@article{21923,
  abstract     = {The appearance of simulated natural phenomena heavily depends on the way surfaces are textured. However, applying texture maps to dynamic deformable surfaces presents a significant challenge, due to ever-shifting differences in length scales involved. When these surfaces move and advect the texture along with them, their final appearance degrades as deformed regions dramatically distort their texture map. Modifications to the texture directly at the pixel level in response to the deformation may introduce ghosting artifacts and look unnatural. In the real world, the appearance of surface details on a deforming material changes through the interplay of physical processes such as rupturing, exposure of internal structure, or wrinkling. Motivated by these behaviors, in this work we explore how physical principles can guide the texturing methods based on the measure of surface deformation.
We present two novel wave-based procedural texturing algorithms which reproduce common physical properties like advection and self-similarity, enabling the plausible animation of deforming objects with extreme texture map distortions. Our algorithms are fully procedural, require no actual physics simulation, and store no state or history of deformation besides the input UV map, making them highly parallelizable on the GPU and efficient enough for real-time applications. We show the versatility of the method by animating physical phenomena with extreme deformations such as flowing lava, stretching putty and outpouring sludge.},
  author       = {Kalinov, Aleksei and Ly, Mickaël and Hafner, Christian and Wojtan, Christopher J},
  issn         = {0730-0301},
  journal      = {ACM Transactions on Graphics},
  keywords     = {Procedural animation},
  location     = {Los Angeles, CA, United States},
  number       = {4},
  publisher    = {ACM},
  title        = {{Physics-inspired procedural texturing of extremely deformable surfaces}},
  doi          = {10.1145/3811353},
  volume       = {45},
  year         = {2026},
}

@article{20628,
  abstract     = {The realistic simulation of sand, soil, powders, rubble piles, and large collections of rigid bodies is a common and important problem in the fields of computer graphics, computational physics, and engineering. Direct simulation of these individual bodies quickly becomes expensive, so we often approximate the entire group as a continuum material that can be more easily computed using tools for solving partial differential equations, like the material point method (MPM). In this paper, we present a method for automatically extracting continuum material properties from a collection of rigid
bodies. We use numerical homogenization with periodic boundary conditions to simulate an effectively infinite number of rigid bodies in contact. We then record the effective stress-strain relationships from these simulations and convert them into elastic properties and yield criteria for the continuum simulations. Our experiments validate existing theoretical models like the Mohr-Coulomb yield surface by extracting material behaviors from a collection of spheres in contact. We further generalize these existing models to more exotic materials derived from diverse and non-convex shapes. We
observe complicated jamming behaviors from non-convex grains, and we introduce a new material model for materials with extremely high levels of internal friction and cohesion. We simulate these new continuum models using MPM with an improved return mapping technique. The end result is a complete system for turning an input rigid body simulation into an efficient continuum simulation with the same effective mechanical properties.},
  author       = {Chen, Yi-Lu and Ly, Mickaël and Wojtan, Christopher J},
  issn         = {1557-7368},
  journal      = {ACM Transactions on Graphics},
  location     = {Hong Kong, China},
  number       = {6},
  publisher    = {Association for Computing Machinery},
  title        = {{Numerical homogenization of sand from grain-level simulations}},
  doi          = {10.1145/3763344},
  volume       = {44},
  year         = {2025},
}

@article{17203,
  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.},
  author       = {Hafner, Christian and Ly, Mickaël and Wojtan, Christopher J},
  issn         = {1557-7368},
  journal      = {Transactions on Graphics},
  keywords     = {Topology Optimization, Mass Moments, Computational Geometry},
  location     = {Denver, Colorado},
  number       = {4},
  publisher    = {Association for Computing Machinery},
  title        = {{Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments}},
  doi          = {10.1145/3658194},
  volume       = {43},
  year         = {2024},
}

@inproceedings{17214,
  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.},
  author       = {Chen, Yi-Lu and Ly, Mickaël and Wojtan, Christopher J},
  booktitle    = {Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers '24},
  isbn         = {9798400705250},
  keywords     = {physical simulation, frictional contact, rigid body mechanics, non-smooth dynamics},
  location     = {Denver, United States},
  publisher    = {Association for Computing Machinery},
  title        = {{Primal-dual non-smooth friction for rigid body animation}},
  doi          = {10.1145/3641519.3657485},
  year         = {2024},
}

@inproceedings{14748,
  author       = {Chen, Yi-Lu and Ly, Mickaël and Wojtan, Christopher J},
  booktitle    = {Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation},
  isbn         = {9798400702686},
  location     = {Los Angeles, CA, United States},
  publisher    = {Association for Computing Machinery},
  title        = {{Unified treatment of contact, friction and shock-propagation in rigid body animation}},
  doi          = {10.1145/3606037.3606836},
  year         = {2023},
}

@misc{15292,
  abstract     = {We present a rigid body animation technique which prevents solids from interpenetrating, dissipates energy through friction, and propagates shocks through contacts. We employ the Alternating Direction Method of Multipliers (ADMM) to couple non-smooth Coulomb friction with impact propagation, allowing efficient and accurate non-smooth dynamics along with a correct transmission of impacts through assemblies of rigid bodies. We further extend our method to model adhesion, dynamic friction and lubricated contact.},
  author       = {Chen, Yi-Lu and Ly, Mickaël and Wojtan, Christopher J},
  booktitle    = {Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation},
  location     = {Los Angeles, CA, United States},
  publisher    = {ACM},
  title        = {{Unified treatment of contact, friction and shock-propagation in rigid body animation}},
  doi          = {10.1145/3606037.3606836},
  year         = {2023},
}