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**cubic bezier curve : get "sub curve" coordinates**

Hi,

I have a standard cubic bezier curve defined by 4 points, what I'm trying to get is a "sub-curve" of this one (from the same point of origin, to one particular point on this curve, with the same curve).

For example, getting the first 10% from this curve, also defined as a bezier curve by 4 points, getting point of origin and end point is easy, but I really have no idea of how to calculate the position of the 2 other points (the points giving directional information). Any idea/hint of how to calculate this ?