>Hi,
>
>Think I'm going to get out of my depth here but...
>
>Given a Bezier spline (that I've defined so I know the end and control points) how can I determine the slope of the tangent at a particular point on the spline?
>
>Actually I *think* I can do that - but it's over simpifying the requirement. What I really need, given a secant of the spline from a known start point and of known length, is to determine its end point (or slope)
>
>I could use a cardinal spline instead of a Bezier if it was easier to obtain the result but that looks more difficult to me...

Good grief, you have to get the prize for most complex math question I've ever seen asked here on the UT ;)

I knew very little about Bezier splines before poking around on the Web a bit, now I feel like I know even less <g>.

One general approach you might be able to look into would be something like this:

1. If you can describe the spline as y = F(x), where F is "some function" of x (this is probably a heck of a big "if"), then

2. The slope of the curve at any point x is simply the first derivative of F(x) with respect to x (elementary differential calculus).

UPDATE: the following link goes into the math somewhat and shows the formulae for first derivative ("velocity") and second derivative ("acceleration"): http://www.everything2.com/index.pl?node_id=922415

Out of general interest, what is it you're trying to do? And is it in Fox (I've seen you on the .Net forum from time to time).