Slides — The Simplicial Complex

Our next lecture dives into some basic ideas about how to digitally encode geometry using a “mesh,” or more specifically a simplicial complex:

SimplicialComplex

3 thoughts on “Slides — The Simplicial Complex”

  1. Is it possible to have a non-orientable simplicial complex? We know that there are non-orientable manifolds (e.g. Möbius strip) in the classical setting, where orientability is defined in terms of, for example, existence of differentiable Gauss map for manifolds in $\mathbb{R}^3$, or, more generally, existence of oriented atlas. I wonder if there are analogous definitions in the discrete setting.

    1. Terrific question. What do you think: is it possible to triangulate a Möbius strip? If so, can you describe this triangulation as a simplicial complex? And if you can do that, can you give an orientation to each element of this complex?

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