Latest post
I probably have discovered a thousand bugs in softwares developed by people other than myself, but this time, for the first time in my life, I found a bug without producing a buggy phenomenon first but by staring at the source codes and deducing mathematical formulas by hand. That was an amazing experience. I wrote a blog article about it: https://ulysseszh.github.io/programming/2025/07/17/blur-filter.html
#development #debugging #graphics #graphicsprogramming #imageprocessing #shader #pixijs
follow me on Mastodon
Articles
-
Multi-pass Gaussian blur filter
According to the central limit theorem, the sum of some i.i.d. samples is normally distributed in the limit of large sample size. This fact can be used to implement a multi-pass Gaussian blur filter, where the total number of passes is equal to the number of samples used in the averaging. Through this, we can also see a nice relation to the heat equation, which is not surprising since the heat kernel is a Gaussian function.
- Categories: programming
- Tags: algorithm, shader, probability, pde
-
The buildup kickroll in Time to beat the odds
There is a gradually-accelerating buildup kickroll at 1:18 in the song Time to beat the odds by 影虎。. In order to know the details of this rhythm, I have to analyze the sample using Python.
- Categories: music
- Tags: fourier transform, python
-
Eigenfunctions of the Laplacian on an annulus with homogeneous Neumann boundary condition
Several features of the eigenfunctions of the Laplacian on an annulus with homogeneous Neumann boundary condition are discussed. The distribution of the eigenvalues is discussed in detail, making use of a phase angle function called . The limiting cases of a disk and a circle are discussed.
- Categories: math
- Tags: mathematical physics, pde, ode, long paper
-
The role of particle indistinguishability in statistical mechanics
Indistinguishability plays an important role in enumerative problems in combinatorics. This article explains the concept and significance of particle indistinguishability in statistical mechanics.
- Categories: physics
- Tags: mathematical physics, statistical mechanics, probability, long paper, combinatorics, quantum mechanics
-
Why it is a bad idea to use GitHub for submiting school homework
It is common for school courses to require students to submit their homework using GitHub. However, this is usually a bad idea for several reasons.
-
How to use JavaScript in GitHub Actions without committing
node_modules
I was creating my first GitHub Action. According to the official documentation, I should commit the node_modulesto the repo or generate a script that bundles the wholenode_modulesif I want to create a JavaScript action. I think this is not good practice, so I try to find another way.- Categories: guide
- Tags: javascript, github
-
Some understanding of Grassmann numbers out of intuition
I was briefly introduced to Grassmann numbers when I studied quantum field theory. I then had the natural question of how we can formally define them. In this article, I went with my intuition and tried to answer this question.
- Categories: math
- Tags: quantum field theory, linear algebra, abstract algebra
-
The notational convenience of imaginary time in the derivation of the metric in Poincaré coordinates
In general relativity, people usually choose one of the two major metric signatures. However, in certain cases, the imaginary time convention can be more convenient. Here is one of such cases: the derivation of the metric in Poincaré coordinates for the anti-de Sitter space.
- Categories: physics
- Tags: general relativity, ads space
-
The smallest wave packet in the lowest Landau level
The smallest wave packet in the lowest Landau level exists, and is a Gaussian wave packet. This turns out to be related to the coherent state of the harmonic oscillator.
- Categories: physics
- Tags: quantum mechanics, condensed matter physics
-
Regularizing the partition function of a hydrogen atom
The partition function of a hydrogen atom diverges (only considering bound states). However, we can regularize it to get finite answers. Different regularizations give the same result. They largely agree with the physical arguments for the case of the hydrogen atom at room or cold temperature, but this should be considered a mere coincidence. The results from regularized partition functions cannot generally be trusted.
- Categories: physics
- Tags: statistical mechanics, complex, regularization, long paper
subscribe via RSS