Projects | Baptiste Genest website

Here is a selection of my favorite and most polished projects/experiments over the last 5 years, sorted by period of interest (Most recent first).

Lattice Boltzman Method (LBM)

Canonical solver of the LBM in D2Q9.

Two Relaxation Time (TRT) method for the collision operator.
Dirichlet boundary conditions: $$ f_i(x,t) = f_i^{eq}(\rho,\vec{0}) \text{, } x\in \partial \Omega. $$

Curl visualized in blue/red. Amazing resources: book blog.

Markov-Chain Diffusion-Limited-Aggregation (MCDLA)

A Markov Chain interpretation of the DLA process. The idea is to replace the individual brownian motion simulation with the computation of the probability: $$ x\in \partial X_n, f_n(x) = \mathbb{P}\left(B_{\tau_n} = x | \tau_n < \infty \right) $$ where tau is the stopping time of a Brownian motion, coming from infinity, touching X_n, the DLA at stage n. Such computation is performed on a discrete grid as the fixpoint of the markov chain transition matrix with uniform diffusion except around the boundary of the DLA where the particles are stuck. The next stage of the DLA is computed as:

$$ X_{n+1} = X_n \cup \bigcup_{i = 1}^{\lfloor\sqrt{n}\rfloor} Y_i, \text{ where } Y_i \sim f_n $$

BSP-OT

Computes very fast (in quasilinear time) an assignation that is a good approximation of the optimal one. (Sadly, it has already been published). It works really well when the optimality is not as important as speed such as in color transfer.

Forest Fire simulation by coupled discrete stochastic processes

Simple discrete model
Geometric laws of growth.
Some interesting properties, for instance fire can disappear completely from a tree and come back later due to spreading.
very tunable and upgradable

Road Generation

A* algorithm for the main track, with weights on the vertices and on the edges to avoid height difference
then, to get closer to a clothoïd, since they have affine curvature, I minimize the second derivative of the curvature by minimizing: $$ \mathcal{E}(\gamma) = \int_0^1 ||\gamma^{(4)}(t)||^2 dt $$ with an implicit scheme, where the curve is re-parametrized by arc-length at each iteration to have : $$||\ddot{\gamma}|| = \kappa$$.

“Estimation of the volume of Voronoi cells in high dimension and control variables in Monte Carlo rendering”

4th year research project supervised by David Coeurjolly and Vincent Nivoliers

Exploration of stochastic techniques in estimating the volume and barycenters of Voronoi cells in high dimension
Improvement of Monte Carlo integration by control variate techniques, new control variate proposed
Caracterization and proofs of domination of the new control variate over the original control variate

Image Segmentation : Region Growing and Split and Merge Algorithms

Region Growing : use of more various metric (Wasserstein distance between histograms, Mahalanobis distance, Lp norms) to compare regions
Efficient Split and Merge implementation using a quadtree structure and binary encoding to compute neighborhoods

Edge Detection : Hough Transform and improvements

Implementation of the Active Contour Method for image segmentation
Implementation of the Hough Transform for line detection
New line detection algorithm based on DBScan in pixel-gradient space

Stable Fluids implementation

Standard Stable Fluids implementation :

Diffusion
Semi-Lagrangian advection
Projection method with prefactored sparse laplacian matrix for poisson problem $$\Delta u = \nabla \cdot v$$

Cloth simulation : Mass Spring System & XPBD

Implementation of Mass Spring System
Implementation of XPBD
Spatial Hashing for fast collision detection

Ambiant Occlusion & Diffusion Limited Aggregation

Quasi Monte Carlo techniques for Ambiant Occlusion on heightfields
Improvement of DLA algorithm by simulating brownian motion in a Walk-On-Sphere way and Octree for closest point search

Use of Normal information to improve differential operators on polygonal meshes

1 month research internship supervised by David Coeurjolly.

Various Spline based approaches to provide better estimates of non-linear edges in order improve the convergence of discretizations of differential operators based on Fernando De Goes et al. (No conclusive results)

Curves & Clouds - A scientific visualization and computing library

A lot a different topics are covered :

standard scientific visualization (1D and 2D plots, points clouds, etc…)
ODE solvers
Dense and Sparse Linear Algebra solvers
ML algorithms (Kmeans, PCA, etc…)
FEM solvers
Quadtree and Delauney Meshing
Semi discrete Optimal Transport
Symbolic Differentiation -> Geodesic equation solver (used for raytracing around black holes)
Discrete Differential Geometry (Heat Geodesic Method, curvatures…)
etc…