About
Hi, I'm Gijs Bellaard. I was born and raised in Geertruidenberg, a little city in The Netherlands. I'm 25 years old and currently doing a PhD at the Eindhoven University of Technology under the supervision of Remco Duits in the Geometric Learning and Differential Geometry group of the Centre for Analysis, Scientific Computing and Applications cluster. My interests lie in simulations, differential geometry, combinatorics, machine learning, and computer graphics.
Academia
Publications
Publications
| Date | Organization | Title | Role | Type |
|---|---|---|---|---|
| 25 November 2022 | TU/e | Analysis of (sub-)Riemannian PDE-G-CNNs | First Author | Preprint |
Supervision
| Date | Organization | Type | Role | Student | Project Title |
|---|---|---|---|---|---|
| 2023 | TU/e | Master Thesis | Co-Supervisor | Sei Sakata | Axioms of PDE-G-CNNs |
| 2022 | TU/e | Master Thesis | Co-Supervisor | Daan Bon | Analysis and Geometric Interpretation of PDE-G-CNNs |
Teaching
| Date | Organization | Course Title | Course Code | Role |
|---|---|---|---|---|
| 2022-2023 Quartile 1 | TU/e | Advanced Calculus | 2DBN10 | Instructor |
| 2021-2022 Quartile 4 | TU/e | Complex Analysis | 2WA80 | Instructor |
| 2021-2022 Quartile 1 | TU/e | Advanced Calculus | 2DBN10 | Instructor |
Presentations
| Date | Occasion | Venue | Title | Slides |
|---|---|---|---|---|
| 13 April 2022 | CASA day | Evoluon Eindhoven | Analysis of PDE-G-CNNs |
Other
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My bachelor final project is about neighbour-swap graphs. Tom Verhoeff was my supervisor during this project. A Dutch introduction to this topic can be read in the so-called "A4-populair", which is meant for high schoolers in the Netherlands.
Paper • Presentation • A4-Populair -
My master thesis is about the simulation of viscoplastic materials using smoothed particle hydrodynamics. This thesis was done under the supervision of Bas van der Linden at Sioux Mathware.
Thesis • Presentation -
My friend Sander Spoelstra's bachelor final project is about the Union-Closed conjecture which I am also interested in. I followed the writing of his paper closely and he allowed me to share it here.
Paper
Articles
Some articles I've written that try to (and/or) illuminate, summarize, formalize, simplify, subjects I've come across. Some of them are purely for the fun of it.
- Algebraically Manipulating the Differential
- Curvature
- Determinant
- Distance Fields
- Equivariant Neural Networks
- Finite difference approximations
- Geometric Series and Positional Notation
- Kaleidoscopic IFS fractals
- Knotting
- Living on the n-sphere
- Rubik's Cube in 1 move
- Simple Atmosphere
Snippets
Here I share pieces of code/maths that can be of use. Currently it consists of mostly distance functions for some fractals and some finite differences. I have put them on my site because I find these to be hard to find in their most basic form.
- Apollonian fractal
- Donuts fractal
- Fathauer crystal
- Four-point stencil for 3D gradient
- Kalibox
- Mandelbox
- Menger sponge
- Nine-point stencil for 2D laplacian
- Sierpinski dodecahedron
- Sierpinski icosahedron
- Sierpinski octahedron
- Sierpinski tetrahedron
- Tree fractal
Shaders
Check out all my shaders on Shadertoy
Apps
- Barnes-Hut Simulation
- Buoyancy Simulation
- Cake Wavelets
- Finite Difference Calculator
- Fluid Simulation
- Function Plotter
- Mandelbrot Viewer
- Node Editor
- Projective Geometry
- Raymarcher IDE
- Rigid Grid Simulation
- Spherical Lens
- Union-Closed Family Visualizer
Gallery
I create renders of fractals using my Raymarcher IDE. You can check them out in the gallery. In the meantime, enjoy this random picture from the gallery:
