[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)