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.
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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_i-z) / sqrt((x_i-x)^2 + (y_i-y)^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_i-z)^2 / ( (x_i-x)^2 + (y_i-y)^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 least-squares 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.