Recent content by Estanho

Hmm I am aware of Gödel's theorems and I should probably have mentioned it on the post, although I don't possesses the technical knowledge to follow the proofs on a fundamental level. What I'm looking for is more on the level as to why such limitations exist. Sorry for repeating this example...

I can understand that we can have limitations on physics, as we are trying to describe nature and so constraints can naturally occur - even meta-constraints that limit our ability to model nature to an arbitrary degree. However, why does that applies to a synthetic system such as mathematics as...

Also, your work reminds me of one other from a professor of my local University. He works with these so-called UNIVs, which are sculptures representing seven-dimensional spaces. You can see his phd thesis here: https://arxiv.org/pdf/math/0305058.pdf

Got it. Nice piece of software, congratulations. I don't have dollars to spare right now since I'm a mere MSc student but I might look forward to buying it in the future.

That's cool. If I understand correctly, you wrote a software to convert from a planar graph into a polyhedron? What language did you use?

Oh, of course. I guess I missed my geometry classes. I will try to work this out. Thanks.

It could be interesting to proof if all polyhedra contain a hamiltonian cycle on its faces. This theorem can be applied to planar graphs, I'm not sure also if every possible polyhedron can have its faces connectivities mapped to a planar graph. I couldn't think of a counter example, though.

Hi, I'm developing a data structure to represent 3-D meshes for numeric simulation. I want those meshes to be able to handle any type of polyhedron (not only the classic tetra and hexahedron). The best data structure that I could find was one based on half-edges (or darts), such as this one...

I see your point, and I appreciate your help. It's just that I will not be able to use a solution like this. I should have made it clear on the first post. Also, I believe that the set of N² tuples and N are both infinite, but countable. I can easily see that the formula for the first element...

That's an interesting one. I will try something on this. Well, that's a classical way to map infinite sets, but it breaks the need for the numbers to stay relatively small. In fact, any of mapping of this nature would grow very fast I think. I'd like to be able to represent numbers up to the...

Hi, I've been trying to find one symmetric "injective" N²->N function, but could not find any. The quotes are there because the function I'm trying to find is not really injective, as I need that the two arguments be interchangeable and the value remains the same. In other words, the tuple (a...

Hi, Suppose I have a data structure that models a polygon, by storing all the nodes of the given polygon, and their connections (i.e. edges). I understand that sorting a set of nodes that may form a concave hull is ill-defined, as there could be many polygons that can be formed with those. But...

Hi, thanks for your answer. Yes, this problem is about perspective, but not the way you're thinking (or maybe I'm wrong). To make things more clear, this problem is going to be used on a computer vision technique. I want to be able to map pixels from a projection (edit: NOT EVERY PIXEL, just one...

Hello, This question might seem silly, but I've tried some approaches and none of them seemed to work. Here's my problem: I need some sort of transform that maps points from any quad to an rectangle. I will be using this on a computer graphics software, so you can think of this rectangle as my...