basic animation questions

Hi all,
I have a path on which I want my object to move. I have generated the path using splines. I have all the points that are used to generate the path in a variable say point[count].
I have the following questions:

  1. If i want to calculate the tangent at any point how do i do it?
    2)How do i calculate the velocity and acceleration at any given point??

can you point me to any resources on the web the above information. Any sort of information will be appreciated.

  1. To find the tangent of a piecewise smooth curve that defines a path, the tangent of the path at any point on the path, x, but not on a point in the set that defines the path, is simply the unit vector parallel to the line segment from point p1 to p2 and x is on that line segment. If x=p1 or x=p2, then it is customary to use the average tanget of the two segments the point straddles. Note: If the spline can be defined by a continuous parameterization [b]s/b, then the tangent [b]T/b=s’(t)/|s’(t)|.

  2. Assuming count is a function of time, then the velocity is just the first time derivative and the acceleration is just the first time derivative of the velocity.

[This message has been edited by DFrey (edited 11-19-2000).]