I think what you are looking for is "Bezier Clipping"

Here is a link to a paper[^] on it but there may be better explanations via google now that you have the algorithm name :-)

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N number of (x,y)points where the spline curve passes through is given.

and line is drawn from (0,0) through a (x,y) point. i have derived a equation of that line using those two points and i found out the remaining points which lie on the line. But i couldn't find out exact intersection point of a spline curve and a line ... Please help me out to solve this.

and line is drawn from (0,0) through a (x,y) point. i have derived a equation of that line using those two points and i found out the remaining points which lie on the line. But i couldn't find out exact intersection point of a spline curve and a line ... Please help me out to solve this.

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