Hi, I'm Gijs Bellaard. I was born and raised in Geertruidenberg, a little city in The Netherlands. I'm 26 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.
- 31 September 2023: As an instructor, I've made my own notes for Remco Duits' Master Course in Typst.
- 17 October 2023: The site now has a dark theme!
- 14 October 2023: I made a simple B-Spline visualization.
- 30 August 2023: I gave a presentation about Neurogeometry and PDE-Based Neural Networks at GSI2023.
- 05 August 2023: The conference paper Functional Properties of PDE-G-CNNs is published in GSI2023.
- 30 June 2023: I made a Kerr-Newman Metric Black Hole simulation.
- 12 May 2023: My conference paper Geometric Adaptations of PDE-G-CNNs is published in SSVM2023.
- 16 April 2023: My article Analysis of (sub-)Riemannian PDE-G-CNNs is published in JMIV.
Functional Properties of PDE-G-CNNsGautam Pai, Gijs Bellaard, Bart M. N. Smets, Remco Duits · Geometric Science of Information 2023 · Send: 20 February 2023 · Online: 01 August 2023Springer · PDF
Geometric Adaptations of PDE-G-CNNsGijs Bellaard, Gautam Pai, Javier Olivan Bescos, and Remco Duits · Scale Space and Variational Methods in Computer Vision 2023 · Send: 30 January 2023 · Online: 10 May 2023Springer · PDF · Poster
Analysis of (sub-)Riemannian PDE-G-CNNsGijs Bellaard, Daan L. J. Bon, Gautam Pai, Bart M. N. Smets, Remco Duits · Journal of Mathematical Imaging and Vision · Received: 21 October 2022 · Accepted: 18 March 2023 · Published: 16 April 2023Springer · arXiv
Axioms of PDE-G-CNNsSei Sakata · Master Thesis · Remco Duits, Gijs Bellaard · 2023
Classical and Quantum PDE-Based Neural NetworksTim Kraakman · Master Thesis · Remco Duits, Gautam Pai, Gijs Bellaard · 2023Thesis
Analysis and Geometric Interpretation of PDE-G-CNNsDaan Bon · Master Thesis · Remco Duits, Gijs Bellaard · 2022Thesis
Differential Geometry for Image ProcessingTU/e · 2MMA70 · Instructor · 2023-2024My Notes
Advanced CalculusTU/e · 2DBN10 · Instructor · 2021-2023
Complex AnalysisTU/e · 2WA80 · Instructor · 2021-2023
Neurogeometry and PDE-Based Neural NetworksGSI 2023 · 30 August 2023Slides (50MB!)
Diffusion and Score Based ModelsAI Reading Group · TU/e · 24 March 2023Notes
Equivariant Neural NetworksAI Reading Group · TU/e · 04 November 2022Notes
Analysis of PDE-G-CNNsCASA day · Evoluon Eindhoven · 13 April 2022Slides
My bachelor final project is about neighbor-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.
AppsInteractive applications ranging from a buoyancy simulation of a cow to a mandelbrot fractal viewer.
- 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
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
- Equivariant Neural Networks
- Finite Difference Approximations
- Kaleidoscopic IFS fractals
- Living on the n-sphere
- Rubiks Cube in 1 Move
- Simple Atmosphere
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
- Menger Sponge
- Raytracer in C
- Schwarzschild Geodesics
- Sierpinski Dodecahedron
- Sierpinski Icosahedron
- Sierpinski Octahedron
- Sierpinski Tetrahedron
- Tree Fractal
Check out all my shaders on Shadertoy
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: