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I am now trying to write program to generate smooth curve by using cubic bezier (4 points, 2 endpoints and 2 control points) through a set of points like the 'insert curve' function in Microsoft Word.

I am wondering how do the curve compute the magnitude of the control points of each point. I noticed that the gradient of the tangent to the curve at that point is the same as the gradient of the straight line formed from prior and next point, so I can compute the gradient of the control point, but what about the magnitude? I also noticed that in the Curve function, at each point, the control point prior to the point and next to the point are of the same magnitude.

At the end points, how do i get the direction and magnitude of the control point?

Please help me out! Thanks in advance!

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# Generating bezier curve through a set of points

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