Keenan Crane
Keenan Crane
  • Видео 105
  • Просмотров 1 531 725
Monte Carlo Geometry Processing
How can we solve physical equations on massively complex geometry? Computer graphics grappled with a similar question in the 1990s, leading to the widespread adoption of Monte Carlo methods for photorealistic image generation. This talk explores how Monte Carlo can also be used to solve a broader class of equations appearing in science and engineering, using the so-called "walk on spheres method" and recent extensions developed at Carnegie Mellon University.
The talk was originally given by Keenan Crane at the Oberwolfach Research Institute for Mathematics on August 22, 2022. It is based primarily on two papers:
1. Sawhney & Crane, "Monte Carlo Geometry Processing: A Grid-Free Approach to ...
Просмотров: 23 043

Видео

Turning a Torus Inside-Out (Punctured Torus Eversion)
Просмотров 4,5 тыс.Год назад
Cut a small hole in a donut. Can you turn it inside-out? The answer, as shown in this looping video, is "yes!" Notice how the blue inside becomes the red outside, and back again. Unlike the classic question of "turning the sphere inside out," which considers non-physical motions where the sphere may pass through itself, here the (punctured) torus turns inside-out without any self-contact. In ot...
Mathematical Magic: Undoing Handcuffs
Просмотров 4,9 тыс.2 года назад
Suppose you have a pair of handcuffs locked to a post. Can you remove one of the cuffs without unlocking them, breaking them, or letting them pass through themselves? With real handcuffs, definitely not! But for handcuffs made out of stretchy rubber, it turns out to be possible-as shown in this short looping video. This motion provides a surprising example of what is known in mathematics as an ...
What's the nicest way to draw a shape with many holes?
Просмотров 2,7 тыс.2 года назад
For millennia human beings have been drawn to the question: what's the nicest possible shape I can make? "Nicest" could mean the most symmetric-for instance, the ancient Greeks discovered there were five so-called Platonic solids where every face and every vertex looks the same (tetrahedron, cube, octahedron, dodecahedron, icosahedron). Or, "nicest" could mean smoothest. For instance, the smoot...
Mathematical Magic: Unlinking a Pair of Handcuffs
Просмотров 3,4 тыс.2 года назад
Suppose you have a pair of handcuffs linked together. Can you pull them apart without unlocking them, breaking them, or letting them pass through themselves? With real handcuffs, definitely not! But for handcuffs made out of stretchy rubber, it turns out to be possible-as shown in this short looping video. This motion provides a surprising example of what is known in mathematics as an "ambient ...
Repulsive Surfaces - paper video
Просмотров 6 тыс.2 года назад
This video accompanies the paper Chris Yu, Caleb Brakensiek, Henrik Schumacher, Keenan Crane "Repulsive Surfaces" SIGGRAPH Asia 2021 (conditionally accepted) More information to come…
Repulsive Shape Optimization
Просмотров 13 тыс.2 года назад
In visual computing, point locations are often optimized using a "repulsive" energy, to obtain a nice uniform distribution for tasks ranging from image stippling to mesh generation to fluid simulation. But how do you perform this same kind of repulsive optimization on curves and surfaces? This talk takes a deep dive into the mathematical and computational challenges of repulsive shape optimizat...
Repulsive Curves
Просмотров 10 тыс.2 года назад
This video accompanies the paper Chris Yu, Henrik Schumacher, Keenan Crane "Repulsive Curves" ACM Transactions on Graphics (2021) For more information, see www.cs.cmu.edu/~kmcrane/Projects/RepulsiveCurves/
End of Winter (1997)
Просмотров 1,8 тыс.3 года назад
Computer animation by Keenan Crane circa 1997 (converted from VHS). Made in NewTek Lightwave 3D and rendered on Mac OS/PowerPC.
Discrete Conformal Equivalence of Polyhedral Surfaces - Fast Forward
Просмотров 2,9 тыс.3 года назад
This video, narrated by Mark Gillespie, is a short 30-second teaser for the paper Gillespie, Springborn, Crane "Discrete Conformal Equivalence of Polyhedral Surfaces" ACM Transactions on Graphics (2021) For more information see: www.cs.cmu.edu/~kmcrane/Projects/CEPS/index.html
Behind the Scenes: Teaser Image for "Discrete Conformal Equivalence of Polyhedral Surfaces"
Просмотров 2 тыс.3 года назад
None of these models overlap when you look at them from the initial viewpoint. But what happens when you move the camera? This is a "just-for-fun" video showing how the teaser image was created for Mark Gillespie, Boris Springborn, Keenan Crane "Discrete Conformal Equivalence of Polyhedral Surfaces" (ACM Transactions on Graphics 2021) www.cs.cmu.edu/~kmcrane/Projects/CEPS/index.html A standard ...
Geometry Processing with Intrinsic Triangulations (Day II)
Просмотров 3,4 тыс.3 года назад
This video is the second in a series of two lectures given by Keenan Crane at the Harvard FRG Workshop on Geometric Methods for Analyzing Discrete Shapes: cmsa.fas.harvard.edu/frg-2021/ Day I: ruclips.net/video/w99UcsgkUgE/видео.html Abstract: The intrinsic viewpoint was a hallmark of 19th century geometry, enabling one to reason about shapes without needing to consider an embedding in space an...
Geometry Processing with Intrinsic Triangulations (Day I)
Просмотров 7 тыс.3 года назад
This video is the first in a series of two lectures given by Keenan Crane at the Harvard FRG Workshop on Geometric Methods for Analyzing Discrete Shapes: cmsa.fas.harvard.edu/frg-2021/ Day II: ruclips.net/video/JQ2burHX710/видео.html Abstract: The intrinsic viewpoint was a hallmark of 19th century geometry, enabling one to reason about shapes without needing to consider an embedding in space an...
Lecture 11: Discrete Curves (Discrete Differential Geometry)
Просмотров 9 тыс.3 года назад
Full playlist: ruclips.net/p/PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see geometry.cs.cmu.edu/ddg
Lecture 12: Smooth Surfaces I (Discrete Differential Geometry)
Просмотров 10 тыс.3 года назад
Full playlist: ruclips.net/p/PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see geometry.cs.cmu.edu/ddg
Lecture 10: Smooth Curves (Discrete Differential Geometry)
Просмотров 15 тыс.3 года назад
Lecture 10: Smooth Curves (Discrete Differential Geometry)
Supplemental: Vector-Valued Differential Forms (Discrete Differential Geometry)
Просмотров 7 тыс.3 года назад
Supplemental: Vector-Valued Differential Forms (Discrete Differential Geometry)
Lecture 9: Discrete Exterior Calculus (Discrete Differential Geometry)
Просмотров 14 тыс.3 года назад
Lecture 9: Discrete Exterior Calculus (Discrete Differential Geometry)
Lecture 8: Discrete Differential Forms (Discrete Differential Geometry)
Просмотров 14 тыс.3 года назад
Lecture 8: Discrete Differential Forms (Discrete Differential Geometry)
Lecture 7: Integration (Discrete Differential Geometry)
Просмотров 18 тыс.3 года назад
Lecture 7: Integration (Discrete Differential Geometry)
Lecture 6: Exterior Derivative (Discrete Differential Geometry)
Просмотров 26 тыс.3 года назад
Lecture 6: Exterior Derivative (Discrete Differential Geometry)
Lecture 5: Differential Forms (Discrete Differential Geometry)
Просмотров 34 тыс.3 года назад
Lecture 5: Differential Forms (Discrete Differential Geometry)
Lecture 4: k-Forms (Discrete Differential Geometry)
Просмотров 25 тыс.3 года назад
Lecture 4: k-Forms (Discrete Differential Geometry)
Lecture 3: Exterior Algebra (Discrete Differential Geometry)
Просмотров 34 тыс.3 года назад
Lecture 3: Exterior Algebra (Discrete Differential Geometry)
Lecture 2A: What is a "Mesh?" (Discrete Differential Geometry)
Просмотров 31 тыс.3 года назад
Lecture 2A: What is a "Mesh?" (Discrete Differential Geometry)
Lecture 2B: Introduction to Manifolds (Discrete Differential Geometry)
Просмотров 47 тыс.3 года назад
Lecture 2B: Introduction to Manifolds (Discrete Differential Geometry)
Lecture 1: Overview (Discrete Differential Geometry)
Просмотров 59 тыс.3 года назад
Lecture 1: Overview (Discrete Differential Geometry)
Discrete Differential Geometry - Welcome Video
Просмотров 56 тыс.3 года назад
Discrete Differential Geometry - Welcome Video
Computer Graphics - Student Creations! (CMU 15-462/662)
Просмотров 11 тыс.3 года назад
Computer Graphics - Student Creations! (CMU 15-462/662)
Lecture 23: Physically Based Animation and PDEs (CMU 15-462/662)
Просмотров 6 тыс.3 года назад
Lecture 23: Physically Based Animation and PDEs (CMU 15-462/662)

Комментарии

  • @maxwang2537
    @maxwang2537 День назад

    7:25 Can someone please tell me where was “link” introduced? Thanks.

  • @maxwang2537
    @maxwang2537 День назад

    46:26 thank you prof for being hopeful of this. 😂

  • @maxwang2537
    @maxwang2537 3 дня назад

    Hi professor, is DDG just another name of computational geometry? If not, what’s the difference? Thank you.

  • @maxwang2537
    @maxwang2537 3 дня назад

    This is true education, and its meaning. Thank you so much!

  • @maxwang2537
    @maxwang2537 4 дня назад

    hi prof, how much tuition should I pay for these lectures?

  • @pedroth3
    @pedroth3 4 дня назад

    Great work, as always! Is there any update on the quad meshing, using stripe patterns ?

  • @adamdarx4403
    @adamdarx4403 11 дней назад

    Is this topic relevant to Loop Quantum Gravity?

  • @zhaobryan4441
    @zhaobryan4441 13 дней назад

    greatest of all time course on CG

  • @zhaobryan4441
    @zhaobryan4441 15 дней назад

    this is the best way to teach the CG, which is all about problem-solving driven instead of exam-driven,so good,salute dude

  • @zhaobryan4441
    @zhaobryan4441 16 дней назад

    truth be told, this is the best intro class for CG on the internet, guaranteed!!!

  • @takyon24
    @takyon24 16 дней назад

    Did anyone try doing this course without much C++ experience? I have a bunch of programming experience in other languages, including C, but not specifically C++.

  • @DianaJianu-mm1ni
    @DianaJianu-mm1ni 18 дней назад

    I'm a bit confused. The video is called discrete surfaces but - as far as I have seen - it only provides a definition for simplicial surfaces. maybe I need to watch the video again or maybe I should know beforehand that they are one and the same, i don't know.

  • @samsunnahar9175
    @samsunnahar9175 23 дня назад

    THANKS A LOT FOR EXCELLENT VIDEO!!

  • @matiassandacz9145
    @matiassandacz9145 23 дня назад

    Hey! I'm a student from Argentina, and was wondering if there is any way I could get access to the Assignments. Thanks very much in advance for posting these amazing video lectures!

  • @aaronkurtz3119
    @aaronkurtz3119 25 дней назад

    These videos are incredibly helpful, thanks so much!

  • @abdulrahman01234
    @abdulrahman01234 27 дней назад

    Isn't the norm of the tangent at 25:58 supposed to be in square root?

  • @Suav58
    @Suav58 Месяц назад

    4-6 coded course with pre-elementary introduction to projective geometry? That's a bit of a surprise.

  • @AlexAlex-go9hg
    @AlexAlex-go9hg Месяц назад

    your videos are great. thanks a lot!

  • @yuanliang733
    @yuanliang733 Месяц назад

    you helped me a lot in research these years, I have watched a lot of your videos, but there is a little problem, as I do not have a cmu email, it seems that I can not sign up to the piazza, do you have any solutions? THank you very much.

  • @bars3073
    @bars3073 Месяц назад

    I got confused by the formula at 31:04, is the domain of gauss map the parametrization space, or the embedded surface given by f(R^2)? Taking the inner product of vectors that belong to different tangent spaces seems inconvenient. There must be more elegant formulation.

  • @chenyang_wu
    @chenyang_wu Месяц назад

    You can't imagine the excitement I felt when I found this course! Thank you very much for sharing!

  • @standalone8314
    @standalone8314 Месяц назад

    his 'okay' sounds cute!

  • @ricardomarino8554
    @ricardomarino8554 Месяц назад

    For the question in 43:09: It's true that if the point x get's closer to x_i, its value get's closer to f_i, since for phi_i the ratio becomes one (the triangles overlap) but for the other ones the ratio becomes zero. However, it doesn't do it in the same way of the other one (the 2d previous linear interpolation). For instance, consider the point just in the middle of the triangle. In the previous linear interpolation the value of phi_i, phi_j and phi_k was the same 0.5 (if the triangle is equilateral), but for the interpolation with the areas it's 0.3 for phi_i, phi_j and phi_k, since the area of each subtriangle is a third of the bigger one.

  • @AkamiChannel
    @AkamiChannel Месяц назад

    Would be great to have a final lecture in the playlist about the history of how the subject was developed. Was it Elie Cartan who majorly did a lot of the legwork in putting this stuff together?

  • @AkamiChannel
    @AkamiChannel Месяц назад

    He really did just go and say "grow some balls" without laughing. What a lad

  • @CallOFDutyMVP666
    @CallOFDutyMVP666 Месяц назад

    Great knowing thank you

  • @lonnybulldozer8426
    @lonnybulldozer8426 2 месяца назад

    You seem to be mistaking angle measure for angle. An angle is a geometric object, while the angle measure is a quantity.

  • @emadjshah
    @emadjshah 2 месяца назад

    No of videos : 25 Average length of video : 1 hour, 10 minutes, 8 seconds Total length of playlist : 1 day, 5 hours, 13 minutes, 25 seconds At 1.25x : 23 hours, 22 minutes, 44 seconds At 1.50x : 19 hours, 28 minutes, 56 seconds At 1.75x : 16 hours, 41 minutes, 57 seconds At 2.00x : 14 hours, 36 minutes, 42 seconds

    • @valentindumitru9492
      @valentindumitru9492 15 часов назад

      If you watch these videos at more than 1 then youre not learning. I literally stop every other sentence to write down stuff and to understand the concept.

  • @AkamiChannel
    @AkamiChannel 2 месяца назад

    Thank you so much for putting this on the tube!

  • @rudypieplenbosch6752
    @rudypieplenbosch6752 2 месяца назад

    This a a great and concise explanation 👏

  • @alivecoding4995
    @alivecoding4995 2 месяца назад

    A short note: I come from machine and deep learning and went through your course specifically to understand what talking about manifolds in higher dimensions is about. Kind of a disappointing moment to see your statements at minute 8. 😂

  • @forheuristiclifeksh7836
    @forheuristiclifeksh7836 2 месяца назад

    19:18

  • @forheuristiclifeksh7836
    @forheuristiclifeksh7836 2 месяца назад

    15:12

  • @forheuristiclifeksh7836
    @forheuristiclifeksh7836 2 месяца назад

    53:07

  • @forheuristiclifeksh7836
    @forheuristiclifeksh7836 2 месяца назад

    0:07

  • @forheuristiclifeksh7836
    @forheuristiclifeksh7836 2 месяца назад

    15:03

  • @forheuristiclifeksh7836
    @forheuristiclifeksh7836 2 месяца назад

    13:23

  • @forheuristiclifeksh7836
    @forheuristiclifeksh7836 2 месяца назад

    12:47

  • @animeshkarnewar3
    @animeshkarnewar3 2 месяца назад

    30:47 That sound effect :D!

  • @oneCtwo
    @oneCtwo 2 месяца назад

    Cool ! Actually, if the Torus is embedded in the 3-dimensional sphere instead of the 3-dimensonal euclidean space, then you can turn it inside out without making a hole in it !

  • @forheuristiclifeksh7836
    @forheuristiclifeksh7836 2 месяца назад

    42:42

  • @forheuristiclifeksh7836
    @forheuristiclifeksh7836 2 месяца назад

    14:11

  • @michaelgreer7306
    @michaelgreer7306 2 месяца назад

    You mention that you have a list of recommended supplementary textbooks; where could we find that list? Thank you for making this content widely available!

  • @forheuristiclifeksh7836
    @forheuristiclifeksh7836 3 месяца назад

    6:42

  • @user-gu2fh4nr7h
    @user-gu2fh4nr7h 3 месяца назад

    That surface is repulsive! I love it.

  • @forheuristiclifeksh7836
    @forheuristiclifeksh7836 3 месяца назад

    5:36

  • @aditya_a
    @aditya_a 3 месяца назад

    Not only is this video an excellent, digestible exploration of the Laplace operator, it is a celebration of it

  • @ivarsfabriciuss3568
    @ivarsfabriciuss3568 3 месяца назад

    Fantastic!

  • @codatheseus5060
    @codatheseus5060 3 месяца назад

    I'm here after some linear algebra and some geometric algebra

  • @shahidkamal8318
    @shahidkamal8318 3 месяца назад

    Thanks professor in Millions 😊. I am from an Electrical Engineering background and I have recently have found interest in computer graphics. Eager to watch the whole lectures.

    • @dontreadmyusername6787
      @dontreadmyusername6787 2 месяца назад

      Why arent there people like you in my EE class I am literally the only one in my class who is interested in this stuff Its so isolating