I'm a little confused on why the bottom example is non-orientable -- could someone explain? I get why the top right is inconsistent, because the left tri is counterclockwise, while the right tri is clockwise -- but why can't all the triangles in the bottom example be in the same orientation (whether clockwise or counterclockwise)?
alanszhang
I think that object looks like a mobius strip, so basically it only has one side. As you go across the strip you notice that the notice that the normal vectors will flip for any given triangle, so it's impossible to orientate.
The pair of triangles on the other hand can have multiple orientations (4 to be exact). Think about which directions the normal vectors would point!
nathanpetreaca
For those confused by the mobius strip, here is another great example of a non-orientable topology https://en.wikipedia.org/wiki/Klein_bottle . As you can see, this would be somewhat difficult to deal with. Thankfully, in this class we do not have to worry about these shapes.
AronisGod
Reminiscent of surface flux integrals...
Staffirisli
How does this non-orientable issue interact with the half-edge property of having the twin edge always in the opposite direction?
Is the direction of the twin the same as the half-edge direction for that twin?
I'm a little confused on why the bottom example is non-orientable -- could someone explain? I get why the top right is inconsistent, because the left tri is counterclockwise, while the right tri is clockwise -- but why can't all the triangles in the bottom example be in the same orientation (whether clockwise or counterclockwise)?
I think that object looks like a mobius strip, so basically it only has one side. As you go across the strip you notice that the notice that the normal vectors will flip for any given triangle, so it's impossible to orientate.
The pair of triangles on the other hand can have multiple orientations (4 to be exact). Think about which directions the normal vectors would point!
For those confused by the mobius strip, here is another great example of a non-orientable topology https://en.wikipedia.org/wiki/Klein_bottle . As you can see, this would be somewhat difficult to deal with. Thankfully, in this class we do not have to worry about these shapes.
Reminiscent of surface flux integrals...
How does this non-orientable issue interact with the half-edge property of having the twin edge always in the opposite direction?
Is the direction of the twin the same as the half-edge direction for that twin?