[HN Gopher] Algebraic Geometry for Computer Graphics
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       Algebraic Geometry for Computer Graphics
        
       Author : bmer
       Score  : 138 points
       Date   : 2022-10-08 15:57 UTC (7 hours ago)
        
 (HTM) web link (courses.cs.washington.edu)
 (TXT) w3m dump (courses.cs.washington.edu)
        
       | raghudotcc wrote:
       | Are there lecture recordings?
        
         | mkaic wrote:
         | This was also my immediate thought. Lecture slides are a
         | fantastic resource but seeing them presented would be even more
         | helpful, especially for someone like me who learns best through
         | video!
        
         | bmer wrote:
         | No, sadly, this is the best we have.
         | 
         | However, Blinn writes that some of this material was presented
         | in more detail in some of his "Jim Blinn's corner" articles.
        
         | darzu wrote:
         | Maybe it should be required that public or publicly funded
         | universities have a set of relatively up-to-date lecture
         | recordings for each course. Since covid, I know for a fact most
         | UW CSE courses were/are being recorded and saved to Canvas CMS
         | for students who miss lecture/have covid/worry about covid/etc.
         | These should be made public!
         | 
         | The hairiest issue here is when there's student participation.
         | But you don't need each quarter to be online, just once every
         | time there are significant course changes. The quarter that
         | will be uploaded could be announced as such and students could
         | consent to being recorded. But this isn't a big deal, MIT has a
         | lot of open courseware with students being recorded. It'd be
         | easy to survey and compare student experiences with/without
         | recordings. But the benefit for the public could be enormous!
         | Think about the public good of every publicly funded
         | university's courseware being accessible online for free.
        
           | tptacek wrote:
           | The majority of the funding in several flagship state
           | universities comes not from the state but from the operations
           | of the university itself: tuition, fees, stores, programs. We
           | the public literally did not pay for all these courses. And
           | the rate on a presentation, speech, or training course,
           | you'll find, is very different when it's delivered to a
           | specific audience versus being put on the Internet for free.
        
             | darzu wrote:
             | UW receives 37% of its funding from the state, the rest
             | comes from tuition[0]. In 2002, it was 70% from the state.
             | And of tuition, at least ~25% of that comes from public
             | sources (grants, subsides loans)[1].
             | 
             | And even if some public universities are self-sustaining
             | now, that doesn't lessen the fact that public money was the
             | major cause that started that flywheel.
             | 
             | And regardless of funding, UW, like all public
             | universities, has an explicit directive to operate for the
             | "benefit of present and future citizens of the State of
             | Washington"[2][3].
             | 
             | As for course lecture quality, if it's worthwhile to the
             | students, it can be worthwhile for the public.
             | 
             | [0] https://www.washington.edu/opb/uw-data/fast-facts/ [1]
             | https://educationdata.org/how-do-people-pay-for-college [2]
             | https://www.washington.edu/regents/ [3]
             | https://apps.leg.wa.gov/RCW/default.aspx?cite=28B.20.130
        
         | timostrating wrote:
         | If you are looking for general advanced graphics video lectures
         | then this might help. The lectures at the university of Utrecht
         | (one of the top universities of the Netherlands) are now often
         | recorded and published sinds covid started. There advanced
         | graphics lecture recordings, slides and exercises from last
         | year are published on this website
         | chttp://www.cs.uu.nl/docs/vakken/magr/2021-2022/index.html
        
       | earleybird wrote:
       | Absent from his bio (and the wikipedia article) is his role in
       | the construction of the Vegreville Pysanka(egg)[0]
       | 
       | "Robert McDermott and Jim Blinn are jointly responsible for the
       | precise mathematics and computer programming which implemented
       | the geometric concept Accomplishment of the highly sophisticated
       | and complex mathematics brought to a close the long-sought-after
       | geometric definition of the faceted Egg." [1]
       | 
       | Came across this little tidbit of information reading the
       | information plaque when my dad was showing us around town.
       | Imagine my surprise coming across the name of probably my first
       | computer graphics books from university.
       | 
       | [0] https://en.wikipedia.org/wiki/Vegreville_egg
       | 
       | [1] http://www.ronresch.org/ronresch/the-egg/easter-egg-
       | booklet/...
        
         | adfm wrote:
         | Don't forget Ron Resch[^1]. If you haven't seen his Paper and
         | Stick film [^2], I highly recommend it. It's a fascinating look
         | into the early beginnings of computer graphics filmed between
         | 1960-1966.
         | 
         | [^1]: https://en.wikipedia.org/wiki/Ron_Resch
         | 
         | [^2]: https://www.youtube.com/watch?v=UXENKmAUL0E
        
       | flakiness wrote:
       | Jim Blinn!
       | 
       | Wondered what he is doing these days then...
       | 
       | > "He is currently retired." -
       | https://www.jimblinn.com/biography/
        
       | mindcrime wrote:
       | _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, and were about to leave, when a grey-bearded gentleman
       | who looked to be of the instructorly persuasion rocked up and
       | started unlocking the door. So we follow him in, and he gets in
       | front of the class and says something approximately like:
       | 
       |  _" Hi, so-and-so, who was scheduled to teach this class, had to
       | back out at the last minute and so the school called me. I'll be
       | your instructor. I was a Physics major 60 years ago, and can do
       | this math, but I've never taught this before and don't really
       | remember anything about it. So we'll all be learning it together
       | as we go."_
       | 
       | It was an, _ahem_ , interesting experience, to say the least.
       | Luckily for me I'd had Discrete before and was only taking it due
       | to a technicality that kept my previous credit from transferring.
        
         | dhosek wrote:
         | 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 Geometry
         | knowledge is more limited than I would like it to be.
        
           | kevinventullo wrote:
           | Projective space, syzygies, Bezier curves, cubic curves
           | aren't algebraic geometry?
        
           | kweingar wrote:
           | Algebraic geometry is also used in robotics
        
         | Sharlin wrote:
         | To be fair, it's _Jim Blinn_ , one of the pioneers of computer
         | graphics, so his admission could be read as a polite way of
         | saying that AG as studied by mathematicians is needlessly
         | abstract and lacking any real-world applications :)
        
           | SideQuark wrote:
           | 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).
        
           | lupire wrote:
           | I don't think Jim Blinn would be so crass toward his
           | colleagues.
        
       | bmer wrote:
       | For those wondering (reasonably): are there videos? Short answer:
       | no.
       | 
       | Long answer:
       | https://news.ycombinator.com/item?id=33133369#33134462
        
       | ncmncm wrote:
       | 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.
        
         | aaaaaaaaaaab wrote:
         | Geometric algebra is not the same as algebraic geometry.
        
         | scentoni wrote:
         | 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
        
           | ncmncm wrote:
           | I am indeed.
        
       | godelski wrote:
       | 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)
        
         | aaaaaaaaaaab wrote:
         | 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.
        
           | godelski wrote:
           | Thanks for the link!!!
        
           | bmer wrote:
           | This is awesome! Thank you!
        
         | bmer wrote:
         | 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 "How many different rational parametric cubic curves are
         | there?" series: https://www.oreilly.com/library/view/jim-
         | blinns-corner/97815...
         | 
         | Part of the reason why I posted this to HN is so that others
         | can hopefully drop some more information on this "field".
         | 
         | See also the author's site: https://www.jimblinn.com/
        
           | fanf2 wrote:
           | Amusingly, algebraic geometry is a very different beast than
           | geometric algebra.
           | 
           | https://en.m.wikipedia.org/wiki/Geometric_algebra
           | https://en.m.wikipedia.org/wiki/Algebraic_geometry
        
             | dxbydt wrote:
             | Just as computational statistics is a very different beast
             | from statistical computation. Got an A in one and C in the
             | other :(
        
           | godelski wrote:
           | That's quite unfortunate. I don't think the slides are
           | approachable alone. I'm sure they are great with a lecture.
           | Another user did link a 2017 lecture below though, which is
           | great.
        
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       (page generated 2022-10-08 23:00 UTC)