This seems to be mostly about formulas for checking for various curve conditions. Which is nice, but there are two problems: (1) computers don't use real numbers (2) operations take time. Regarding the second, it is probably possible to use the AlphaTensor work to find an optimized algorithm. But for the real number issue I don't think AlphaTensor is flexible enough to handle floating point yet and there is probably still some work to be done.
Algebraic Geometry for Computer Graphics
41–44 of 44 posts
Re: Algebraic Geometry for Computer Graphics
#42Earlier quoted context omitted.
AG as studied by mathematicians has produced an incredible amount of applications that would not exist without that level of abstract tooling. And it's highly nontrivial to learn those tools (as someone that has worked through Hartshorne... And then put 20 years into applications).
What are some of those applications?
Besides the other list, places results from AG have uses in tech include statistics, control theory, robotics, error-correcting codes, phylogenetics, geometric modelling, string theory, game theory, graph matchings, solitons , integer programming, computer vision, computer aided design.....
Some of these are likely why Blinn decided to make an entire course on using it just in computer graphics alone.
Re: Algebraic Geometry for Computer Graphics
#43Earlier quoted context omitted.
What are some of those applications?
Besides the other list, places results from AG have uses in tech include statistics, control theory, robotics, error-correcting codes, phylogenetics, geometric modelling, string theory, game theory, graph matchings, solitons , integer programming, computer vision, computer aided design..... Some of these are likely why Blinn decided to make an entire course on using it just in computer graphics alone.
Thanks, I am aware of the general uses, I was just wondering what you in particular have used it for :-)
Re: Algebraic Geometry for Computer Graphics
#44Earlier quoted context omitted.
Besides the other list, places results from AG have uses in tech include statistics, control theory, robotics, error-correcting codes, phylogenetics, geometric modelling, string theory, game theory, graph matchings, solitons , integer programming, computer vision, computer aided design..... Some of these are likely why Blinn decided to make an entire course on using it just in computer graphics alone.
Thanks, I am aware of the general uses, I was just wondering what you in particular have used it for :-)
I've used it professionally for error correcting code design, robotic control, crypto (ecc and multivariate polynomial), lots of computer vision uses, grobner bases to simplify algorithms, and geometric modeling. Perhaps more if I look over lists of past projects...