Convert GPS coordinates to coordinate plane

Question

This is somewhat related to another question I asked: Translate GPS coordinates to location on PDF Map. That got me to this point, now I'm stuck on the math.

Let's say I have a floor plan of a building, I've taken gps coordinate readings from each corner of the building. Also assume that the floor plan is lined up with the latitude and longitude.

How do I convert a GPS coordinate to a X,Y position on this map? I can't seem to get the math right.

Answer 1

Let delta_long and delta_lat be the differences, in degrees, in the GPS coordinates of the building's corners. Let delta_x = 320 and delta_y = 480 (feet, let's say). Then:

vertical_scale = delta_y/delta_lat with units feet/degree latitude

horizontal_scale = delta_x/(cos(latitude)*delta_long) with units feet/degree longitude.

The cos(latitude) factor compensates for the varying length of 1 degree of longitude as one moves from the equator to the poles. We can assume for this application that it won't change appreciably between the north and south ends of the building.

Then for any nearby (lat,long) point, subtract off the coordinates of the southwest corner of the building, and apply the vertical and horizontal scales in the obvious way to locate that point with respect to the building layout.