I have line features representing overhead power lines, and for these power lines, I have height attribute values at three different locations: the start of the line, the end of the line and (using a distance attribute from start) the point of maximal sag of the line between start and end points. I do not want to create straight lines between start point, sag point and end point but a curved line of best fit between the three points. Note that the "sag" point is not always midway between the start and end point. I need to do this in a python program as I have to calculate this for a large volume of lines, so the editing "arc" tool is not really something I can use.
I looked into trying to fit an ellipsoid between the points but that is no good as this would mean I have one ellipsoid between start point and sag point and another ellipsoid between sag point and end point. I need a single curve that fits all three points. I tried the spline tool, which creates a raster surface from points (which means I can perhaps get back from raster to more points), but 3 points is not enough to create a raster surface. I also tried non spatial tools such as scipy interpolate (fitting a spline between sets of np.array values), but here also, I only have 3 points which is not sufficient to do the interpolation and create the "spline" line.
Anyone knows how to create a curve of best fit between three point locations? In my case these points are z (height) values so either a curved "best fit" line is calculated directly or intermediate points are calculated from which I create a new line feature. However, in that case I also would have to find the X and Y coordinates of the newly created (intermediate) z height values.
Difficult problem, I know, I am just wondering if someone has worked this out, or can help me in any way.
Thanks very much.