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I have three points in

**3D space**, and I would like to find the equation of a parabola that goes between them. My final goal is to sample about 20-25 points that lie on the parabola between these three points (ie, the user of my program will provide 3 points, then I will draw a "dotted line" version of the parabola between them through more discretized sampling).

I know how to find the parabola that goes through 3 points in

*2D space*, and I know how to find the equation of the unique plane that runs through these 3 points.

I just don't know how to connect the two pieces (or if there is an easier way to accomplish my above goal).

Any help would be greatly appreciated!