I noticed that is a Catmull-rom spline. Are you the one I told that you couldn't convert between catmull-rom and beziers. If so I was wrong. Here is a link showing how to do so.

I don't see any reason for a numeric method here. Numeric methods have their place, but this doesn't seem to be one of them. I don't think it will be quite as simple as you are thinking and I suspect it will be more computationally expensive than just using the derived formula. You can simplify deriving the formula by using a substitution so that you have the equation a*t^3+b*t^2+c*t+d. The derivative is the same whether a, b, c and d are scalars or vectors of constants since they are just coefficents. The advantage of using vectors and the dot product is that it isn't limited to just the y direction but rather can be any direction you please.

It occured to me that it might worth mentioning that since the dot product is distributive (a*t^2 + b*t + c).n = (a.n)*t^2 + (b.n)*t + (c.n) so you can apply the quadradic formula without expanding it out. Also you are finding the max/min with respect to a plane and the direction is simply the normal for that plane. The quadradic equals zero is a plane passing through the origin. That may be useful if you want to find if the curve crosses a plane (max one side, min the other) that does not pass through the origin.

[edited by - LilBudyWizer on January 20, 2003 12:44:27 AM]

Hi again

I''ve been away for the past week, so I''ve begun working on again on this problem

And using your simplified derivation (substitution somehow did not occur to me...) I got it working perfectly

First time I''ve used calculus out of the classroom =)

Nice to know all those hours spent studying didn''t go to waste!