17 ms·

Algebraic Geometry for Computer Graphics

221 points by bmer 4y ago

raghudotcc 4y ago
Are there lecture recordings?
- bmer 4y ago
  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.
- mkaic 4y ago
  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!
- darzu 4y ago
  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 4y ago
    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 4y ago
      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/ https://www.washington.edu/opb/uw-data/fast-facts/ [1] https://educationdata.org/how-do-people-pay-for-college https://educationdata.org/how-do-people-pay-for-college [2] https://www.washington.edu/regents/ https://www.washington.edu/regents/ [3] https://apps.leg.wa.gov/RCW/default.aspx?cite=28B.20.130 https://apps.leg.wa.gov/RCW/default.aspx?cite=28B.20.130
- timostrating 4y ago
  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 http://www.cs.uu.nl/docs/vakken/magr/2021-2022/index.html
  - raghudotcc 4y ago
    Thanks a lot.. Been watching Keenan Crane’s videos on YouTube. This would be really helpful. For anyone else interested in Alg geo, Ravi Vakhil’s videos are very good and accessible.
flakiness 4y ago
Jim Blinn! Wondered what he is doing these days then... > "He is currently retired." - https://www.jimblinn.com/biography/ https://www.jimblinn.com/biography/
godelski 4y ago
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)
- bmer 4y ago
  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 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/9781558608603/B9781558608603500157.xhtml 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/ https://www.jimblinn.com/
  - fanf2 4y ago
    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/Geometric_algebra https://en.m.wikipedia.org/wiki/Algebraic_geometry https://en.m.wikipedia.org/wiki/Algebraic_geometry
    - dxbydt 4y ago
      Just as computational statistics is a very different beast from statistical computation. Got an A in one and C in the other :(
  - godelski 4y ago
    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.
earleybird 4y ago
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 https://en.wikipedia.org/wiki/Vegreville_egg [1] http://www.ronresch.org/ronresch/the-egg/easter-egg-booklet/designing-the-egg/ http://www.ronresch.org/ronresch/the-egg/easter-egg-booklet/...
- adfm 4y ago
  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 https://en.wikipedia.org/wiki/Ron_Resch [^2]: https://www.youtube.com/watch?v=UXENKmAUL0E https://www.youtube.com/watch?v=UXENKmAUL0E
mindcrime 4y ago
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.
- Sharlin 4y ago
  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 :)
  - lupire 4y ago
    I don't think Jim Blinn would be so crass toward his colleagues.
  - SideQuark 4y ago
    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).
    - auggierose 4y ago
bmer 4y ago
For those wondering (reasonably): are there videos? Short answer: no. Long answer: https://news.ycombinator.com/item?id=33133369#33134462 https://news.ycombinator.com/item?id=33133369#33134462
ncmncm 4y ago
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.
- scentoni 4y ago
  I think you’re confusing https://en.wikipedia.org/wiki/Algebraic_geometry https://en.wikipedia.org/wiki/Algebraic_geometry with https://en.wikipedia.org/wiki/Geometric_algebra https://en.wikipedia.org/wiki/Geometric_algebra which is a type of https://en.wikipedia.org/wiki/Clifford_algebra https://en.wikipedia.org/wiki/Clifford_algebra and a generalization of https://en.wikipedia.org/wiki/Quaternion https://en.wikipedia.org/wiki/Quaternion
  - ncmncm 4y ago
    I am indeed.
- aaaaaaaaaaab 4y ago
  Geometric algebra is not the same as algebraic geometry.
  - auggierose 4y ago
    The article mentions Clifford algebras, so while not the same, it is certainly related.
npalli 4y ago
Wow, Jim Blinn a legend in the Computer Graphics field. Looking forward to reading these lectures. Ivan Sutherland, Turing award winner and himself a legend in the Computer Graphics field (Sketchpad and other works) had this to say about Jim Blinn "There are about a dozen great computer graphics people and Jim Blinn is six of them.” https://www.fxguide.com/fxfeatured/founders-series-industry-legend-jim-blinn/ https://www.fxguide.com/fxfeatured/founders-series-industry-...
6gvONxR4sf7o 4y ago
I read the first slide deck, and by total coincidence I’ve been getting really into using tensor diagrams lately. Once you grok grouping and splitting, a lot of things you might otherwise do with block matrices becomes so much more straightforward. Deriving gradients gets a lot easier too. I’d recommend anyone who regularly has to compute gradients to play around with it.
Mathnerd314 4y ago
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.

221 points by bmer 4y ago

raghudotcc 4y ago

Are there lecture recordings?

bmer 4y ago
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.
mkaic 4y ago
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!
darzu 4y ago
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 4y ago
  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 4y ago
    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/ https://www.washington.edu/opb/uw-data/fast-facts/ [1] https://educationdata.org/how-do-people-pay-for-college https://educationdata.org/how-do-people-pay-for-college [2] https://www.washington.edu/regents/ https://www.washington.edu/regents/ [3] https://apps.leg.wa.gov/RCW/default.aspx?cite=28B.20.130 https://apps.leg.wa.gov/RCW/default.aspx?cite=28B.20.130
timostrating 4y ago
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 http://www.cs.uu.nl/docs/vakken/magr/2021-2022/index.html
- raghudotcc 4y ago
  Thanks a lot.. Been watching Keenan Crane’s videos on YouTube. This would be really helpful. For anyone else interested in Alg geo, Ravi Vakhil’s videos are very good and accessible.

flakiness 4y ago

Jim Blinn! Wondered what he is doing these days then... > "He is currently retired." - https://www.jimblinn.com/biography/ https://www.jimblinn.com/biography/

godelski 4y ago

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)

bmer 4y ago
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 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/9781558608603/B9781558608603500157.xhtml 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/ https://www.jimblinn.com/
- fanf2 4y ago
  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/Geometric_algebra https://en.m.wikipedia.org/wiki/Algebraic_geometry https://en.m.wikipedia.org/wiki/Algebraic_geometry
  - dxbydt 4y ago
    Just as computational statistics is a very different beast from statistical computation. Got an A in one and C in the other :(
- godelski 4y ago
  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.

earleybird 4y ago

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 https://en.wikipedia.org/wiki/Vegreville_egg [1] http://www.ronresch.org/ronresch/the-egg/easter-egg-booklet/designing-the-egg/ http://www.ronresch.org/ronresch/the-egg/easter-egg-booklet/...

adfm 4y ago
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 https://en.wikipedia.org/wiki/Ron_Resch [^2]: https://www.youtube.com/watch?v=UXENKmAUL0E https://www.youtube.com/watch?v=UXENKmAUL0E

mindcrime 4y ago

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.

Sharlin 4y ago
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 :)
- lupire 4y ago
  I don't think Jim Blinn would be so crass toward his colleagues.
- SideQuark 4y ago
  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).
  - auggierose 4y ago

bmer 4y ago

For those wondering (reasonably): are there videos? Short answer: no. Long answer: https://news.ycombinator.com/item?id=33133369#33134462 https://news.ycombinator.com/item?id=33133369#33134462

ncmncm 4y ago

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.

scentoni 4y ago
I think you’re confusing https://en.wikipedia.org/wiki/Algebraic_geometry https://en.wikipedia.org/wiki/Algebraic_geometry with https://en.wikipedia.org/wiki/Geometric_algebra https://en.wikipedia.org/wiki/Geometric_algebra which is a type of https://en.wikipedia.org/wiki/Clifford_algebra https://en.wikipedia.org/wiki/Clifford_algebra and a generalization of https://en.wikipedia.org/wiki/Quaternion https://en.wikipedia.org/wiki/Quaternion
- ncmncm 4y ago
  I am indeed.
aaaaaaaaaaab 4y ago
Geometric algebra is not the same as algebraic geometry.
- auggierose 4y ago
  The article mentions Clifford algebras, so while not the same, it is certainly related.

npalli 4y ago

Wow, Jim Blinn a legend in the Computer Graphics field. Looking forward to reading these lectures. Ivan Sutherland, Turing award winner and himself a legend in the Computer Graphics field (Sketchpad and other works) had this to say about Jim Blinn "There are about a dozen great computer graphics people and Jim Blinn is six of them.” https://www.fxguide.com/fxfeatured/founders-series-industry-legend-jim-blinn/ https://www.fxguide.com/fxfeatured/founders-series-industry-...

6gvONxR4sf7o 4y ago

I read the first slide deck, and by total coincidence I’ve been getting really into using tensor diagrams lately. Once you grok grouping and splitting, a lot of things you might otherwise do with block matrices becomes so much more straightforward. Deriving gradients gets a lot easier too. I’d recommend anyone who regularly has to compute gradients to play around with it.

Mathnerd314 4y ago

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.