Spline interpolation. Hi I've been reading about splines recently. For what I've understood splines actually don't interpolate, they approximate (touch the polygon defined by the control points at certain points). Is there a way to make the spline interpolate them?

Splines usually do interpolate (although there are versions that do not), see e.g. http://mathworld.wolfram.com/CubicSpline.html
A typic example is cubic spline which interpolates 2 successive points with a degree 3 polynomial, whence with 4 coefficients. As there are two coeffs more than the conditions you use the last coeffs to assure continuity of the first and second derivative at touching spline points. This gives the effect of a fairly smooth curve (it is $C^2$) through your interpolation points.
