= Parametric curve interrogation
A <parametric curve> interface supplies its parameter domain, evaluation, and <derivatives> where they exist. Robust geometric algorithms also need restricted subcurves and certified range or <derivative> bounds on parameter intervals. Tangent, speed and <curvature> are derived from point and <derivative> enquiries when the relevant <derivatives> are regular. Finite point samples alone cannot certify the absence of every plane intersection of an arbitrary smooth curve.
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