Have you ever looked at Google maps in satellite view and noticed the “3D” button?
Push it and marvel.
In even moderately sized metro areas it brings up gorgeous 3D renditions of everything. Everything! Trees, cars, houses, huts, etc., all with photorealistic sides and accurately sloped roofs. 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.
The graphic has a more detailed description of the calculation. None of this comes easily to me and, thankfully, all the trigonometry is described on various websites.
How High is the Satellite?
A footnote to this brain teaser is: can you figure out high high the satellite (or airplane) is?Could do that with a picture in your house? Like if you have a known size shoe box, for example, could you look at a photo of it and calculate the distance?
As you zoom in on something with parallel edges, those edges look progressively more parallel. Do you need to know the camera’s focal length? Or can you tell from parallax? I don’t know but I’d love to sort it out some day.