Keenan Crane
@keenancrane.bsky.social
Digital Geometer, Associate Professor of Computer Science & Robotics at Carnegie Mellon University. There are four lights.
https://www.cs.cmu.edu/~kmcrane/
https://www.cs.cmu.edu/~kmcrane/
Fantastic video from @SciShow about our work that turns any shape into fair dice:
youtu.be/-gp7AbYD9NI?...
Get all the details on Hossein Baktash’s page here: hbaktash.github.io
youtu.be/-gp7AbYD9NI?...
Get all the details on Hossein Baktash’s page here: hbaktash.github.io
How to Make Fair DnD Dice from ANY Shape
YouTube video by SciShow
youtu.be
October 29, 2025 at 1:07 PM
Fantastic video from @SciShow about our work that turns any shape into fair dice:
youtu.be/-gp7AbYD9NI?...
Get all the details on Hossein Baktash’s page here: hbaktash.github.io
youtu.be/-gp7AbYD9NI?...
Get all the details on Hossein Baktash’s page here: hbaktash.github.io
“Fair dice” might make you think of perfect cubes with equal frequencies (say, 1/6 on all sides) 🎲
But “fair” really just means you get the frequencies you expect (say, 1/4, 1/4 & 1/2)
We can now design fair dice with any frequencies—and any shape! 🐉
hbaktash.github.io/projects/put...
But “fair” really just means you get the frequencies you expect (say, 1/4, 1/4 & 1/2)
We can now design fair dice with any frequencies—and any shape! 🐉
hbaktash.github.io/projects/put...
September 25, 2025 at 1:39 PM
“Fair dice” might make you think of perfect cubes with equal frequencies (say, 1/6 on all sides) 🎲
But “fair” really just means you get the frequencies you expect (say, 1/4, 1/4 & 1/2)
We can now design fair dice with any frequencies—and any shape! 🐉
hbaktash.github.io/projects/put...
But “fair” really just means you get the frequencies you expect (say, 1/4, 1/4 & 1/2)
We can now design fair dice with any frequencies—and any shape! 🐉
hbaktash.github.io/projects/put...
Nicely produced clip by Matt Wein and Marylee Williams about our recent dice design project at @scsatcmu.bsky.social and @adobe.com
youtube.com/shorts/jD0ag...
🎲 🎥 🐉 🪙
youtube.com/shorts/jD0ag...
🎲 🎥 🐉 🪙
Rethinking Fair Dice
YouTube video by CMU School of Computer Science
youtube.com
September 24, 2025 at 3:39 PM
Nicely produced clip by Matt Wein and Marylee Williams about our recent dice design project at @scsatcmu.bsky.social and @adobe.com
youtube.com/shorts/jD0ag...
🎲 🎥 🐉 🪙
youtube.com/shorts/jD0ag...
🎲 🎥 🐉 🪙
I got tired of mashing together tools to write long threads with 𝐫𝐢𝐜𝐡 𝑓𝑜𝑟𝑚𝑎𝑡𝑡𝑖𝑛𝑔 and ℳα†ℏ—so I wrote La𝑇𝑤𝑒𝑒𝑡!
It converts Markdown and LaTeX to Unicode that can be used in “tweets”, and automatically splits long threads. Try it out!
keenancrane.github.io/LaTweet/
It converts Markdown and LaTeX to Unicode that can be used in “tweets”, and automatically splits long threads. Try it out!
keenancrane.github.io/LaTweet/
September 11, 2025 at 1:28 PM
I got tired of mashing together tools to write long threads with 𝐫𝐢𝐜𝐡 𝑓𝑜𝑟𝑚𝑎𝑡𝑡𝑖𝑛𝑔 and ℳα†ℏ—so I wrote La𝑇𝑤𝑒𝑒𝑡!
It converts Markdown and LaTeX to Unicode that can be used in “tweets”, and automatically splits long threads. Try it out!
keenancrane.github.io/LaTweet/
It converts Markdown and LaTeX to Unicode that can be used in “tweets”, and automatically splits long threads. Try it out!
keenancrane.github.io/LaTweet/
“Everyone knows” what an autoencoder is… but there's an important complementary picture missing from most introductory material.
In short: we emphasize how autoencoders are implemented—but not always what they represent (and some of the implications of that representation).🧵
In short: we emphasize how autoencoders are implemented—but not always what they represent (and some of the implications of that representation).🧵
September 6, 2025 at 9:20 PM
“Everyone knows” what an autoencoder is… but there's an important complementary picture missing from most introductory material.
In short: we emphasize how autoencoders are implemented—but not always what they represent (and some of the implications of that representation).🧵
In short: we emphasize how autoencoders are implemented—but not always what they represent (and some of the implications of that representation).🧵
I can't* fathom why the top picture, and not the bottom picture, is the standard diagram for an autoencoder.
The whole idea of an autoencoder is that you complete a round trip and seek cycle consistency—why lay out the network linearly?
The whole idea of an autoencoder is that you complete a round trip and seek cycle consistency—why lay out the network linearly?
August 29, 2025 at 10:46 PM
I can't* fathom why the top picture, and not the bottom picture, is the standard diagram for an autoencoder.
The whole idea of an autoencoder is that you complete a round trip and seek cycle consistency—why lay out the network linearly?
The whole idea of an autoencoder is that you complete a round trip and seek cycle consistency—why lay out the network linearly?
I don't have a strong opinion about whether video models “understand the world.”
But I do think the first bar should be checking whether you can recover consistent geometry from video—not whether it makes accurate predictions of physics.
But I do think the first bar should be checking whether you can recover consistent geometry from video—not whether it makes accurate predictions of physics.
August 12, 2025 at 6:56 PM
I don't have a strong opinion about whether video models “understand the world.”
But I do think the first bar should be checking whether you can recover consistent geometry from video—not whether it makes accurate predictions of physics.
But I do think the first bar should be checking whether you can recover consistent geometry from video—not whether it makes accurate predictions of physics.
Awesome work by two awesome former students. 🦖🏁
Logarithmic maps are incredibly useful for algorithms on surfaces--they're local 2D coordinates centered at a given source.
Yousuf Soliman and I found a better way to compute log maps w/ fast short-time heat flow in "The Affine Heat Method" presented @ SGP2025 today! 🧵
Yousuf Soliman and I found a better way to compute log maps w/ fast short-time heat flow in "The Affine Heat Method" presented @ SGP2025 today! 🧵
July 2, 2025 at 1:16 PM
Awesome work by two awesome former students. 🦖🏁
Working on a Walk on Spheres tutorial for #SIGGRAPH2025, and love the ads I'm getting served. 😂
Stay tuned for more…👣
Stay tuned for more…👣
June 29, 2025 at 9:52 AM
Working on a Walk on Spheres tutorial for #SIGGRAPH2025, and love the ads I'm getting served. 😂
Stay tuned for more…👣
Stay tuned for more…👣
Quick “teaser” for a fun #SIGGRAPH2025 project, led by Hossein Baktash, on optimizing a shape to have the desired rolling statistics.
Basically we can turn arbitrary objects into fair dice, or make dice which capture the statistics of other objects—like several coin flips.
Basically we can turn arbitrary objects into fair dice, or make dice which capture the statistics of other objects—like several coin flips.
June 28, 2025 at 3:05 AM
Quick “teaser” for a fun #SIGGRAPH2025 project, led by Hossein Baktash, on optimizing a shape to have the desired rolling statistics.
Basically we can turn arbitrary objects into fair dice, or make dice which capture the statistics of other objects—like several coin flips.
Basically we can turn arbitrary objects into fair dice, or make dice which capture the statistics of other objects—like several coin flips.
Making good on this promise—in the fastest turnaround time ever—my collaborator Etienne Corman has just posted MATLAB code for #RectangularSurfaceParameterization here:
github.com/etcorman/Rec...
(C++ version is still in the works…)
github.com/etcorman/Rec...
(C++ version is still in the works…)
June 26, 2025 at 3:34 PM
Making good on this promise—in the fastest turnaround time ever—my collaborator Etienne Corman has just posted MATLAB code for #RectangularSurfaceParameterization here:
github.com/etcorman/Rec...
(C++ version is still in the works…)
github.com/etcorman/Rec...
(C++ version is still in the works…)
Meshes with 90° angles are super useful, providing asymptotically faster convergence for finite element simulation, and optimal shape approximation (when aligned with curvature).
Amazingly, no past quad meshing method could guarantee 90° angles under refinement—until now. #RSP
Amazingly, no past quad meshing method could guarantee 90° angles under refinement—until now. #RSP
June 26, 2025 at 3:03 PM
Meshes with 90° angles are super useful, providing asymptotically faster convergence for finite element simulation, and optimal shape approximation (when aligned with curvature).
Amazingly, no past quad meshing method could guarantee 90° angles under refinement—until now. #RSP
Amazingly, no past quad meshing method could guarantee 90° angles under refinement—until now. #RSP
Very happy that Jiří Minarčík will join our research group at @cmu.edu, the Geometry Collective, as a Fulbright visiting scholar! 🥳
Jiří is a world expert in space curves, and one of the core contributors to Penrose (penrose.cs.cmu.edu). Check out his beautiful work here: minarcik.com
Jiří is a world expert in space curves, and one of the core contributors to Penrose (penrose.cs.cmu.edu). Check out his beautiful work here: minarcik.com
June 23, 2025 at 11:14 AM
Very happy that Jiří Minarčík will join our research group at @cmu.edu, the Geometry Collective, as a Fulbright visiting scholar! 🥳
Jiří is a world expert in space curves, and one of the core contributors to Penrose (penrose.cs.cmu.edu). Check out his beautiful work here: minarcik.com
Jiří is a world expert in space curves, and one of the core contributors to Penrose (penrose.cs.cmu.edu). Check out his beautiful work here: minarcik.com
Folks in the #SIGGRAPH community:
You may or may not be aware of the controversy around the next #SIGGRAPHAsia location, summarized here www.cs.toronto.edu/~jacobson/we...
If you're concerned consider signing this letter docs.google.com/document/d/1...
via this form
docs.google.com/forms/d/e/1F...
You may or may not be aware of the controversy around the next #SIGGRAPHAsia location, summarized here www.cs.toronto.edu/~jacobson/we...
If you're concerned consider signing this letter docs.google.com/document/d/1...
via this form
docs.google.com/forms/d/e/1F...
June 20, 2025 at 4:13 PM
Folks in the #SIGGRAPH community:
You may or may not be aware of the controversy around the next #SIGGRAPHAsia location, summarized here www.cs.toronto.edu/~jacobson/we...
If you're concerned consider signing this letter docs.google.com/document/d/1...
via this form
docs.google.com/forms/d/e/1F...
You may or may not be aware of the controversy around the next #SIGGRAPHAsia location, summarized here www.cs.toronto.edu/~jacobson/we...
If you're concerned consider signing this letter docs.google.com/document/d/1...
via this form
docs.google.com/forms/d/e/1F...
Very happy to receive a SIGGRAPH 2025 Best Paper Award (Honorable Mention) for our RSP algorithm, which dices surfaces into near-perfect rectangles.
Such meshes are useful for everything from retopology, to microfluidic simulation, to textile design, to architectural geometry.
Such meshes are useful for everything from retopology, to microfluidic simulation, to textile design, to architectural geometry.
June 20, 2025 at 10:53 AM
Very happy to receive a SIGGRAPH 2025 Best Paper Award (Honorable Mention) for our RSP algorithm, which dices surfaces into near-perfect rectangles.
Such meshes are useful for everything from retopology, to microfluidic simulation, to textile design, to architectural geometry.
Such meshes are useful for everything from retopology, to microfluidic simulation, to textile design, to architectural geometry.
Shout out today to parents, grandparents, aunts, uncles, or anyone else who helps raise a kid.
It didn’t really click until I was a dad: without parents, human civilization ends.
Only with good parents does the future look bright.
So, give a nod to anyone putting in the work.
It didn’t really click until I was a dad: without parents, human civilization ends.
Only with good parents does the future look bright.
So, give a nod to anyone putting in the work.
June 15, 2025 at 3:30 PM
Shout out today to parents, grandparents, aunts, uncles, or anyone else who helps raise a kid.
It didn’t really click until I was a dad: without parents, human civilization ends.
Only with good parents does the future look bright.
So, give a nod to anyone putting in the work.
It didn’t really click until I was a dad: without parents, human civilization ends.
Only with good parents does the future look bright.
So, give a nod to anyone putting in the work.
Reposted by Keenan Crane
Mesh intersections is hard ! Three years of agonizing pain summarized in my article that just got accepted to ACM Transactions on Graphics
dl.acm.org/doi/10.1145/...
The implementation and the expansion-based arithmetic kernel are available in geogram: github.com/BrunoLevy/ge...
dl.acm.org/doi/10.1145/...
The implementation and the expansion-based arithmetic kernel are available in geogram: github.com/BrunoLevy/ge...
June 13, 2025 at 8:33 AM
Mesh intersections is hard ! Three years of agonizing pain summarized in my article that just got accepted to ACM Transactions on Graphics
dl.acm.org/doi/10.1145/...
The implementation and the expansion-based arithmetic kernel are available in geogram: github.com/BrunoLevy/ge...
dl.acm.org/doi/10.1145/...
The implementation and the expansion-based arithmetic kernel are available in geogram: github.com/BrunoLevy/ge...
Hey @nervousjesse.bsky.social @nervousjessica.bsky.social, how come you don't sell a waste basket (or recycling bin) in your shop? Would be a welcome alternative to conventional wicker or wire baskets. (Maybe modeled after lysosomes or peroxisomes?)
June 13, 2025 at 1:36 PM
Hey @nervousjesse.bsky.social @nervousjessica.bsky.social, how come you don't sell a waste basket (or recycling bin) in your shop? Would be a welcome alternative to conventional wicker or wire baskets. (Maybe modeled after lysosomes or peroxisomes?)
Generative art circa 2004. Inspired by Piet Mondrian and rendered in acrylic. (Currently on display at my grandmother’s house)
June 7, 2025 at 1:06 PM
Generative art circa 2004. Inspired by Piet Mondrian and rendered in acrylic. (Currently on display at my grandmother’s house)
More in-depth article, on Ars Technica, about our recent dice design/rigid body project led by Hossein Baktash at CMU: arstechnica.com/science/2025...
You can find the full paper and 3D printable STL files on Hossein's webpage here: hbaktash.github.io
You can find the full paper and 3D printable STL files on Hossein's webpage here: hbaktash.github.io
Your next gaming dice could be shaped like a dragon or armadillo
Statistically, “the real behavior of a rolling object is largely a function of its geometry.”…
arstechnica.com
May 30, 2025 at 3:32 PM
More in-depth article, on Ars Technica, about our recent dice design/rigid body project led by Hossein Baktash at CMU: arstechnica.com/science/2025...
You can find the full paper and 3D printable STL files on Hossein's webpage here: hbaktash.github.io
You can find the full paper and 3D printable STL files on Hossein's webpage here: hbaktash.github.io
Reposted by Keenan Crane
Terrific new work in designing fair dice with arbitrary shapes, by Hossein Baktash at CMU:
• www.newscientist.com/article/2482...
• hbaktash.github.io/files/rollin...
• www.newscientist.com/article/2482...
• hbaktash.github.io/files/rollin...
hbaktash.github.io
May 29, 2025 at 4:26 AM
Terrific new work in designing fair dice with arbitrary shapes, by Hossein Baktash at CMU:
• www.newscientist.com/article/2482...
• hbaktash.github.io/files/rollin...
• www.newscientist.com/article/2482...
• hbaktash.github.io/files/rollin...
Anyone interested in 3D printing some funky dice—like a "fair dragon" which can land in three different ways, or a single die equivalent to to 2D6?
We've now put printable STL files online: www.cs.cmu.edu/~kmcrane/Pro...
More info here: hbaktash.github.io
We've now put printable STL files online: www.cs.cmu.edu/~kmcrane/Pro...
More info here: hbaktash.github.io
May 29, 2025 at 4:08 AM
Anyone interested in 3D printing some funky dice—like a "fair dragon" which can land in three different ways, or a single die equivalent to to 2D6?
We've now put printable STL files online: www.cs.cmu.edu/~kmcrane/Pro...
More info here: hbaktash.github.io
We've now put printable STL files online: www.cs.cmu.edu/~kmcrane/Pro...
More info here: hbaktash.github.io
Great writeup by @stokel.bsky.social about our #SIGGRAPH paper on dice design (and rigid body analysis), led by my awesome PhD student Hossein Baktash: hbaktash.github.io
May 29, 2025 at 3:11 AM
Great writeup by @stokel.bsky.social about our #SIGGRAPH paper on dice design (and rigid body analysis), led by my awesome PhD student Hossein Baktash: hbaktash.github.io
Fun new paper at #SIGGRAPH2025:
What if instead of two 6-sided dice, you could roll a single "funky-shaped" die that gives the same statistics (e.g, 7 is twice as likely as 4 or 10).
Or make fair dice in any shape—e.g., dragons rather than cubes?
That's exactly what we do! 1/n
What if instead of two 6-sided dice, you could roll a single "funky-shaped" die that gives the same statistics (e.g, 7 is twice as likely as 4 or 10).
Or make fair dice in any shape—e.g., dragons rather than cubes?
That's exactly what we do! 1/n
May 21, 2025 at 4:29 PM
Fun new paper at #SIGGRAPH2025:
What if instead of two 6-sided dice, you could roll a single "funky-shaped" die that gives the same statistics (e.g, 7 is twice as likely as 4 or 10).
Or make fair dice in any shape—e.g., dragons rather than cubes?
That's exactly what we do! 1/n
What if instead of two 6-sided dice, you could roll a single "funky-shaped" die that gives the same statistics (e.g, 7 is twice as likely as 4 or 10).
Or make fair dice in any shape—e.g., dragons rather than cubes?
That's exactly what we do! 1/n