finding value of a point between measured points on a 2D plane

Question

I'm trying to find the best way to calculate this. On a 2D plane I have fixed points all with an instantaneous measurement value. The coordinates of these points is known. I want to predict the value of a movable point between these fixed points. The movable point coodinates will be known. So the distance betwwen the points is known as well. This could be comparable to temperature readings or elevation on topography. I this case I'm wanting to predict ionospheric TEC of the mobile point from the fixed point measurements. The fixed point measurements are smoothed over time however I do not want to have to store previous values of the mobile point estimate in RAM. Would some sort of gradient function be the way to go here?

Answer 1

This is the same algorithm for interpolating the height of a point from a triangle.

In your case you don't have z values for heights, but some other float value for each triangle vertex, but it's the same concept, still 3D points.

Where you have 3D triangle points p, q, r and test point pt, then pseudo code from the above mathgem is something like this:

Vector3 v1 = q - p;
Vector3 v2 = r - p;
Vector3 n = v1.CrossProduct(v2);

if n.z is not zero
  return ((n.x * (pt.x - p.x) + n.y * (pt.y - p.y)) / -n.z) + p.z

As you indicate in your comment to @Phpdevpad, you do have 3 fixed points so this will work.

Answer 2

You can try contour plots especially contour lines. Simply use a delaunay triangulation of the points and a linear transformation along the edges. You can try my PHP implementations https://contourplot.codeplex.com for geographic maps. Another algorithm is conrec algorithm from Paul Bourke.