Vanishing torsion of parametric curves
We consider the class of parametric curves that can be represented by combination of control points and basis functions. A control point is let vary while the rest is held fixed. It’s shown that the locus of the moving control point that yields points of zero torsion is the osculating plane of the corresponding discriminant curve at its point of the same parameter value. The special case is studied when the basis functions sum to one.
Key wordsParametric curve Torsion Discriminant curve
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