Mickaël Ly

Spin-It Faster: Quadrics Solve All Topology Optimization Problems That Depend Only On Mass Moments
(website, paper, supplemental, video)
Christian Hafner, Mickaël Ly, Chris Wojtan
ACM Transactions on Graphics (Siggraph 2024)
Honorable Mention from the Siggraph 2024 Technical Papers Awards
Abstract ⤵ The behavior of a rigid body primarily depends on its mass moments, which consist of the mass, center of mass, and moments of inertia. It is possible to manipulate these quantities without altering the geometric appearance of an object by introducing cavities in its interior. Algorithms that find cavities of suitable shapes and sizes have enabled the computational design of spinning tops, yo-yos, wheels, buoys, and statically balanced objects. Previous work is based, for example, on topology optimization on voxel grids, which introduces a large number of optimization variables and box constraints, or offset surface computation, which cannot guarantee that solutions to a feasible problem will always be found. In this work, we provide a mathematical analysis of constrained topology optimization problems that depend only on mass moments. This class of problems covers, among others, all applications mentioned above. Our main result is to show that no matter the outer shape of the rigid body to be optimized or the optimization objective and constraints considered, the optimal solution always features a quadric-shaped interface between material and cavities. This proves that optimal interfaces are always ellipsoids, hyperboloids, paraboloids, or one of a few degenerate cases, such as planes. This insight lets us replace a difficult topology optimization problem with a provably equivalent non-linear equation system in a small number (<10) of variables, which represent the coefficients of the quadric. This system can be solved in a few seconds for most examples, provides insights into the geometric structure of many specific applications, and lets us describe their solution properties. Finally, our method integrates seamlessly into modern fabrication workflows because our solutions are analytical surfaces that are native to the CAD domain.

Primal–Dual Non-Smooth Friction for Rigid Body Animation
(website, paper, supplemental, video, additional video,)
Yi-Lu Chen, Mickaël Ly, Chris Wojtan
ACM Siggraph 2024 Conference Papers
Abstract ⤵ Current numerical algorithms for simulating friction fall in one of two camps: smooth solvers sacrifice the stable treatment of static friction in exchange for fast convergence, and non-smooth solvers accurately compute friction at convergence rates that are often prohibitive for large graphics applications. We introduce a novel bridge between these two ideas that computes static and dynamic friction stably and efficiently. Our key idea is to convert the highly constrained non-smooth problem into an unconstrained smooth problem using logarithmic barriers that converges to the exact solution as accuracy increases. We phrase the problem as an interior point primal-dual problem that can be solved efficiently with Newton iteration. We observe quadratic convergence despite the non-smooth nature of the original problem, and our method is well-suited for large systems of tightly packed objects with many contact points. We demonstrate the efficacy of our method with stable piles of grains and stacks of objects, complex granular flows, and robust interlocking assemblies of rigid bodies.

Unified treatment of contact, friction and shock-propagation in rigid body animation
(website)
Yi-Lu Chen, Mickaël Ly, Chris Wojtan
Proceedings of the Symposium on Computer Animation 23 (SCA)

Test et validation de codes de simulation d'informatique graphique pour les structures élastiques minces et le contact frottant
(website, paper)
Victor Romero, Mickaël Ly, Abdullah-Haroon Rasheed, Raphaël Charrondière, Arnaud Lazarus, Sébastien Neukirch, Florence Bertails-Descoubes
CSMA 2022 - 15ème Colloque National en Calcul des Structures

Static inverse modelling of clothes
(website, manuscript)
Mickaël Ly - PhD Thesis, 2021

Physical validation of simulators in Computer Graphics: A new framework dedicated to slender elastic structures and frictional contact
(website, paper, accompanying video, supplemental , recipe manual for the tests )
Victor Romero, Mickaël Ly, Abdullah-Haroon Rasheed, Raphaël Charrondière, Arnaud Lazarus, Sébastien Neukirch, Florence Bertails-Descoubes
ACM Transactions on Graphics 2021 (SIGGRAPH)

Projective Dynamics with Dry Frictional Contact
(website, paper, accompanying video, code )
Mickaël Ly, Jean Jouve, Laurence Boissieux, Florence Bertails-Descoubes
ACM Transactions on Graphics 2020 (SIGGRAPH)

Inverse Elastic Shell Design with Contact and Friction
(website, paper, accompanying video, press release)
Mickaël Ly, Romain Casati, Florence Bertails-Descoubes, Mélina Skouras, Laurence Boissieux
ACM Transactions on Graphics 2018 (SIGGRAPH Asia)

Unilaterally Incompressible Skinning
(website, paper)
Mickaël Ly, Florence Bertails-Descoubes, Damien Rohmer
Inria Research Report