To preface, I’m speaking here as someone who is not any kind of math genius.

What I want to make is a script where, taking 2 ends of a bezier spline segment, and specifying several points between, the bezier in/out handles will be adjusted such that the spline segment touches all the intervening points. If I have figured this correctly, it should be theoretically possible to make the spline segment touch up to 3 specified points (with some restrictions on where those points can be.)

I’ve figured out several ways to access and manipulate a spline’s bezier curve data, and plan on building a matrix based on the 2 splines ends and the world up vector. So, just assuming that end points A and B of a spline segment are laying flat along the x-axis, what kind of formula do I need to control the bezier curve to touch the points?