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Humans have an intuitive understanding of "up", so there's usually a single obvious way to orient a camera when taking photos. However, what happens when you po
by itishappy 3y ago
Humans have an intuitive understanding of "up", so there's usually a single obvious way to orient a camera when taking photos. However, what happens when you point a camera straight up or down? There's no longer an obvious choice, any direction you choose is reasonable (orthogonal)!
Another way to think about it is assigning cardinal directions to the Earth. Which way is north from the north pole? There's no possible way to create a map that has defined directions at every point.
The pictures in the Wikipedia article give a great intuitive understanding, particularly if you can figure out why a sphere and torus behave differently. (You can build a globally consistent map on a torus.)
- bmacho 3y ago> (You can build a globally consistent map on a torus.) No, you can not, there is no global map on the torus.
- itishappy 3y agoMy language may be imprecise. What I mean is that you can assign a direction to each point of the torus, and have it be consistent with it's neighbors (free of discontinuities) throughout the entire surface. This is in contrast to a sphere, which will always have tufts (poles) at at least one point. Note that this only applies within the surface itself, not to it's embedding in 3d space (the donut shape we're all familiar with). If north points up on the outside edge, it'll point down to us on the inside edge, but an ant on the surface would experience no contradictions. https://en.wikipedia.org/wiki/Torus#/media/File:Torus_cycles.svg https://en.wikipedia.org/wiki/Torus#/media/File:Torus_cycles...