I'm a bit confused. You say that the problem is to "find a curve that lines up to a series of data points." That's fine. There's loads of ways to do that. But then this statement, "all points along curve are divided by the same denomonator minus the starting angle" is nonsensical. I don't see how you can properly say that a point can be divided by the same denominator.
And then you say that you need the "location of 2 points on a second grid". What does that mean? Which two points? What is a grid?
You say you need the "length of tangent lines at two points". Again, that sentence does not parse mathematically.
I have a hunch that cubic splines might serve your purpose well, whatever that is.