tinyspline software library. ansi c, mit license, nurbs, b-splines and bezier curves. no api overview except for the header file, always generic for any number of dimensions with many heap memory allocations
b-splines seem to have the highest continuity in general, but go only through the first and last point
natural cubic splines seem to have the highest continuity while going through all points
nurbs seem to be a generalisation of b-splines which seem to be a generalisation of bezier curves
hermite and catmull-rom interpolation seem to be variations of cubic interpolation
interpolation, curve fitting and splines: interpolation goes at least to start and end points, curve fitting approximates a curve between values, splines combine interpolation piecewiese
gsl can do only one and two dimensional interpolation
energy-minimising curve fitting might be a topic of interest