Summer of Math Exposition

Nice topic, well explained

Happy to see that you extended your previous video. I also appreciate taking the comments into account. The flow of the video was really good and the final result was beautiful.

Beautiful and clear explanation. I would have enjoyed more detailing in the derivations and longer time spent on the iterative process in for the final algorithm. Overall, well done!

Excellent in general. It would be cool to see some more example images at the end, it's just satisfying :)

Your video was informative and easy to follow, which I really appreciated. However, incorporating more visual examples throughout could enhance the clarity of the concepts being explained. For instance, when you discussed the choice of using maximum darkness per length of the line instead of absolute maximum darkness, it was helpful to see the final result and the issues with not implementing average darkness per length. However, breaking this down with a simpler example would have made it even easier to intuitively grasp why maximum average darkness per length leads to a better image compared to maximum absolute darkness. Overall, the video was well thought out, and I feel much more confident in my understanding of the algorithm after watching it.

Great job building on previous video (which I watched last year!) motivation was clear, math steps were easy to follow, the result at the end was astounding in how good it was. Overall fantastic job.

Definitely makes me want to have a go at line art.

Well explained, and beautiful video. It's really cool to see how you show a simple mistake because you made a "sensible" assumption and then showed the real solution. I wanted to know what it was the original motivation or Radon Transform and why it is used in CNC...

Please make the text/equations bigger for my eye health thanks.

interesting math is masked which is a little frustrating, I must say I could not follow totally the reasoning, will have to deepen by looking at the papers.

AAA! Where did the weighted sum come from? Quite a few assumptions here. Highly engaging though!

This is a very good video, with both abstract concepts and nice examples. However, I believe it is too strongly based on last year's winning video. In particular, two things I would like to mention. - I was aware of the string art video from last year but hadn't watched it prior to watching this year's entry. So, when the technical part of the pseudo-inverse appeared and was brushed off only to say that it was covered last year, I was a bit disappointed. - After watching this year's entry, I checked the other video from last year, and do not believe that this year's video covers anything notably new, it simply provides the continuous equivalent of last year's method. In particular, while it introduces the radon transform, it ends up using it to make once again discrete string art and shifts from the (alpha, s) space back to the (psi1, psi2), thus not really providing novel insights compared to last year's video. - The video starts with a strong relation: string art is pretty much the same as CT scanners. I loved this parallel, but was then disappointed not to see this comparison kept for the rest of the video. I would have liked a word at the end on CT scanners. I appreciate the potential of these concepts and believe that it would have still been possible for the video to be based on last year's concepts while providing new insights. - I think it would have been ok to simply say that this video intends to generalize last year's method to the continuous space, using ideas similar to that of CT scanners. Then, instead of using radon transforms, to then not invert them, directly use the (psi1, psi2) space, but in a continuous way this time. - It would have also been ok to explain how you expand the method to multi-coloured pictures. In particular, why use CMYB and not just CMY, or RGB? And how do you decide on which colour to put first? Does the order of the colours actually matter? - Another generalization would have been to consider a non-circular canvas. What happens if we consider a square instead? Or any shape? Is it feasible in your workshop? Overall, this is once again a very good quality video, with interesting concepts and visuals. However, I believe it is not novel enough compared to last year's entry and it relies too strongly on the previous video (also assuming that people knew about it).

Another great submission. Nice improvement. Keep up the good work.

Ok this is neat. I like the immediate grounding of this math with applications using scanners. The radon transformation animation from 1:30 to 3:30 looked very professional in their design, nicely done!

The first video in the series was awesome, and this one did not disappoint as well.

Really wonderful visualisations and great pace in explaining. Small spelling mistake "strictly speaking we want to *minimize*.... "