I don't know how to classify this problem, so I thought I'd stick it under Other.

I wrote a python program to help me solve this, but the process takes much too long and I can't get the accuracy down to where I'd like it. Close, but no cookie.

This problem is one of a few variations, so if a method is found to solve this, then I could use it to finish what I started 2 years ago. I'm not a math expert, but I would like to understand.

Problem:

Finding a curve that lines up to a series of data points.

Answer needs accuracy of 10 decimal places. 10 may be overkill but I do need precision

Data:

starting at point 'a' with tangent angle=90 degrees

ending at point 'b' with tangent angle=140 degrees

all points along curve are divided by the same denomonator minus the starting angle

For this example I'm using 61 points. 0-60. 140-90==50 and 50/60 == .8333

data points formula: .8333 * (point1of60) + 90 would make the first midpoint 90.8333

so we are looking at a chart of tangents

140

139.1667

...

92.5

91.6667

90.8333

90

Needed:

Location of two points on a 2d grid

Length of tangent lines at two points

Given:

Point 'a' lies along line( x>0, y=0 )

Point 'b' lies along line( x>0, y=60 )

Hint:

Point 'a' can start at (0,0), what is needed is rise and run of ending point 'b'

It sounds like a circle, but that idea doesn't work for other variations. But maybe I've applied it wrong too.

I know many other people have asked for bezier formulas and been told that such formulas don't exist. So I've tried to provide as much information as possible as simplified as possible regarding my own problem.

Any response would be appreciated.