We derive the dynamics of harmonic components for incompressible inviscid fluids, which has previously been overlooked in the vorticity-streamfunction formulation for Euler equations. We elucidate the physical laws associated with the new equations and show their importance in reproducing physically correct behaviors of fluid flows on domains with general topology.
This is a comprehensive course for graphics researchers to fill the gap between their undergraduate curriculum of multivariable calculus and cutting-edge graphics research. We use relevant examples from computer graphics to illustrate the theory of exterior calculus leading to advanced topics including continuum mechanics, fluid dynamics, and geometric optimizations.
We present a method for solving the wave equation on the entire infinite domain using only finite computation time and memory. We perform wave simulations in infinite spacetime using a finite discretization of the bounded spacetime with no additional loss of accuracy introduced by the Kelvin transformation.
We address the problem of synthesizing physical animations that can loop seamlessly. Compared to traditional keyframe animation approaches, our formulation is constraint-free, which allows us to apply a standard Gauss-Newton solver. Our method can handle a variety of physical cyclic animations.
We simulate Euler equations for inviscid fluids by using a novel formulation based on covectors. This new formulation is an entirely velocity-based method in the vein of advection-projection methods while emulating vortex methods. This allows for capturing more intricate vortex dynamics and reducing dissipation of energy with low computational overhead.
We solve infinite-domain simulation problems by applying the Kelvin transform. The transformation turns infinite-domain PDEs into bounded-domain ones via a domain inversion and a singularity factorization.
News
May 2nd 2023: Talk on Covector Fluids paper at Southern California Fluids Conference. (In-person)
April 10th 2023: Talk on Covector Fluids paper at Pixel Cafe at UCSD CSE department. (In-person)
April 4th 2023: Talk on Covector Fluids paper at Geometric Mechanics at UCSD Math department. (In-person)
November 4th 2022: Talk on Covector Fluids paper at joint oceanography seminar at UCSD Scripps Institution of Oceanography. (In-person)
August 10th 2022: Talk on Covector Fluids paper at SIGGRAPH 2022. (In-person) recording here
August 4th 2022: Talk on Covector Fluids paper at Stanford University. (In-person)
June 9th 2022: Talk on Covector Fluids paper at Visual Computing Center's retreat. (In-person)
June 7th 2022: Discussion on Covector Fluids paper at McGill Univeristy. (Remote)
June 2nd 2022: Talk on Covector Fluids paper at University of Waterloo Computer Graphics Lab (CGL). (Remote)
May 10th 2022: Talk on Covector Fluids paper at SideFX Software. (Remote)
September 24th 2021: Talk on Kelvin Transform paper at Toronto Geometry Colloquium (TGC). (Remote) recording here
August 11th 2021: Talk on Kelvin Transform paper at SIGGRAPH 2021. (Remote) recording here
Experience
Throughout my studies, I've managed to intern at various places with a focus on my passion for computer graphics, animation, and gaming.
Weta Digital x Unity
Incoming Research Intern
Wellington, New Zealand (remote)
June, 2023 - September, 2023
Mentors: Alexey Stomakhin, Steve Lesser
Pixar
Research Intern
Emeryville, California, USA
June, 2022 - September, 2022
Mentors: Fernando de Goes, Andrew Butts, Mark Meyer Worked on cloth deformation and simulation.
Treyarch
Graphics Engineer Intern
Santa Monica, California, USA (remote)
June, 2021 - September, 2021
Mentor: Jose Doran Worked on Call of Duty: Warzone 2.
Activision Central Tech
Computer Graphics Intern
Portland, Maine, USA (remote)
May, 2020 - September, 2020
Mentor: Michael Vance, Akimitsu Hogge Worked on Call of Duty Black Ops: Cold War.
University of Waterloo
Research Assistant
Waterloo, Ontario, Canada
January, 2018 - April, 2020
Mentor: Prof. Christopher Batty Worked on adaptive quad/octree viscous fluid simulation.
Ubisoft Toronto
3D Programmer Intern
Toronto, Ontario, Canada
January, 2019 - April, 2019
Mentor: Ruben Penalva, Randy Tjandra Worked on Watch Dogs Legion.
Side Effects Software
3D Software Developer Intern
Toronto, Ontario, Canada
May, 2018 - August, 2018
Mentor: Jeff Lait Worked on Houdini 17 release.
Side Effects Software
3D Software Developer Intern
Toronto, Ontario, Canada
September, 2017 - December, 2017
Mentor: Neil Dickson, Derrick Moser Worked on Houdini 16.5 release.