Olivier MercierResearch Scientist - Display Systems Research
Facebook Reality Labs
Journal of Computational Physics, 2021
Xi-Yuan Yin, Olivier Mercier, Badal Yadav, Kai Schneider, Jean-Christophe Nave
We propose an efficient semi-Lagrangian method for solving the two-dimensional incompressible Euler equations with high precision on a coarse grid. The new approach evolves the flow map using the gradientaugmented level set method (GALSM). Since the flow map can be decomposed into submaps (each over a finite time interval), the error can be controlled by choosing the remapping times appropriately. This leads to a numerical scheme that has exponential resolution in linear time. Error estimates are provided and conservation properties are analyzed. The computational efficiency and the high precision of the method are illustrated for a vortex merger and a four mode and a random flow. Comparisons with a Cauchy-Lagrangian method are also presented.
SIAM Journal on Scientific Computing, 2020
Olivier Mercier, Xi-Yuan Yin, Jean-Christophe Nave
We present a new numerical method for transporting arbitrary sets in a velocity field. The method computes a deformation mapping of the domain and advects particular sets by function composition with the map. This also allows for the transport of multiple sets at low computational cost. Our strategy is to separate the computation of short time advection from the storage and representation of long time deformation maps, employing appropriate grid resolution for each of these two parts. We show through numerical experiments that the resulting algorithm is accurate and exhibits significant reductions in computational time over other methods. Results are presented in two and three dimensions, and accuracy and efficiency are studied.
Olivier Mercier, Derek Nowrouzezahrai
We present a flexible model reduction method for simulating incompressible fluids. We derive a novel vector field basis composed of localized basis flows which have simple analytic forms and can be tiled on regular lattices, avoiding the use of complicated data structures or neighborhood queries. Local basis flow interactions can be precomputed and reused to simulate fluid dynamics on any simulation domain without additional overhead. We introduce heuristic simulation dynamics tailored to our basis and derived from a projection of the Navier-Stokes equations to produce physically plausible motion, exposing intuitive parameters to control energy distribution across scales. Our basis can adapt to curved simulation boundaries, can be coupled with dynamic obstacles, and offers simple adjustable trade-offs between speed and visual resolution.
Ph.D. Thesis, Université de Montréal, 2018
Olivier Mercier, supervised by Derek Nowrouzezahrai
In this thesis by publication, we present three papers where iterative algorithms play a major role in a simulation or rendering method. First, we propose a method to improve the visual quality of fluid simulations. By creating a high-resolution surface representation around an input fluid simulation, stabilized with iterative methods, we introduce additional details atop of the simulation. Second, we describe a method to compute fluid simulations using model reduction. We design a novel vector field basis to represent fluid velocity, creating a method specifically tailored to improve all iterative components of the simulation. Finally, we present an algorithm to compute high-quality images for multifocal displays in a virtual reality context. Displaying images on multiple display layers incurs significant additional costs, but we formulate the image decomposition problem so as to allow an efficient solution using a simple iterative algorithm.
SIGGRAPH Asia 2017 (ACM TOG)
Olivier Mercier, Yusufu Sulai, Kevin Mackenzie, Marina Zannoli, James Hillis, Derek Nowrouzezahrai, Douglas Lanman
We present an efficient algorithm for optimal scene decompositions on multifocal displays, incorporating insights from vision science. Our method is amenable to GPU implementations and achieves a three-orders-of-magnitude speedup over previous work. We further show that eye tracking can be used for adequate plane alignment with efficient image-based deformations, adjusting for both eye rotation and head movement relative to the display. We also build the first binocular multifocal testbed with integrated eye tracking and accommodation measurement, paving the way to establish practical eye tracking and rendering requirements for this promising class of display. Finally, we report preliminary results from a pilot user study utilizing our testbed, investigating the accommodation response of users to dynamic stimuli presented under optimal decomposition.
SIGGRAPH Asia 2015 (ACM TOG)
Olivier Mercier, Cynthia Beauchemin, Nils Thuerey, Theodore Kim, Derek Nowrouzezahrai
We present a method to increase the apparent resolution of particle-based liquid simulations. Our method first outputs a dense, temporally coherent, regularized point set from a coarse particle-based liquid simulation. We then apply a surface-only Lagrangian wave simulation to this high-resolution point set. We develop novel methods for seeding and simulating waves over surface points, and use them to generate high-resolution details. We avoid error-prone surface mesh processing, and robustly propagate waves without the need for explicit connectivity information. Our seeding strategy combines a robust curvature evaluation with multiple bands of seeding oscillators, injects waves with arbitrarily fine-scale structures, and properly handles obstacle boundaries. We generate detailed fluid surfaces from coarse simulations as an independent post-process that can be applied to most particle-based fluid solvers.
Master's Thesis, McGill University, 2013
Olivier Mercier, supervised by Jean-Christophe Nave
In many cases, the simulation of a physical system requires to track the evolution of a set. This set can be a piece of cloth in the wind, the boundary between a body of water and air, or even a fire front burning through a forest. From a numerical point of view, transporting such sets can be difficult, and algorithms to achieve this task more efficiently and with more accuracy are always in demand. In this thesis, we present various methods to track sets in a given vector field. We also apply those techniques to various physical systems where the vector field is coupled to the advected set in a non-linear way.
Starting with individual frames of a particle fluid simulation generated by an external source, we import the points into Houdini 13 Apprentice (free), create a mesh around the points, and export the mesh. All frames are processed automatically. We show how to customize the import and export nodes to adapt it to any readable and writable format.
University Of Montreal, 2015
A coding event aimed at CEGEP students (16-19 years old) in a computer science (or related) program. The participants had two days to recreate level 1-1 of the original Super Mario Bros. using the provided starting code and graphic resources. All was done using the Processing framework. I was one of the two people in charge of creating the code base. I was also in charge of writting the instructions, building the website, and supervising the students during the event. This project has been reused in following hackathons at DIRO.
Course Project, 2014
This project is based on the paper Matrix Row-Column Sampling for the Many-Light Problem [Hasan et al. 2007]. The paper shows a way of approximating the contributions of many lights (e.g. 100,000 lights) by using a sampling approach to cluster the lights.
Course Project, 2013
Caustics are a key ingredient to produce believable refractive fluid simulations. However, their complex nature makes them very costly to evaluate accurately. For this reason, caustics are often omitted in real-time applications. In this paper, we present a novel method for creating caustics using the eikonal equation. We focus mainly on underwater caustics created by a water interface represented by a height field, with emphasis on interactive frame rates.