C has an implicit equation and a tangential equation . The tangential equation defines a dual curve to C. Starting with a parametrization of C , we find a parametrization of the dual curve , and the tangential equation and implicit equation of C in a novel way . We also find equations whose roots are the parameter values of the cusps and inflection points of C. Methods include polar reciprocation and the theory of envelopes
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