Google's 3D Buildings
20170108 Ever Wonder How They Do It?
Oh boy, another squirrel.
Have you ever looked at Google maps in satellite view and noticed the
"3D" button in the lower right corner? I have. Push it sometime and
marvel: in even moderately sized metro areas it brings up gorgeous 3D
renditions of everything. Everything! Trees, cars, houses, huts, etc.
How the He!l do they do that!?!?
So I got to thinking.
As a satellite travels overhead it's taking pictures looking down.
When it's directly overhead a building wall looks like it takes no
distance. As it travels past overhead the apparent wall size increases.
Google knows quite precisely the inches per pixel of flat ground or else
they couldn't put them in the right place.
Once the satellite has moved some distance from the wall, it has an
apparent size. That's not the correct size because you're seeing it at
an angle. If you knew the angle, you could sort out the height. Well you
*DO* know the angle. The satellite knows where it is, and Google knows
the latitude of the building, so it has this angle to many significant
digits.
That apparent distance becomes the opposite side to a right triangle
for which you know the angle in gory detail. Voila: height is the
hypotenuse.
Of COURSE I should be working on the book but this little puzzle
piqued my interest and I just couldn't let go. There is more detail that
must be sorted out, namely the slope of objects that aren't vertical,
but that seems like it would only be a bit more difficult to figure out.
The biggest breakthrough is extremely high resolution satellite
imagery, probably in the one foot per pixel range or even more.
Kudos to Google for an amazing product, served up for the cost of
seeing ads to the general public.
Below is a graphic with a more detailed description of the
calculation. None of this comes easily to me and, thankfully, all the
trigonometry is described on various websites.
