如何获得曲线和直线之间的交点？

Question

I performed a tensile tests of the material and here is my data. I need to determine the intersection of line with my data, this will give me my yield stress. The data is written in form of:

 A = -0.0033   -2.6120
     -0.0037   -2.6309
     -0.0051   -2.6246
     -0.0018   -2.6309
     -0.0030   -2.6120
     -0.0004   -2.5806
     -0.0036   -2.6120
     -0.0026   -2.6120
     -0.0024   -2.5995
     -0.0020   -2.5618... etc.

And a line, y=a*(x-0.2)+b .

I have tried to with intersect function after interpreting the line as a:

C =  0  -19.3677
1.0000   48.4377
2.0000  116.2431`

But it does not helps. Any suggestions of the problem solution? I have a bunch of an experimental data and would like to write it as a macro. The data has the same pattern of the curve.

Image is here:

Answer 1

Do you know how to calculate the intersection of two lines? If so, you can just do this for all the segments that form the curve, and chose the one that makes sense.

Answer 2

a) Binary search through your data along the line

b) Locate the segments of data nearest the line

c) Intersect the lines

Binary search will find the mid-point of the approximate curve between the nearest data segments, this is similar to calculating a Bezier curve at any rate.

If accuracy maters, do it analytically.