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I have equation

bezier cubic curve

As much I know, I have four points lets say A(x1,y1), B(x2,y2), C(x3,y3), D(x4, y4). How these 'P' are related to these set of points. And what might a Cubic Bézier curves be for the this (A, B, C, D) given set of points.

[UPDATE]

Having problem uploading image, but image somewhat looks like this

https://stackoverflow.com/questions/5142556/algorithm-to-add-color-in-bezier-curves

Regards,

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    @Henry thanks, i think in understand. Certainly, those two equations were helpful.2011-03-11

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That depends on what relationship you want your points $A$ to $D$ to have to the spline. It may be that you want them to have exactly the relationship to the splines that the points $P_0$ to $P_3$ have, which is explained here. Strangely, the equation in your question looks as if you copied it from there, but in that case you'd have to explain what part of the explanation there of what $P_0$ to $P_3$ mean you don't understand, and what you want your points $A$ to $D$ to mean instead.

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    thanks it was helpful ... just someone had posted and script for printing this function, i was just wondering how could i improve it. see the result in the updated section.2011-03-11