Research Statement

My thesis work focuses on the robust treatment of collisions in a variety of domains. We start by looking at finite element hyper-elastic materials in our paper, "Incremental Potential Contacts." Our approach is unconditionally robust, requires no parameter tuning, and provides a direct way of controlling the trade-off between running time and accuracy. Matching experimental data in one shot is finally an achievable goal.

We follow up this work by proposing a large-scale benchmark for continuous collision detection (CCD) methods. We evaluate each method on accuracy, correctness, and efficiency. Surprisingly, many algorithms miss collisions, and those that do not are overly conservative. To address these shortcomings we introduce a new method that is provably conservative, results in fewer false positives, and is on par with the fastest methods. Additionally, our method is the first method to provide minimum separation CCD (MSCCD) with guarantees.

Using both the IPC formulation and our conservative MSCCD, we propose a method for simulating rigid body dynamics with an intersection-free guarantee at every step. We do this by introducing a novel CCD method for curved trajectories (roto-translations). Our method works by using a series of linear CCD queries with minimal separation to bound the error in linearizing. We show the robustness of our method in several scenes including complicated mechanisms, frictional contact, and large time steps.

Ph.D. Dissertation, New York University, 2023
Summary: In this thesis, we introduce Incremental Potential Contact (IPC), the first simulation algorithm for deformable and rigid bodies that is efficient, accurate, and unconditionally robust. To verify these claims, we evaluate the efficiency and correctness of Continuous Collision Detection (CCD) algorithms and introduce the first provably correct and efficient algorithm. For improved accuracy and efficiency, we extend IPC to curved meshes and high-order bases and introduce the first physically-based adaptive meshing strategy.
Liam Martin, Pranav Jain, Zachary Ferguson, Torkan Gholamalizadeh, Faezeh Moshfeghifar, Kenny Erleben, Daniele Panozzo, Steven Abramowitch, Teseo Schneider
Computer Methods and Programs in Biomedicine, 2023
Summary: We validate PolyFEM's (including Incremental Potential Contact) capabilities towards simulating biomechanical systems by comparing it against the well-established finite element solver, FEBio.
ACM Transactions on Graphics (SIGGRAPH), 2023
Summary: We propose a fully coupled, adaptive meshing algorithm for contacting elastodynamics where remeshing steps are tightly integrated, implicitly, within the time-step solve. Our algorithm refines and coarsens the domain automatically by measuring physical energy changes within each ongoing time-step solve while guaranteeing invariants (maintaining intersection- and inversion-free trajectories) are preserved.
ACM SIGGRAPH 2023 Conference Proceedings
Summary: We extend the Incremental Potential Contact method to high-order finite element basis and curved meshes. We do so by coupling together a high-order volumetric representation with a linear surface representation. This provides improved accuracy while maintaining efficient collision detection and response, leading to significant improvements in running times.
Faezeh Moshfeghifar, Torkan Gholamalizadeh, Zachary Ferguson, Teseo Schneider, Michael Bachmann Nielsen, Daniele Panozzo, Sune Darkner, Kenny Erleben
Computer Methods and Programs in Biomedicine, 2022
Summary: Population-based finite element analysis of hip joints allows us to understand the effect of inter-subject variability on simulation results. To aid in this direction, we reconstruct 11 subject-specific models from CT scans and release them as an open-access repository. We evaluate our models using both mesh quality metrics and simulation experiments.
Torkan Gholamalizadeh, Faezeh Moshfeghifar, Zachary Ferguson, Teseo Schneider, Daniele Panozzo, Sune Darkner, Masrour Makaremi, François Chan, Peter Lampel Søndergaard, Kenny Erleben
Computer Methods and Programs in Biomedicine, 2022
Summary: We share an open-access repository of 17 patient-specific computational models of human jaws and the utilized pipeline for generating them. The pipeline minimizes the required time for processing and any potential biases in the model generation process caused by human intervention.
International Conference on Parallel Processing and Applied Mathematics (PPAM), 2022
Summary: We introduce a benchmark for interval arithmetic computation and test it on four C/C++ libraries: filib, filib++, Boost, and BIAS. Each library is evaluated based on correctness, output interval size, speed, consistency, and portability.
Computer Graphics Forum (Eurographics), 2022
Summary: We introduce the first exact root parity method for continuous collision detection that is robust to degenerate configurations and is implemented directly using floating-point numbers while accounting for rounding errors.
ACM Transactions on Graphics (SIGGRAPH), 2021
Summary: We introduce the first algorithm for time-stepping rigid body dynamics, with contacts and friction, which guarantees intersection-free configurations at every time step. Additionally, we propose a novel collision detection algorithm for curved trajectories.
Bolun Wang*, Zachary Ferguson*, Teseo Schneider, Xin Jiang, Marco Attene, Daniele Panozzo (*Joint first authors)
ACM Transactions on Graphics, 2021 (presented at SIGGRAPH 2022)
Summary: We introduce a benchmark to evaluate the accuracy, correctness, and efficiency of continuous collision detection algorithms; and a fast algorithm capable of detecting all collisions using floating-point computation.
ACM Transactions on Graphics (SIGGRAPH Asia), 2020
Summary: We introduce an automatic method for the fabrication of complex geometric objects. We start by decomposing them into bounded thickness 3-axis millable slices. Each slice is then milled and assembled to form the target object.
ACM Transactions on Graphics (SIGGRAPH), 2020
Summary: We propose Incremental Potential Contact (IPC) for robust and accurate time-stepping of nonlinear elastodynamics. IPC guarantees intersection- and inversion-free trajectories regardless of materials, time step sizes, velocities, or deformation severity.
ACM Transactions on Graphics (SIGGRAPH), 2018
Summary: We introduce the first fully automatic pipeline for converting arbitrary 3D models into knit structures that can be animated with yarn-level simulation and fabricated via 3D printing.
ACM Transactions on Graphics (SIGGRAPH Asia), 2017
Summary: We present seam-aware mesh processing techniques that eliminate seam artifacts in textures and decimate a mesh, including its seams, while preserving its parameterization and seam-free appearance. This allows the artifact-free display of surface signals (color, normals, positions, displacements, skin weights) with the standard GPU rendering pipeline.