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. We are working further to apply our method to applications in robotics and reinforcement learning.

Publications

A Cross-Platform Benchmark for Interval Computation Libraries

Xuan Tang, Zachary Ferguson, Teseo Schneider, Denis Zorin, Shoaib Kamil, Daniele Panozzo

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.

LibHip: An open-access hip joint model repository suitable for finite element method simulation

Faezeh Moshfeghifar, Torkan Gholamalizadeh, Zachary Ferguson, Teseo Schneider, Michael Bachmann Nielsen, Daniele Panozzo, Sune Darkner, Kenny Erleben

Computer Methods and Programs in Biomedicine

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.

Open-Full-Jaw: An open-access dataset and pipeline for finite element models of human jaw

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

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.

Fast and Exact Root Parity for Continuous Collision Detection

Bolun Wang, Zachary Ferguson, Xin Jiang, Marco Attene, Daniele Panozzo, Teseo Schneider

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 error.

Intersection-free Rigid Body Dynamics

Zachary Ferguson, Minchen Li, Teseo Schneider, Francisca Gil-Ureta, Timothy Langlois, Chenfanfu Jiang, Denis Zorin, Danny M. Kaufman, Daniele Panozzo

ACM Transactions on Graphics (SIGGRAPH 2021)

Summary: We introduce the first algorithm for time-stepping rigid body dynamics, with contacts and friction, that guarantees intersection-free configurations at every time step. Additionally, we propose a novel collision detection algorithm for curved trajectories.

A Large Scale Benchmark and an Inclusion-Based Algorithm for Continuous Collision Detection

Bolun Wang*, Zachary Ferguson*, Teseo Schneider, Xin Jiang, Marco Attene, Daniele Panozzo (*Joint first authors)

ACM Transactions on Graphics (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.

DHFSlicer: Double Height-Field Slicing For Milling Fixed Thickness Materials

Jinfan Yang, Chrystiano Araújo, Nicholas Vining, Zachary Ferguson, Enrique Rosales, Daniele Panozzo, Sylvain Lefebvre, Paolo Cignoni, Alla Sheffer

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.

Incremental Potential Contact: Intersection- and Inversion-free, Large-Deformation Dynamics

Minchen Li, Zachary Ferguson, Teseo Schneider, Timothy Langlois, Denis Zorin, Daniele Panozzo, Chenfanfu Jiang, Danny M. Kaufman

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.

Stitch Meshing

Kui Wu, Xifeng Gao, Zachary Ferguson, Daniele Panozzo, Cem Yuksel

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.

Seamless: Seam erasure and seam-aware decoupling of shape from mesh resolution

Songrun Liu*, Zachary Ferguson*, Alec Jacobson, Yotam Gingold (*Joint first authors)

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.