Monday, 11 May 2009

Surface Turtle

This is an implementation of a turtle walking around on a NURBS surface. If the turtle is going straight in small steps, the resulting path is close to a geodesic.







In general relativity, the straight path in curved spacetime is a geodesic

2 comments:

Matsch said...

Hi Lorenz,

first I want to say thanks for posting this definition, it's a very useful alternative to the shortest path command for finding geodesics. I'm just trying to understand exactly how it works by updating it to the new vb.net component, which seems to work and I'm also trying to get it to work for meshes. Anyway, my question is regarding this section of code:

"tmp.PerpendicularTo(pos, pos + axis, pos + dir)
tmp.unitize()
dir.PerpendicularTo(pos, pos + tmp, pos + axis)
dir.unitize()"

To me it looks like this is setting tmp to the cross product of axis and dir and then setting dir to the cross product of tmp and axis. Shouldn't this just give you dir back again? It seems like it should but that can't be the case because it would make this section of code redundant, but when you comment it out it does have an effect on the resulting geodesic...

I'm confused, perhaps you could shed some light on how it works. Thanks again for posting your work, it has been so very helpful!

Lorenz Lachauer said...

Hi Matsch, I can send you an explaining sketch, if you send me your email adress. Best, Lorenz.

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