Summer of Math Exposition

Hi, thanks for your submission!

I really liked your blog post, especially the fact that it makes a research paper accessible. Here is a short list of various questions and comments that I hope will help you improve your post a little.

• How does Bridson’s algorithm differ from what previoulsy existed? Is it only the grid partitioning of the space that does it? I think it could deserve more emphasize
• Add a drawing about why the $\frac{r}{\sqrt{d}}$ partitioning guarantees each cell can have at most one point inside of it
• Add a word on how to easily accept/reject a Poisson disk sample easily
• About both improvements, you did not (or I did not see it) mention the time the simulation ran for. To my understanding, these are improvements because they allow to sample more points for the same $k$ value. However, if for a given $k$ both improvements take 10 times more time to run, it may be not so great
• About Mitchell’s algorithm, the choice of the $c$ notation for the cell is redundant with the exponent $c$ of the second improvement, which can be confusing
• The last animation shows the uniform sampling of $p$ in $t$ in a way I do not understand. A(n extended) radius is drawn from a blue point already placed, which then sweep a certain area of $t$ to stop nearly in the middle and then a new point is place. How is this a uniform sample in $t$? I’m not saying it is false, it may only require some knowledge I do not have (yet?).

This article genuinely got me interested in a topic I’ve never heard of before! It’s a really cool concept and the animations in the article are super helpful in visualizing the concepts described in the algorithms being talked about. Some concepts are a bit hard to follow and I would’ve loved some explanations to be a bit more dumbed down.

I’m probably biased, since Poisson disc sampling is one of my favourite topics. But this was very well presented!

The blog is good in most aspects, it does have some small improvements I think. What I enjoyed the most were in the interactive visualisations. Being able to rerun randomized algorithms, or having the ‘difficult to understand’ pseudocode then visualised step by step greatly helped the text. The text itself was quite good to follow, except the following two points that I would like to mention: In the paragraph ‘Some of hte trees would be on top of each other! … Bridson’s algorithm gives us an efficient way to do this.’ Explain what ‘this’ is, as the goal of the algorithm is hidden a few sentences back, and to be honest, I thought the algorithm was made for the rejection of points, not for generating the points itself. Also, in the pseudo code, the ‘annulus’ is mentioned. I had to look up what this is (although you could probably understand it from the visualisation), but it would be easy to quickly mention this structure, for people who haven’t heard from it.

All in all, a good blog for undergraduate students, although it did go over some terms a bit quick, but with very nice visualisations that greatly improve the understandability.

This is brilliant! I am missing a discussion on exactly what we are trying to achieve in the beginning (i.e. rewrite the paragraph right under the first figure). If you want to go a bit longer with this, there is some discussion to be had regarding what is random, what feels random etc.

I was shook when I reached the bottom and saw a ‘no boyfriend’ post

Extremely well motivated and explains several techniques and why they work very well.

Really cool blog post! Fairly easy to follow, and I love the amount of graphs and interactivity! Keep it up!

Well written, easy to follow and understand. Nice visuals ands interactive animations.

it’s amazing! I love it