在图中搜索两个样条线的交点

Question

I am stuck at this point. I am trying to find where two lines in graph intersects. I have 10 points for each spline, but they intersects between this points.

I am using c# graph. (System.Windows.Forms.DataVisualization.Charting.Chart chart2;) Do you have an idea how to solve this?

Here is this situation. Points are measured manually so there is minimum posibility that it will intersetcs on this given points.

Answer 1

Refine the splines to the degree of precision you need and then intersect (straight) line pairs, as Matthew suggested. This can be done quite efficient if you chose the right data structure to store the line segments, so that it supports fast range queries (kd-tree perhaps?).

Doing it analytically is going to be really hard, I guess.

Answer 2

I found the solution, I used least squares theory and polynomial function to represent equation of curve and after that solve the equation. If anybody needs solution just write me.