Lately, I've been studying cubic splines in order to be able to make my 2d polygon graphics look more rounded and "organic". I've implemented both Catmull-Rom and Hermite cubic splines successfully, but I'm having trouble understanding something from the wikipedia article. In the article topic "Interpolating a data set", several methods for choosing a tangent vector is described: finite difference, cardinal spline and catmull-rom spline. A data set (P

_{k}, t

_{k}) for k = 1, ..n can be used to find a tangent, m

_{k}for each control point. The trouble is, that both t

_{k}and m

_{k}are described as tangents, and the article isn't clear about the difference between them, except thart you need to know the value of t

_{k}to calculate m

_{k}. Could someone please explain what t

_{k}represents in the data set (P

_{k}, t

_{k})? The only thing I can think of, is that t

_{k}might be an arbitrarily chosen tangent vector set by the user. I've implemented the tangent equations as I assumed they were supposed to, but they return garbage.

Cheers,

Mike