Drawing a bezier from multiple points

Question

I have a set with 50 points in x,y. I need to draw the smoothest bezier that passes in all points, or in other words, the bezier that will best fit the points.

How do I do that? thanks

Answer 1

I am undergoing a similar problem in 3D. It is slightly easier in 2D because lines will always intersect if not parallel.

Firstly, read up on quadratic bezier curves. Each curve is represented by three points. The line will not pass through the middle point. Thus, your middle point cannot be one of the points you are trying to fit, or it won't go through it.

Instead, the beginning and end point of your quadratic bezier curve must be two consecutive points you want it to pass through. So what is your middle point going to be?

One way of solving this (never tried it myself HENCE it might not look perfect, but Im thinking off the top of my head) is to calculate the tangents from your -1st data point to your 0th data point, and find the intersection between that and the 1st data point to the 2nd data point. Then draw the line between the 0th data point and the 1st data point using this intersection as the middle bezier curve value.

Obviously you may have trouble at the ends of the curves, that may require some inventive thinking to make them look good. (the first point has no -1st point).

Sorry about the lack of diagrams. I would draw one but I'm on an iPad.