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Jul
27
answered Voronoi cells and the dual complexes in Riemannian manifolds
Jun
25
awarded  Yearling
Jul
25
comment Techniques for refining or constraining a Voronoi diagram?
If you have the Voronoi diagram then farthest point sampling (Delaunay refinement) seems like the obvious choice. The farthest point from a station will always be a Voronoi vertex, (or a point where a Voronoi edge intersects your quadrilateral boundary, or a corner of your boundary). Insert a new "station" at that point, and continue until the farthest point is close enough to a station.
Jul
7
comment Are properties of geodesics on a cylinder unique to cylinders?
Could we not graft a cylinder (with $z$-axis) to the $xy$-plane (with disk removed) in such a way that no geodesic can self-intersect?
Apr
9
comment How to show that the “bing's house with two rooms” is contractible?
An update to jc's comment above: Ken Baker made a subsequent post that describes a deformation retraction: sketchesoftopology.wordpress.com/2010/06/23/…
Feb
25
comment Examples of eventual counterexamples
Another relevant blog post: scottaaronson.com/writings/bignumbers.html
Feb
2
comment Conic neighborhoods ⇔ Polyhedral
I guess in the definition of a cone you meant to say that $r\alpha$ is the distance from $\xi$ to $\zeta$ in $\Sigma$?
Jan
23
answered Delaunay triangulations and convex hulls
Nov
2
comment Why is the half-torus rigid?
The rigidity of the punctured torus is listed as an open problem (number 13) by Ghomi here: people.math.gatech.edu/~ghomi/Papers/op.pdf . I guess either the list is wrong, or I am missing a distinction between things I don't understand.
May
22
comment Is there a combinatorial analogue of Ricci flow?
D. Glickenstein has done some work that might interest you, "Combinatorial Yamabe flow in three dimensions" arxiv.org/abs/math/0506182
May
5
awarded  Commentator
May
5
comment Sexy vacuity …
de Boor's "An empty exercise" on vacuity in linear algebra: ftp.cs.wisc.edu/Approx/empty.pdf or here: dx.doi.org/10.1145%2F122272.122273
May
5
comment Sexy vacuity …
There is a neat article by de Boor An empty exercise (doi), where he argues for the inclusion of $0\times n$ and $m \times 0$ matrices in Matlab. He discusses definitions of span and determinant etc. I found this from a link on the Wikipedia page for determinant.
Apr
23
comment How to respond to “I was never much good at maths at school.”
A thoughtful answer. There is an arithmetical error on the first page of the short article linked at the end of the post. It is quite amusing in its context, so I am not entirely sure it isn't intentional.
Apr
17
comment Conformal structure determined by principal curvatures
This metric is sometimes used in constructing an approximating inscribed polyhedron for the surface. There are some optimality results, e.g. K. Clarkson (2006) "Building triangulations using epsilon nets" and the works of P. M. Gruber cited therin.
Feb
18
comment Gaussian curvature radius
By smaller I mean that $\rho_K(x) \leq \rho_G(x)$ for all $x$, where $\rho_G$ is the original definition. They agree everywhere except when the curvature is negative and $\rho_G$ provides no bound. I would be surprised if you found this to be a useful way to capture the geometry of negatively curved surfaces. Since it is purely intrinsic, you will never be able to control triangle normals this way, for example. It is not clear to me what is represented by the bound you're proposing to introduce. I don't recall seeing it anywhere previously.
Feb
18
comment Hypersurfaces and Elliptic Points
In a response to his own question here: mathoverflow.net/questions/31222/… Joseph O'Rourke linked to a paper by Zalgaller: springerlink.com/content/hu76g212137g2864 which describes a PL embedding of a flat torus in $R^3$. I am curious to know where that paper sits in the line of successive rediscoveries.
Feb
17
answered Gaussian curvature radius
Dec
7
comment Is there a complex structure on the 6-sphere?
A topical preprint has been posted on ArXiv (asserting that $S^6$ has a complex structure): front.math.ucdavis.edu/0505.5634
Nov
22
comment Examples of using physical intuition to solve math problems
Another relevant question is about translating a physical argument into a mathematical one.