Algebraic Geometry for Computer Graphics

Post by ncmncm » Sat, Oct 08, 2022, 7:36 PM UTC

scentoni wrote: post #18

ncmncm wrote: post #14

I thought that algebraic geometry was really cool when I first encountered it. But people with a lot of experience insist that for computational processes it is slower than more familiar methods. So it is convenient and intuitive for one-off transformations, but not preferred in computational kernels. I see room for both, and for quaternions, which I gather are also a bit slower.

I think you’re confusing https://en.wikipedia.org/wiki/Algebraic_geometry with https://en.wikipedia.org/wiki/Geometric_algebra which is a type of https://en.wikipedia.org/wiki/Clifford_algebra and a generalization of https://en.wikipedia.org/wiki/Quaternion

Post by aaaaaaaaaaab » Sat, Oct 08, 2022, 7:53 PM UTC

godelski wrote: post #8

These are just slides btw and unfortunately probably not helpful without a lecture recording (which is not included). The slides really look great, but I wish there was commentary along with them. (they are not self contained)

Post by godelski » Sat, Oct 08, 2022, 8:34 PM UTC

bmer wrote: post #12

godelski wrote: post #8

These are just slides btw and unfortunately probably not helpful without a lecture recording (which is not included). The slides really look great, but I wish there was commentary along with them. (they are not self contained)

Well, this is sadly the best we have in the field, where by "field" I mean: "accessible algebraic geometry for graphics". Blinn provides some notes as to where his material comes from (see the page). He also mentions that some of this material was presented previously in some of his Jim Blinn's Corner articles. In particular: * the "Lines in Space" series: https://ieeexplore.ieee.org/abstract/document/7047281 * the "…

Post by bmer » Sat, Oct 08, 2022, 9:19 PM UTC

aaaaaaaaaaab wrote: post #24

godelski wrote: post #8

These are just slides btw and unfortunately probably not helpful without a lecture recording (which is not included). The slides really look great, but I wish there was commentary along with them. (they are not self contained)

I remember watching this Jim Blinn seminar on tensor diagrams from the University of Utah: https://youtu.be/40TdlWURkS8 I understood maybe a third of what he’s talking about, but it’s fascinating. He seems to be using similar slides to those on this page.

Post by kweingar » Sat, Oct 08, 2022, 10:18 PM UTC

dhosek wrote: post #29

mindcrime wrote: post #11

Algebraic Geometry as studied by Mathematicians often deals with very abstract and general issues that I admit that I don’t completely understand myself. Nice to see this kind of honesty and/or modesty from an instructor! Reminds me of the time I took Discrete Math at a local community college. We all showed up at the room for the scheduled first session, and found no instructor. We waited around about 20 minutes, an…

Yeah, I was looking over the materials and thinking, where’s the Algebraic Geometry? I don’t think that Algebraic Geometry (as opposed to algebraic geometry in the sense that the author here is using it) has any applications to computer graphics, but definitely can be applied to other aspects of computer science (I can imagine it being potentially useful in cryptographic applications), although my own Algebraic Geome…