There are basically approximated and interpolated curves.
http://www.vrvis.at/vr/cgr4/slides/CGR4-2002-KurvenEtc.pdf
For modelling parameterized curves using controlpoints some algorithms are Bezier and Catmull rom spline .
Basic information for curve interpolation linear and polynomial can be found in
http://en.wikipedia.org/wiki/Interpolation
See also splines such as the catmull rom spline
http://en.wikipedia.org/wiki/Cubic_Hermite_spline
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