xyz (latitude longitude elevation) position on a surface

Question

how do I find a the xyz position on a surface created with multiple points. Say I survey the perimeter of a parking lot sloped in 2 directions not necessarily on a flat plan to create a surface. If i walk to any area with in the perimeter of the points with a gps device telling me the latitude and longitude? how would I calculate the elevation to the surface at that point? using c#

Answer 1

To transform [latitude, longitude, radius] to [x,y,z] (being (0,0,0) the center of the Earth) you can use the formulas from this answer

Now you can have all vertices of the perimeter of a surface expressed in [x,y,z] coords.

To get the z of a given (px,py) inner point you may suppose that the surface is formed by straights going from any vertex to any other vertex. If the surface is plain enough, the error is low; otherwise you need points inside the surface.

Given such a "smooth" surface, you can define a straight passing through the point (px,py), with any heading. And intersect that line with the polygon, get the two intersections, I1(x1,y1) and I2(x2,y2).
For each intersection you get the edge of the polygon, and interpolate with its two vertices the elevation (z) of the intersection.

Now interpolate the required 'z' with the two coords and elevations you have freshly calculated.

For more accuracy, you can use several straights, all passing through the point but with different headings, and get the average of the interpolated elevations.