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.
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.
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.
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 :)
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.
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...
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.
I'd say they're more algebraic representations of regular geometries.
Algebraic Geometry as a mathematical field is interested in solving highly non-trivial geometric problems (think, from differential geometry, functional analysis, etc.), using tools from Abstract Algebra (think Galois Fields, Lie Groups etc.)
It saddles a bridge between traditional geometry, and abstract algebra, and allows insights from one field of mathematics to be applied to the other. As such, it allows practitioners skilled in these tools to make many useful inferences about incredibly complicated systems.
It's also incredibly dense. In part because many of the tools of algebra are incredibly involved. But also, in part because to define an algebraic object in a way that is equivalent to a geometric object, sometimes requires a fairly complicated definition.
Algebraic geometry existed before Grothendieck lol. It's still algebraic geometry even it looks boring next to etale cohomology of infinity stacks or whatever.
Even before Grothendieck's scheme theory, algebraic geometry was already pretty focused on varieties in rings of polynomials and other such constructions.
The heart of the domain is still using abstract algebraic arguments to solve geometric problems.
E.g.; Euclid's method for finding the midpoint of a line is to draw two concentric circles centred at the vertices with radius the length of the line. The straight line that passes through the two intersection points of the circles, also passes through the midpoint of the line.
This is the same as saying the midpoint of a line is the intersection of an algebraic variety with a root at one vertex, and another algebraic variety with a root at the other vertex.
You don't need schemes, or projective curves, or local rings to prove it.
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.”
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.
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:
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.
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.
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.
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.
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.
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
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!
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.
"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/...