# Tag Info

7

I've wrapped up @ybeltukov's code into a function that works for an arbitrary MeshRegion surface. First we need to find the boundary vertices, which will remain fixed. If the MeshRegion represents a 2-dimensional manifold with boundary, then every internal vertex has as many edges as it has faces, but every boundary vertex has one extra edge. ...

17

Yes, it can! Unfortunately, not automatically. There are different algorithms to do it (see special literature, e.g. Dziuk, Gerhard, and John E. Hutchinson. A finite element method for the computation of parametric minimal surfaces. Equadiff 8, 49 (1994) [pdf] and references therein). However I'm going to implement the simplest method as possible. Just ...

12

After all this time I came up with a very nice tensor calculus proof of the Hairy Ball Theorem. It only depends on Stokes theorem and standard laws of tensor calculus like the Ricci identity and symmetries of curvature tensors. All the topology is done by Stokes theorem. The remainder of the proof is equational, local and geometrical. It is coordinate/basis ...

0

What if you used the orientation of the triangle as a clue to choosing sides? TriangleOrientation[{x1_, y1_}, {x2_, y2_}, {x3_, y3_}] := Sign[x3 (y1 - y2) + x1 (y2 - y3) + x2 (-y1 + y3)] Any triangle in your mesh has three sides, say vertices U to V, V to W, and W back to U. Say your current midpoint is in side $k$, where $k=1$, $2$, or $3$. If the ...

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