Full playlist: • Discrete Differential ... For more information see geometry.cs.cmu.edu/ddg
Пікірлер: 97
@kolavithonduraski50313 жыл бұрын
i am not your student, but interresting in this topic, because it is rare that someone with so much expertise, shares such well structured knowledge from ground up. Why am i interested in this ? (i know you didn't ask 😂) It is like you mentioned: you need it for almost everything now, engineering, AI, architecture, graphics and so on. Thank's for sharing this content for free 👍 This is Science ! Awesome !
@Anil-vf6ed3 жыл бұрын
Thank you very much Prof. Keenan Crane for being generous to share the course content. Looking forward to more courses from you. Thank you!
@webgpu2 жыл бұрын
This is the soul of Teachers. To pass on information in order for our society to advance in many areas ( in our case, it is Technology ) Thank you very much.
@JoelHough3 жыл бұрын
This is great. It's refreshing to see computation treated as a first class citizen instead of an afterthought like other math lectures. My cold programmer heart grew three sizes today, which I can compute with a discrete curve lengthening flow.
@shiv0933 жыл бұрын
0:38 Why we might want to study geometry? 1:48 Applications of Discrete Differential Geometry 6:09 What will we Learn in This Class? 8:06 What won't we learn in this class? 9:38 Assignments 11:26 What is Differential Geometry? 13:17 What is Discrete Differential Geometry? 15:32 Grand Vision 16:31 How can we get there? (Game) 18:53 Example: Discrete Curvature of Plane Curves 19:55 Curvature of a Curve - Motivation 20:54 Curves in the Plane 21:45 Example 22:16 Discrete Curves in the Plane 23:17 Example 23:50 Tangent of a Curve 25:22 Example 26:27 Normal of a Curve 27:37 Example 29:29 Curvature of a Plane Curve 32:46 Curvature: From Smooth to Discrete 34:57 When is a Discrete Definition "Good"? 36:36 Playing the Game 37:46 Turning Angle 39:04 Integrated Curvature 41:15 Discrete Curvature (Turning Angle) 43:03 Length Variation 45:14 Gradient of Length for a Line Segment 46:46 Gradient of Length for a Discrete Curve 48:03 Discrete Curvature (Length Variation) 49:19 A Tale of Two Curvatures 50:52 Steiner Formula 51:56 Discrete Normal Offsets 54:24 Discrete Curvature (Steiner Formula) 55:51 Osculating Circle 56:51 Discrete Curvature (Osculating Circle) 57:27 A Tale of Four Curvatures 58:04 Pick the Right Tool for the Job! 58:55 Curvature Flow 59:53 Toy Example: Curve Shortening Flow 1:01:10 Discrete Curvature Flow - No Free Lunch 1:03:25 No Free Lunch - Other Examples 1:04:56 Course Roadmap 1:07:26 Applications & Hands-On Exercises
@loxoloop3 жыл бұрын
Thanks for the index!
@putin_navsegda64873 жыл бұрын
thank you 😇
@chriso82836 ай бұрын
thanks
@ralfaralf68052 жыл бұрын
Sometimes when I come across resources like this that are free of cost it truly makes me happy to live in today's day and age! How amazing is this?! Thank you
@Karim-nq1be2 жыл бұрын
Amazing course, really well structured and more entertaining than Netflix.
@harrypotter11552 жыл бұрын
Some courses are in huge demands but little in supplies. It has 15k views for 5 months since it was uploaded (a super impressive number for a pure academic course). Been looking everywhere last year for an introductory differential geometry courses for engineering, thank you for making this freely available online professor!
@scottcourtney88782 жыл бұрын
It was evident after listening for only a minute or two that you are a confident and experienced lecturer. It is rare to encounter a speaker who so deftly combines informality and polish. You've made a complex topic understandable and interesting. Thank you so much for sharing your expertise freely with everyone. You are a credit to the best traditions of scholarship. Subscribed!
@jeremie37382 жыл бұрын
I have rarely seen such a perfect pedagogy on youtube, everything is perfect, the examples, the breaks to think... And on a fascinating subject! Keep it up!
@bryanbischof43513 жыл бұрын
This was excellent. I really enjoy this “game”. In general in mathematics this sort of generalization in all directions is always such a thrill.
@plouf19692 жыл бұрын
Hey Keenan, great video. This reminds me of a simple interview question I sometimes ask: if you have a rope going around the equator, and you increase it by 1m, by how much can you raise the rope above the ground? Most people think it's going to be microscopic (because 1m is very little compared to the circumference of the earth), when in fact it's 1m/(2*pi). This relates to some of the concepts in your video. When I try to explain why the intuition of people is wrong, I resort to imagining a 2D equivalent, a rope around the border of a circular lake, and then thinking of a rope around a square lake - and how much the rope needs to be extended if you want to 'lift' the rope, i.e. bring it a bit further away from the border of the lake. If you try that, you'll notice that the places where you need more rope are the corners, i.e. the places where there is curvature (as seen by the fact that the normal turns there). I always saw that as a 'Dirac' distribution of curvature, but your lecture explains how this can be seen in various different ways. Looking forward to watching the rest (btw I got a PhD in diff. geometry 20y ago, but went to work in an applied field since).
@juliogodel3 жыл бұрын
This is a teaching masterpiece!
@zhehaoli19992 жыл бұрын
Wow, the idea that discrete differential geometry is the language of a new world really fascinates me... and the GAME of searching for different perspectives of translating between smooth and discrete geometry seems really interesting. Thank you, sir!
@madhavpr3 жыл бұрын
Thanks a lot Professor Crane. I'm not your student and have no knowledge about differential geometry (continuous and discrete) but geometry of curves and surfaces is my absolute favourite topic to think about in mathematics. I'm totally looking forward to your videos. Thanks a lot again for sharing your expertise for free!!! :)
@manikabindal8853 жыл бұрын
These lectures are absolute Gold....Thank you Prof.
@jgiuguigiugigiugugiuuig40503 жыл бұрын
Wow, absolutely high-end presentation. Thank you!
@MalUmKo894 ай бұрын
@keenan crane The inner product does not only preserve the sign. We also want to extract the normal component of the derivative so that we can negate any change in the speed at which we are traveling along the curve, of course this is 0 in the case of arc length parametrized curve.I really like the lectures so far. Thank you for sharing them with the world and putting the effort in!
3 жыл бұрын
Thank you for this, 10/10 ❤️. Looking forward to seeing more advanced topics!
@jaideepkhadilkar3 жыл бұрын
Correction: @38:12 - It should be the second derivate of the curve, not the first derivative in the Curvature formula.
@suhailmohammed75593 жыл бұрын
I have been waiting for this. Thanks a lot for sharing!
@lessthan12parsecs_2 жыл бұрын
I just stumbled on this course after reading one of your papers and i must say it's really awesome, thank you for sharing it!
@lcfrod3 жыл бұрын
Excellent class!! Thanks so much for sharing the knowledge so clearly.
@gijsb47083 жыл бұрын
Thank you so much for recording/uploading the complete set of lectures!
@TheNinjaDwarfBiker Жыл бұрын
I feel extremely privileged to have access to content of this quality for free. Thank you
@hericklenin3 жыл бұрын
OMG this is gold. Thanks for this playlist.
@familywu38694 ай бұрын
Thank you so much Prof. Keenan Crane for generously sharing your knowledge and wisdom to help people gain knowledge and wisdom to improve humanity all together. You and many other teachers who generously shared your wisdom and knowledge inspired me to share my knowledge and wisdom to people in the future when I become an expert in some areas. Thank you so much again!
@loxoloop3 жыл бұрын
Great presentation of a subject that I want to learn. Thanks for making them available!
@AndresFH72333 жыл бұрын
I'm starting this curse a little late, but thank you so much for uploading all the material. This looks really interesting.
@i3fonov3 жыл бұрын
It's a very interesting lecture!
@sunsooora3 жыл бұрын
Just started my research on this topic and my advisor suggested one of your articles, came here by chance and I must say I'm not disappointed! Awesome :) thank you for the classes!
@user-zu8bx7hq8k3 жыл бұрын
Finally here!
@user-ef3ej4pq4f3 жыл бұрын
Really nice and intuitive explaination
@sergeimerekin81933 жыл бұрын
Amazing course, thank you!
@16baad3 жыл бұрын
I love your teaching style. Thank You
@nicolaskrause79662 жыл бұрын
Thank you so much! I'd taken a classic differential geometry course in university, and this is great stuff! Really clearing up a lot about how to apply the things I learned in a computational setting!
@pinklady71843 жыл бұрын
I love how you are using illustrations to explain your maths. Graphics help me commit things to memory. Thank you for making tutorials. I hope you will make more videos.
@overfour96839 ай бұрын
Very brief and deep course. this is art!
@user-gc5bw7zu2i3 жыл бұрын
great course, thx for sharing
@user-oe5vu3xd4l7 ай бұрын
Thank you for sharing these valuable lecture series!
@yuxiangfu49113 жыл бұрын
thank you! I like your lectures!
@walkernet44262 жыл бұрын
Thank you so much for sharing this course! This is really helpful for students who not only require understandings from pure mathematics point of view but also from a more applied prospective, for building intuitions.
@garfieldnate2 жыл бұрын
Thanks for sharing the class materials! I'm really excited to get started here. Could you share what tool you used to generate the beautiful purple and black cell-shaded plots? They are wonderful!
@jianchenghao56513 жыл бұрын
Good professor and great content!
@chanhaenglee91343 жыл бұрын
Thank you for sharing this great stuff !!
@ChrisDjangoConcerts2 жыл бұрын
38:35 shouldn't curvature be given by a second derivative? I think there is a derivative missing there
@user-zl1sl5cn6j2 жыл бұрын
Amazing videos, I am learning so many useful concepts and deep understandings towards to advanced topology and algebra!
@kuriankattukaren Жыл бұрын
Thanks Keenan. The course has been extremely helpful..
@grincheuxsuper9842 жыл бұрын
Thank you for sharing those lectures.
@p4ymak3 жыл бұрын
Thank you so much!
@adityachetan483 жыл бұрын
Hi Prof. Crane, thank you for the amazing lectures! I had a question about minimizing discrete curvature flow at 1:02:27 I think earlier in the lecture you mentioned that the normal is not defined at the vertices. Then how do we move the vertices in the direction of the normal N_i? Or is N_i here the same as the N_i that we computed in the case of Length Variation curvature, i.e., the direction of the perpendicular bisector of the angle at \gamma_i. Apologies if I missed something obvious.
@taoufikahanchaou69803 жыл бұрын
Thank you very much
@markomwansa3 жыл бұрын
Hey Prof. I was wondering what are you using to produce your images? Thank you for the lectures!
@RifatAhmed-yn6ie Жыл бұрын
Excellent lecture. Thank you sir.
@nathanhenry77113 жыл бұрын
Yesss TYSM!
@devanshtanna46403 жыл бұрын
Your slides are pretty neat and intuitive !! Thank you sir for sharing this lecture series !!! How did you make these slides? LaTeX and TikZ? Just for curiosity...
@keenancrane3 жыл бұрын
I use Apple's Keynote; most equations are typeset in TeX via LaTeXiT! and imported as images. I don't use TikZ for images-you can find out more here: www.cs.cmu.edu/~kmcrane/faq.html#figures
@ronaldjensen29483 жыл бұрын
I find it interesting that as theta approaches zero (meaning we approach a smooth function), theta = 2 sin(theta/2) = 2 tan(theta/2). At 50:08 Dr. Crane mentioned the small angle approximation for sin(x) but did not mention it holds for tan(x) as well. As x->0, sin(x)->x and cos(x) -> 1 so tan(x) -> x/1.
@Tannz0rz9 ай бұрын
Hello Dr. Crane, what are your thoughts on geometric algebra and geometric calculus and its relationship with differential geometry?
@gaboqv3 жыл бұрын
fabulous! I was tirsty for this subject in my college curriculum
@kenichimori85333 жыл бұрын
Discrete diffrential dream geometry.
@K13ization3 жыл бұрын
Hi Keenan, I was wondering if the coding assignments across the course would also be available for us KZbin students? :) Thanks again for this invaluable contribution to making geometry processing research intuitive, exciting and accessible!
@keenancrane3 жыл бұрын
Yes, absolutely. Everything will be posted online at geometry.cs.cmu.edu/ddg as the course progresses. In fact, you can already find all the same material from last year's course at brickisland.net/DDGSpring2020/
@CarlosValero Жыл бұрын
When deriving the length variation formula. Aren't you using the half of the integral of the norm square of the derivative (i.e "elastic energy")?
@randalllionelkharkrang40479 ай бұрын
thanks for this. Im interested in topological data analysis, and algebraic topology. This course is a gem. Anyone wants to create a discord group to discuss ideas and assignments?
@alikhatami6610 Жыл бұрын
Sorry couldn't find your discord server. And I am stock in some problems . Is the discord server down?
@CarlosValero Жыл бұрын
When defining curvature using the angle, shouldn't you divide by length somehow? Couldn't you define length at a vertex as the the sum of the lengths from the vertex to the midpoint of adjacent edges. Mirroring what you do when using the Hodge star using the dual mesh.
@senri- Жыл бұрын
At 31:50 why can we not simply say the curvature is the second derivative, that way you dont lose the directional info in the first place, what does the inner product with the norm do?
@seremetvlad3 жыл бұрын
thank you
@47lokeshkumar74 Жыл бұрын
I want to do coding in this subject. Can you show.... How to put algorithms into the programming
@minyeongchoi79143 жыл бұрын
If I'm interested in Differential geometry specifically for theoretical physics, you know, much more in the technical and rigorous maths side, would this course still be useful for me? As you may know, the more mathematical Differential geometry courses at CMU are rarely, if at all, offered anymore, and they require quite mathematically intensive prereqs. Obviously I understand this class probably won't be a substitute, but if I still plan on learning Diff Geo myself, would it help to take this class?
@keenancrane3 жыл бұрын
Yes, this would be a great intro if you haven't taken any course in differential geometry before. A lot of the motivation comes from algorithms and applications in geometry processing, but the core tools (and intuition) should serve you well for any further study. In particular, the course puts an emphasis on differential forms, which are fundamental in modern mathematical physics-a good companion book for the course if you want to go deeper is "Manifolds, Tensor Analysis, and Applications" by Abraham, Marsden, and Ratiu. I learned differential forms from Marsden, and his book (and others) served as inspiration for that part of the course.
@minyeongchoi79143 жыл бұрын
@@keenancrane Very helpful reply! Thank you, I hope you continue offering this course in the coming years and I can take it with you. And even if my schedule doesn't work out, I'll be sure to go through these videos.
@yizhang70272 жыл бұрын
26:55 how do you determine the normal direction in 3d? unlike in 2d, you don't have a fixed rotation axis in 3d.
@keenancrane2 жыл бұрын
Check out this lecture on curves, which discusses the definition of the normal for space curves, and more generally the Frenet frame: kzbin.info/www/bejne/qZavlIN4lt1mhas
@Canadianishere2 жыл бұрын
where can i find the derivation of Discrete curvature (osculating circle) k = 2sin(theta)/w
@simonsun64712 жыл бұрын
Quite good. It is very useful. (Does anyone research using Discrete Element Method? How can DDG be applied in that?)
@m2rahman3 жыл бұрын
Hi Prof Crane, thanks for sharing the lecture videos! I had a clarification question on the example of circle as a parameterized curve at time @22:05. You expressed the constraint gamma(0) = gamma(2*pi), but the domain of gamma is [0,2*pi), so not defined on 2*pi.
@keenancrane3 жыл бұрын
Yes, that is true; I should be more careful here. The reason for not simply defining the map over the closed interval [0,2π] (or the whole real line) is that we will later use this example to understand the concept of homeomorphism, which captures the notion of the "topology" of a shape. Specifically, this example will make it clear that a continuous injective map does not always have a continuous inverse.
@Canadianishere2 жыл бұрын
at 54:21 how is the new length is smaller than the old length, shouldnt it be bigger
@wojtekkrupski85832 жыл бұрын
Yeah, also why in 43:19 we are talking about decrease of length of curve? Didn't we increase a length of the curve after transformation by eta? Is it related to choose normal as JT, and not -JT?
@TC-rv6sz7 ай бұрын
I'm crocheter and I'm watching in order to understand pattern design, esp for 3D non-symmetrical objects (think more crochet realism than amigurimi) 😂.
@Prepcrep2 жыл бұрын
can I have the name of the book
@FaizanAli-zq2wg Жыл бұрын
May Allah give you Hidaya. Aameen!
@drscott1 Жыл бұрын
👍🏼
@benmokhtarlotfi523 Жыл бұрын
wooooooooooow
@martinhazard5982 Жыл бұрын
Why "discrete" in the name???
@user-sl2xe3jr1h2 жыл бұрын
Думаю автор удивится, откуда тут столько русскоязычных. Так вот: мы от New Deal
@forheuristiclifeksh7836Ай бұрын
5:36
@ClydeCoulter3 жыл бұрын
Have you looked at John Gabriel's new calculus? It may help here.
@98danielray3 жыл бұрын
that is quite literally crankery, buddy
@PetroUralov2 жыл бұрын
Так! Я не понял. А почему не по по-русски?
@NewCalculus3 жыл бұрын
Why call it "differential geometry" when in fact it's nothing but plain calculus?
@keenancrane3 жыл бұрын
Sometimes it's called "calculus on manifolds" (in fact, this is the title of a classic differential geometry textbook by Michael Spivak). Basically how do you apply calculus on spaces that are topologically different from R^n. A basic tool is indeed to apply ordinary calculus in local coordinate charts on R^n. But this is just the means, rather than the end-differential geometry is all about discovering the amazing things that can happen on spaces beyond ordinary Euclidean R^n…