Abstract
We state and motivate a general definition of geometric continuity. In the case of analytic sets, we derive a general algebraic characterization of geometric continuity. We then use this characterization to show that the following representation-related notions are equivalent: • Derivative continuity for explicitly-defined surfaces. • Rescaling continuity for implicitly-defined surfaces. • Reparameterization continuity for parametrically-defined surfaces. • Intersection multiplicity for algebraic surfaces. In the implicit case, a new, equational characterization of geometric continuity is given and used to derive implicit curves and surfaces that meet with a given order of continuity.
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