Quote:
Originally Posted by rgarri4
I'm flying around my Chicago model and it's hard to get the Sears tower to line up. haha.

The apparent height is given by the arctan of the actual height (relative to where you're standing) divided by the lateral distance. (Note that here we're inventing a cartesian grid, so x and y aren't exactly positions on the geoid as that would neglect earth curvature).
So for a building with at (x_i,y_i,z_i), the apparent height for an observer at (x,y,z) is atan( (z_iz) / sqrt((x_ix)^2 + (y_iy)^2). We also have the constraint that (x,y,z) must be above the local geoid.
In order for n buildings to have the same apparent height, we must therefore have:
C = (z_iz)^2 / ( (x_ix)^2 + (y_iy)^2)
for i = (1..n).
For two buildings, one can with sufficient algebra find a relation z(x,y) of positions where the two buildings have the same height. Adding another building, one gets three such relations. It's possible z(x,y) = z'(x,y) = z''(x,y) somewhere but I am not sure how likely that is. For 5 I would think some very special symmetry relations must be needed. It would be fun to write a program to find the leastsquares solution to the "equal height" problem for an arbitrary set of buildings. I have a 15 hour flight to NZ coming up... if I feel bored and don't feel like doing real work maybe I'll do that.