Paul G. Kry
Associate Professor

Contact
 
School of Computer Science, McGill University
3480 University Street
McConnell Building, Room 318
Montréal, QC, H3A 0E9
Canada

office: MC423
phone: +1 514 398 2577
email:
kry@ cs. mcgill.ca
   
Teaching

Courses for Fall 2024 and Winter 2025

  • COMP 557 Fall 2024, Fundamentals of Computer Graphics
  • COMP 602 Fall 2024, Computer Science Seminar 1
  • COMP 604 Fall 2024, Graduate School Fundamentals
  • COMP 603 Winter 2025, Computer Science Seminar 2
  • COMP 273 Fall 2024, Introduction to Computer Systems.

Note that COMP 559 will not be offered in Winter 2025, but will return in Winter 2026.

+ Previous Courses 

Research Interests and Information

My research interests include computer graphics, physically based animation, skin deformations of articulated characters, motion capture, interaction, and physically based modeling of humans and animals. I am specifically interested in human and animal motor control (e.g., locomotion, grasping, manipulation) in combination with natural phenomena such as the physics of rigid objects, deformation, and contact. Example application areas include computer animation for video games and movies, training simulations, ergonomics, and biologically inspired robotics and programming by demonstration. An important aspect of my work is the combination of real world measurements, approximate models, and physically based simulation. I am also interested in machine learning, numerical methods, and audio.

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+ Current and Previous Students and Lab Members 

+ Computer Animation and Interaction Capture Lab 

+ Workshops 

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McGill University Computer Animation Research YouTube Channel


Research Projects and Selected Publications  



Cone-Traced Supersampling with Subpixel Edge Reconstruction
A Chubarau, Y Zhao, R Rao, D Nowrouzezahrai, PG Kry
IEEE TVCG, 2023
While signed distance fields (SDFs) in theory offer infinite level of detail, they are typically rendered using the sphere tracing algorithm at finite resolutions, which causes the common rasterized image synthesis problem of aliasing. Most existing optimized antialiasing solutions rely on polygon mesh representations; SDF-based geometry can only be directly antialiased with the computationally expensive supersampling or with post-processing filters that may produce undesirable blurriness and ghosting. In this work, we present cone-traced supersampling (CTSS), an efficient and robust spatial antialiasing solution that naturally complements the sphere tracing algorithm, does not require casting additional rays per pixel or offline prefiltering, and can be easily implemented in existing real-time SDF renderers. CTSS performs supersampling along the traced ray near surfaces with partial visibility – object contours – identified by evaluating cone intersections within a pixel's view frustum. We further introduce subpixel edge reconstruction (SER), a technique that extends CTSS to locate and resolve complex pixels with geometric edges in relatively flat regions, which are otherwise undetected by cone intersections. Our combined solution relies on a specialized sampling strategy to minimize the number of shading computations and correlates sample visibility to aggregate the samples. With comparable antialiasing quality at significantly lower computational cost, CTSS is a reliable practical alternative to conventional supersampling.

DOI



Reconstruction of Machine-Made Shapes from Bitmap Sketches
I Puhachov, C Martens, PG Kry, M Bessmeltsev
ACM Transactions on Graphics (SIGGRAPH Asia), 2023
We propose a method of reconstructing 3D machine-made shapes from bitmap sketches by separating an input image into individual patches and jointly optimizing their geometry. We rely on two main observations: (1) human observers interpret sketches of man-made shapes as a collection of simple geometric primitives, and (2) sketch strokes often indicate occlusion contours or sharp ridges between those primitives. Using these main observations we design a system that takes a single bitmap image of a shape, estimates image depth and segmentation into primitives with neural networks, then fits primitives to the predicted depth while determining occlusion contours and aligning intersections with the input drawing via optimization. Unlike previous work, our approach does not require additional input, annotation, or templates, and does not require retraining for a new category of man-made shapes. Our method produces triangular meshes that display sharp geometric features and are suitable for downstream applications, such as editing, rendering, and shading.

PAPER



AdaptNet: Policy Adaptation for Physics-Based Character Control
P Xu, K Xie, S Andrews, PG Kry, M. Neff, M. McGuire, I Karamouzas, V. Zordan
ACM Transactions on Graphics (SIGGRAPH Asia), 2023
Motivated by humans' ability to adapt skills in the learning of new ones, this paper presents AdaptNet, an approach for modifying the latent space of existing policies to allow new behaviors to be quickly learned from like tasks in comparison to learning from scratch. Building on top of a given reinforcement learning controller, AdaptNet uses a two-tier hierarchy that augments the original state embedding to support modest changes in a behavior and further modifies the policy network layers to make more substantive changes. The technique is shown to be effective for adapting existing physics-based controllers to a wide range of new styles for locomotion, new task targets, changes in character morphology and extensive changes in environment. Furthermore, it exhibits significant increase in learning efficiency, as indicated by greatly reduced training times when compared to training from scratch or using other approaches that modify existing policies.

LINK



Data-Free Learning of Reduced-Order Kinematics
N Sharp, C Romero, A Jacobson, E Vouga, PG Kry, DIW Levin, J Solomon
ACM Transactions on Graphics (SIGGRAPH), 2023
Physical systems ranging from elastic bodies to kinematic linkages are defined on high-dimensional configuration spaces, yet their typical low-energy configurations are concentrated on much lower-dimensional subspaces. This work addresses the challenge of identifying such subspaces automatically: given as input an energy function for a high-dimensional system, we produce a low-dimensional map whose image parameterizes a diverse yet low-energy submanifold of configurations. The only additional input needed is a single seed configuration for the system to initialize our procedure; no dataset of trajectories is required. We represent subspaces as neural networks that map a low-dimensional latent vector to the full configuration space, and propose a training scheme to fit network parameters to any system of interest. This formulation is effective across a very general range of physical systems; our experiments demonstrate not only nonlinear and very low-dimensional elastic body and cloth subspaces, but also more general systems like colliding rigid bodies and linkages. We briefly explore applications built on this formulation, including manipulation, latent interpolation, and sampling.

LINK



Temporal Set Inversion for Animated Implicits
K Jazar, PG Kry
ACM Transactions on Graphics (SIGGRAPH), 2023
We exploit the temporal coherence of closed-form animated implicit surfaces by locally re-evaluating an octree-like discretization of the implicit field only as and where is necessary to rigorously maintain a global error invariant over time, thereby saving resources in static or slowly-evolving areas far from the motion where per-frame updates are not necessary. We treat implicit surface rendering as a special case of the continuous constraint satisfaction problem of set inversion, which seeks preimages of arbitrary sets under vector-valued functions. From this perspective, we formalize a temporally-coherent set inversion algorithm that localizes changes in the field by range-bounding its time derivatives using interval arithmetic. We implement our algorithm on the GPU using persistent thread scheduling and apply it to the scalar case of implicit surface and swept volume rendering where we achieve significant speedups in complex scenes with localized deformations like those found in games and modelling applications where interactivity is required and bounded-error approximation is acceptable.

LINK



Too Stiff, Too Strong, Too Smart: Evaluating Fundamental Problems with Motion Control Policies
K Xie, P Xu, S Andrews, VB Zordan, PG Kry
Symposium on Comptuer Animation (SCA/PACM), 2023
Deep reinforcement learning (DRL) methods have demonstrated impressive results for skilled motion synthesis of physically based characters, and while these methods perform well in terms of tracking reference motions or achieving complex tasks, several concerns arise when evaluating the naturalness of the motion. In this paper, we conduct a preliminary study of specific quantitative metrics for measuring the naturalness of motion produced by DRL control policies beyond their visual appearance. Namely, we propose to study the stiffness of the control policy, in anticipation that it will influence how the character behaves in the presence of external perturbation. Second, we establish two baselines for strength that allow evaluating the use of joint torques in comparison to human performance. Third, we propose the study of variability to reveal the unnatural precision of control policies and how they compare to real human motion. In sum, we aim to establish repeatable measures to assess the naturalness of control policies produced by DRL methods, and we present a set of comparisons from state-of-the-art systems. Finally, we propose simple modifications to improve realism on these axes.

LINK



Adaptive Rigidification of Discrete Shells
A Mercier-Aubin, PG Kry
Symposium on Computer Animation (SCA/PACM), 2023
We present a method to improve the computation time of thin shell simulations by using adaptive rigidification to reduce the number of degrees of freedom. Our method uses a discretization independent metric for bending rates, and we derive a membrane strain rate to curvature rate equivalence that permits the use of a common threshold. To improve accuracy, we enhance the elastification oracle by considering both membrane and bending deformation to determine when to rigidify or elastify. Furthermore, we explore different approaches that are compatible with the previous work on adaptive rigidifcation and enhance the accuracy of the elastification on new contacts without increasing the computational overhead. Additionally, we propose a scaling approach that reduces the conditioning issues that arise from mixing rigid and elastic bodies in the same model.

LINK



On Understanding Disentanglement Puzzles
X Zhang, PG Kry, E Vouga
Bridges, 2023
Rigid disentanglement puzzles are fascinating brainteasers consisting of two or more rigid (usually metal) pieces. The puzzle begins in a tangled state, and the goal is to separate the pieces through a sequence of rigid motions; interest in these puzzles comes from the juxtaposition of the small number of pieces and the complex, unintuitive steps needed to disentangle them. The prototypical rigid disentanglement puzzle is the alpha puzzle. Separating its two pieces requires a twist after aligning the gaps in each loop; despite the geometric simplicity of the pieces, the required twist motion is counter-intuitive. The same is not true for, e.g., separating a nut screwed onto a bolt: unscrewing the nut requires a long, twisty screw motion, but few humans would characterize this process as solving a puzzle.

LINK



Cone-Traced Supersampling for Signed Distance Field Rendering
A Chubarau, Y Zhao, R Rao, PG Kry, D Nowrouzezahrai
Graphics Interface, 2023

BEST PAPER
While Signed Distance Fields (SDFs) in theory offer infinite level of detail, they are typically rendered using the sphere tracing algorithm at finite resolutions, which causes the common rasterized image synthesis problem of aliasing. Most existing optimized antialiasing solutions rely on polygon mesh representations; SDF-based geometry can only be directly antialiased with the computationally expensive supersampling or with post-processing filters that often lead to undesirable blurriness and ghosting. In this work, we present cone-traced supersampling (CTSS), an efficient and robust spatial antialiasing solution that naturally complements the sphere tracing algorithm, does not require casting additional rays per pixel or offline pre-filtering, and can be easily implemented in existing real-time SDF renderers. CTSS performs supersampling along the traced ray near surfaces with partial visibility identified by evaluating cone intersections within a pixel's view frustum. We further devise a specialized sampling strategy to minimize the number of shading computations and aggregate the collected samples based on their correlated visibility. Depending on configuration, CTSS incurs roughly 15-30% added computational cost and significantly outperforms conventional supersampling approaches while offering comparative antialiasing and visual image quality for most geometric edges.

LINK



Parallel Block Neo-Hookean XPBD using Graph Clustering
QM Ton-That, PG Kry, S Andrews
Computers & Graphics (MIG), 2022
The eXtended Position Based Dynamics algorithm (XPBD) enables unified simulation of various materials from fluids to both elastic solids and stiff solids. In particular, finite element based neo-Hookean models can simulate near incompressible materials by means of a decoupled compliant constraint formulation. Due to XPBD’s reliance on local constraint projections in the solver loop, its computational nature lends itself to parallelization by means of graph coloring algorithms used to determine partitions of independent constraints which can be solved simultaneously. However, minimal graph coloring is bounded from below by the maximum valence of the finite element mesh, thus hindering parallelization opportunities. In this paper, we propose a novel graph clustering approach on the constraint graph which groups highly dependent constraints into supernodes. By applying graph coloring on the supernodal constraint graph, we are able to significantly reduce the number of partitions, thus enhancing parallelization of the solver. Furthermore, we accelerate convergence of the neo-Hookean XPBD solver by a coupled constraint formulation, resulting in enhanced stability and efficiency compared to previous approaches.

LINK



Differentiable Depth for Real2Sim Calibration of Soft Body Simulations
K Arnavaz, M Kragballe Nielsen, PG Kry, M Macklin, K Erleben
Computer Graphics Forum, 2022
In this work, we present a novel approach for calibrating material model parameters for soft body simulations using real data. We use a fully differentiable pipeline, combining a differentiable soft body simulator and differentiable depth rendering, which permits fast gradient-based optimizations. Our method requires no data pre-processing, and minimal experimental set-up, as we directly minimize the L2-norm between raw LIDAR scans and rendered simulation states. In essence, we provide the first marker-free approach for calibrating a soft-body simulator to match observed real-world deformations. Our approach is inexpensive as it solely requires a consumer-level LIDAR sensor compared to acquiring a professional marker-based motion capture system. We investigate the effects of different material parameterizations and evaluate convergence for parameter optimization in both single and multi-material scenarios of varying complexity. Finally, we show that our set-up can be extended to optimize for dynamic behaviour as well.

DOI



Constraint-based Simulation of Passive Suction Cups
A Bernardin, E Coevoet, PG Kry, S Andrews, C Duriez, M Marchal
ACM Transactions on Graphics (TOG), 2022
In this paper, we propose a physics-based model of suction phenomenon to achieve simulation of deformable objects like suction cups. Our model uses a constraint-based formulation to simulate the variations of pressure inside suction cups. The respective internal pressures are represented as pressure constraints which are coupled with anti-interpenetration and friction constraints. Furthermore, our method is able to detect multiple air cavities using information from collision detection. We solve the pressure constraints based on the ideal gas law while considering several cavity states. We test our model with a number of scenarios reflecting a variety of uses, for instance, a spring loaded jumping toy, a manipulator performing a pick and place task, and an octopus tentacle grasping a soda can. We also evaluate the ability of our model to reproduce the physics of suction cups of varying shapes, lifting objects of different masses, and sliding on a slippery surface. The results show promise for various applications such as the simulation in soft robotics and computer animation.

LINK
DOI



Adaptive rigidification of elastic solids
A Mercier-Aubin, A Winter, PG Kry, DIW Levin
ACM Transactions on Graphics (SIGGRAPH), 2022
We present a method for reducing the computational cost of elastic solid simulation by treating connected sets of non-deforming elements as rigid bodies. Non-deforming elements are identified as those where the strain rate squared Frobenius norm falls below a threshold for several frames. Rigidification uses a breadth first search to identify connected components while avoiding connections that would form hinges between rigid components. Rigid elements become elastic again when their approximate strain velocity rises above a threshold, which is fast to compute using a single iteration of conjugate gradient with a fixed Laplacian-based incomplete Cholesky preconditioner. With rigidification, the system size to solve at each time step can be greatly reduced, and if all elastic element become rigid, it reduces to solving the rigid body system. We demonstrate our results on a variety of 2D and 3D examples, and show that our method is likewise especially beneficial in contact rich examples.

PROJECT PAGE
CODE
DOI



Active Learning Neural C-space Signed Distance Fields for Reduced Deformable Self-Collision
X Cai, E Coevoet, A Jacobson, PG Kry
Graphics Interface (GI), 2022
We present a novel method to preprocess a reduced model, training a neural network to approximate the reduced model signed distance field using active learning technique. The trained neural network is used to evaluate the self-collision state as well as the self-collision handling during real time simulation. Our offline learning approach consists of two passes of learning. The first pass learning generates positive and negative point cloud which is used in the second pass learning to learn the signed distance field of reduced subspace. Unlike common fully supervised learning approaches, we make use of semi-supervised active learning technique in generating more informative samples for training, improving the convergence speed. We also propose methods to use the learned SDF function in real time self-collision detection and assemble it in the constraint Jacobian matrix to solve the self-collision.

OPEN REVIEW PAGE
DOI



Catching and throwing control of a physically simulated hand
Y Luo, K Xie, S Andrews, PG Kry
Motion, Interaction and Games (MIG), 2021
We design a nominal controller for animating an articulated physics-based human arm model, including the hands and fingers, to catch and throw objects. The controller is based on a finite state machine that defines the target poses for proportional-derivative control of the hand, as well as the orientation and position of the center of the palm using the solution of an inverse kinematics solver. We then use reinforcement learning to train agents to improve the robustness of the nominal controller for achieving many different goals. Imitation learning based on trajectories output by a numerical optimization is used to accelerate the training process. The success of our controllers is demonstrated by a variety of throwing and catching tasks, including flipping objects, hitting targets, and throwing objects to a desired height, and for several different objects, such as cans, spheres, and rods. We also discuss ways to extend our approach so that more challenging tasks, such as juggling, may be accomplished.

PROJECT PAGE
DOI



Coupling friction with visual appearance
S Andrews, L Nassif, K Erleben, PG Kry
Symposium on Computer Animation (SCA/PACM), 2021
We present a novel meso-scale model for computing anisotropic and asymmetric friction for contacts in rigid body simulations that is based on surface facet orientations. The main idea behind our approach is to compute a direction dependent friction coefficient that is determined by an object's roughness. Specifically, where the friction is dependent on asperity interlocking, but at a scale where surface roughness is also a visual characteristic of the surface. A GPU rendering pipeline is employed to rasterize surfaces using a shallow depth orthographic projection at each contact point in order to sample facet normal information from both surfaces, which we then combine to produce direction dependent friction coefficients that can be directly used in typical LCP contact solvers, such as the projected Gauss-Seidel method. We demonstrate our approach with a variety of rough textures, where the roughness is both visible in the rendering and in the motion produced by the physical simulation.

PROJECT PAGE
DOI



Global Position Prediction for Interactive Motion Capture
P Schreiner, M Perepichka, H Lewis, S Darkner, PG Kry, K Erleben, V Zordan
Symposium on Comptuer Animation (SCA/PACM), 2021
We present a method for reconstructing the global position of motion capture where position sensing is poor or unavailable. Capture systems, such as IMU suits, can provide excellent pose and orientation data of a capture subject, but otherwise need post processing to estimate global position. We propose a solution that trains a neural network to predict, in real-time, the height and body displacement given a short window of pose and orientation data. Our training dataset contains pre-recorded data with global positions from many different capture subjects, performing a wide variety of activities in order to broadly train a network to estimate on like and unseen activities. We compare training on two network architectures, a universal network (u-net) and a traditional convolutional neural network (CNN) - observing better error properties for the u-net in our results. We also evaluate our method for different classes of motion. We observe high quality results for motion examples with good representation in specialized datasets, while general performance appears better in a more broadly sampled dataset when input motions are far from training examples.

PREPRINT
DOI



Inverse Dynamics Filtering for Sampling-based Motion Control
K Xie, PG Kry, Computer Graphics Forum (CGF), 2021
We improve the sampling-based motion control method proposed by Liu et al. using inverse dynamics. To deal with noise in the motion capture we filter the motion data using a Butterworth filter where we choose the cutoff frequency such that the zero-moment point falls within the support polygon for the greatest number of frames. We discuss how to detect foot contact for foot and ground optimization and inverse dynamics, and we optimize to increase the area of supporting polygon. Sample simulations receive filtered inverse dynamics torques at frames where the ZMP is sufficiently close to the support polygon, which simplifies the problem of finding the PD targets that produce physically valid control matching the target motion. We test our method on different motions and we demonstrate that our method has lower error, higher success rates, and generally produces smoother results.

PREPRINT
DOI



Learning Elastic Constitutive Material and Damping Models
B Wang, Y Deng, PG Kry, U Ascher, H Huang, B Chen Pacific Graphics (CGF), 2020
Commonly used linear and nonlinear constitutive material models in deformation simulation contain many simplifications and only cover a tiny part of possible material behavior. In this work we propose a framework for learning customized models of deformable materials from example surface trajectories. The key idea is to iteratively improve a correction to a nominal model of the elastic and damping properties of the object, which allows new forward simulations with the learned correction to more accurately predict the behavior of a given soft object. Space-time optimization is employed to identify gentle control forces with which we extract necessary data for model inference and to finally encapsulate the material correction into a compact parametric form. Furthermore, a patch based position constraint is proposed to tackle the challenge of handling incomplete and noisy observations arising in real-world examples. We demonstrate the effectiveness of our method with a set of synthetic examples, as well with data captured from real world homogeneous elastic objects.

PROJECT PAGE
DOI
SUPPLEMENTARY VIDEO
PREVIOUS NEURAL MATERIAL WORK



Distant Collision Response in Rigid Body Simulations
E Coevoet, S Andrews, D Relles, PG Kry SCA, 2020
We use a finite element model to predict the vibration response of objects in a rigid body simulation, such that rigid objects are augmented to provide a plausible elastic collision response between distant objects due to vibration. We start with a generalized eigenvalue decomposition of the elastic model to precompute a response to an impact at any point on an elastic object with fixed boundary conditions. Then, given a collision between objects, we generate an approximate response impulse to distribute to other objects already in contact with the colliding bodies. This can lead to distant impacts causing an object to slip, or a delicate stack of objects to fall. We also use a geodesic distance based spatial attenuation approximation for traveling waves in objects to respond to an impact at one contact with an impulse at other locations. This response ultimately allows a long distance relationship between contacts, both across a single object being struck, but also traversing the contact graph of a larger collection of objects. We qualitatively validate our approach with a ground truth simulation, and demonstrate a number of scenarios where a long distance relationship between contacts is valuable.

PROJECT PAGE
DOI
SUPPLEMENTARY VIDEO
PRESENTATION VIDEO
SUMMARY VIDEO



Adaptive Merging for Rigid Body Simulation
E Coevoet, O. Benchekroun, PG Kry SIGGRAPH, 2020
We reduce computation time in rigid body simulations by merging collections of bodies when they share a common spatial velocity. Merging relies on monitoring the state of contacts, and a metric that compares the relative linear and angular motion of bodies based on their sizes. Unmerging relies on an inexpensive single iteration projected Gauss-Seidel sweep over contacts between merged bodies, which lets us update internal contact forces over time, and use the same metrics as merging to identify when bodies should unmerge. Furthermore we use a contact ordering for graph traversal refinement of the internal contact forces in collections, which helps to correctly identify all the bodies that must unmerge when there are impacts. The general concept of merging is similar to the common technique of sleeping and waking rigid bodies in the inertial frame, and we exploit this too, but our merging is in moving frames, and unmerging takes place at contacts between bodies rather than at the level of bodies themselves. We discuss the previous relative motion metrics in comparison to ours, and evaluate our method on a variety of scenarios.

PROJECT PAGE
DOI
SUPPLEMENTARY VIDEO



C-Space Tunnel Discovery for Puzzle Path Planning
X Zhang, R. Belfer, PG Kry, E. Vouga SIGGRAPH, 2020
Rigid body disentanglement puzzles are challenging for both humans and motion planning algorithms because their solutions involve tricky twisting and sliding moves that correspond to navigating through narrow tunnels in the puzzle's configuration space (C-space). We propose a tunnel-discovery and planning strategy for solving these puzzles. First, we locate important features on the pieces using geometric heuristics and machine learning, and then match pairs of these features to discover collision free states in the puzzle's C-space that lie within the narrow tunnels. Second, we propose a Rapidly-exploring Dense Tree (RDT) motion planner variant that builds tunnel escape roadmaps and then connects these roadmaps into a solution path connecting start and goal states. We evaluate our approach on a variety of challenging disentanglement puzzles and provide extensive baseline comparisons with other motion planning techniques.

PROJECT PAGE
DOI
PRESENTATION VIDEO
SUPPLEMENTARY VIDEO
FF VIDEO



Schur complement-based substructuring of stiff multibody systems with contact
 A Peiret, S Andrews, J Kövecses, PG Kry, M Teichmann SIGGRAPH Asia, 2019
We investigate a procedural shape modeling approach based on reaction-diffusion equations and physically based growth of thin shells. This inspiration of this work comes from the morphological development of living tissues, such as plants leaves. There are numerous choices that can be made in assembling a computer simulation of these growth system. We explore two main approaches, one where a reaction-diffusion simulation is first run with the results used to identify regions of growth, and the other where we simulate shell growth concurrently with a reaction-diffusion simulation in the manifold. We demonstrate that a variety of interesting shapes can be grown in this manner, and provide some intuition to the challenging problem of associating changes in parameter settings with the final shape.

PAPER
VIDEO
DOI



The Matchstick Model for Anisotropic Friction Cones
 K. Erleben, M. Macklin, S. Andrews, P. G. Kry Computer Graphics Forum, 2020
Inspired by frictional behaviour that is observed when sliding matchsticks against one another at different angles, we propose a phenomenological anisotropic friction model for structured surfaces. Our model interpolates isotropic and anisotropic elliptical Coulomb friction parameters for a pair of surfaces with perpendicular and parallel structure directions (e.g., the wood grain direction). We view our model as a special case of an abstract friction model that produces a cone based on state information, specifically the relationship between structure directions. We show how our model can be integrated into LCP and NCP based simulators using different solvers with both explicit and fully implicit time-integration. The focus of our work is on symmetric friction cones, and we therefore demonstrate a variety of simulation scenarios where the friction structure directions play an important part in the resulting motions. Consequently, authoring of friction using our model is intuitive and we demonstrate that our model is compatible with standard authoring practices, such as texture mapping.

PAPER
VIDEO
DOI



Procedural Modelling with Reaction Diffusion and Growth of Thin Shells
 C. Gingras, P. G. Kry Graphics Interface, 2019
We investigate a procedural shape modeling approach based on reaction-diffusion equations and physically based growth of thin shells. This inspiration of this work comes from the morphological development of living tissues, such as plants leaves. There are numerous choices that can be made in assembling a computer simulation of these growth system. We explore two main approaches, one where a reaction-diffusion simulation is first run with the results used to identify regions of growth, and the other where we simulate shell growth concurrently with a reaction-diffusion simulation in the manifold. We demonstrate that a variety of interesting shapes can be grown in this manner, and provide some intuition to the challenging problem of associating changes in parameter settings with the final shape.

PAPER
DOI



Automated Acquisition of Anisotropic Friction
 K. Dreßel, K. Erleben, P. G. Kry, S. Andrews, Computer and Robot Vision, 2019
Automated acquisition of friction data is an interesting approach to more successfully bridge the reality gap in simulation than conventional mathematical models. To advance this area of research, we present a novel inexpensive computer vision platform as a solution for collecting and processing friction data, and we make available the open source software and data sets collected with our vision robotic approach. This paper is focused on gathering data on anisotropic static friction behavior as this is ideal for inexpensive vision approach we propose. The data set and experimental setup provide a solid foundation for a wider robotics simulation community to conduct their own experiments.

PAPER
DOI



Fast non-uniform radiance probe placement and tracing
 Y. Wang, S. Khiat, P. G. Kry, D. Nowrouzezahrai, ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games, 2019,
BEST STUDENT PRESENTATION
Light field probes extend standard precomputed light probes to reduce light leaks and enable efficient filtered world-space ray tracing queries. When probes are placed uniformly in the scene volume, they permit an efficient querying algorithm. Manually increasing the grid resolution, however, is the only way to eliminate geometric feature undersampling, increasing the memory and computation cost of the approach. We present an automatic non-uniform probe placement method to correctly sample visibility information and eliminate superfluous probes. We organize non-uniform probes in an efficient structure for fast run-time ray tracing. Our probe placement relies on 3D scene skeletons and a gradient descent-based refinement to achieve full geometric coverage and reduce grazing angle sampling biases. Our adaptive probe ray tracer caches visibility information in a sparse voxel octree, augmenting probes with metadata used to apply a hierarchical-Z acceleration when marching rays in distant probes. We benchmark our approach on a variety of scenes and consistently demonstrate better performance, and fewer probes, in equal-quality comparisons to the state-of-the-art.

PAPER
VIDEO
DOI



Single stroke aerial robot light painting
 K. Ren, P. G. Kry, Expressive Graphics, 2019
This paper investigates trajectory generation alternatives for creating single-stroke light paintings with a small quadrotor robot. We propose to reduce the cost of a minimum snap piecewise polynomial quadrotor trajectory passing through a set of waypoints by displacing those waypoints towards or away from the camera while preserving their projected position. It is in regions of high curvature, where waypoints are close together, that we make modifications to reduce snap, and we evaluate two different strategies: one that uses a full range of depths to increase the distance between close waypoints, and another that tries to keep the final set of waypoints as close to the original plane as possible. Using a variety of one-stroke animal illustrations as targets, we evaluate and compare the cost of different optimized trajectories, and discuss the qualitative and quantitative quality of flights captured in long exposure photographs.

PAPER
PRESENTATION
VIDEO
DOI
POSTER at ICRA-X 2019



Defocus Discrimination in Video: Motion in Depth
V. A. Petrella, S. Labute, M. S. Langer, P. G. Kry, i-Perception, 2017
We perform two psychophysics experiments to investigate a viewer’s ability to detect defocus in video; in particular, the defocus that arises in video during motion in depth when the camera does not maintain sharp focus throughout the motion. The first experiment demonstrates that blur sensitivity during viewing is affected by the speed at which the target moves towards the camera. The second experiment measures a viewer’s ability to notice momentary defocus and shows that the threshold of blur detection in arc minutes decreases significantly as the duration of the blur increases. Our results suggest that it is important to have good control of focus while recording video and that momentary defocus should be kept as short as possible so it goes unnoticed.

PAPER
SAGE
DOI



Tethered flight control of a small quadrotor robot for stippling
B. Galea, P. G. Kry, IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2017
We investigate tethered flight of a small quadrotor robot in the context of creating stippled prints. At a low level, we use motion capture to measure the position of the robot and the canvas, and a robust control algorithm to command the robot to fly to different stipple positions to make contact with the canvas using an ink soaked sponge. With the objective of fully autonomous flight, we power our quadrotor using a wired tether. We compensate for the tether in our control of the robot by assuming a static catenary curve of fixed length between the robot and the power source. We evaluate accuracy of hovering and flight on simple paths, and compare the results to untethered flight.

PAPER
VIDEO
DOI



Task-based design of cable-driven articulated mechanisms
 J. Li, S. Andrews, K. Birkas, P. G. Kry, Symposium on Computational Fabrication, 2017
We present a framework for the automatic design of articulated cable-driven mechanisms performing push and pick-and-place tasks. Provided an initial topology and task specification, our system optimizes the morphology and cable mechanisms such that the resulting mechanism can perform the desired task successfully. Optimizing for multiple tasks and multiple cables simultaneously is possible with our framework. At the core of our approach is an optimization algorithm that analyzes the kinematics of the design to evaluate the mechanism's ability to perform the task. Dynamical attributes, such as the ability to produce forces at the end effector, are also considered. Furthermore, this paper presents a novel approach for fast inverse kinematics using cable-driven mechanisms, which is used in the morphology optimization process. Several examples of mechanisms designed using our framework are presented. We also present results of physics based simulation, and evaluate 3D printed versions of an example mechanism.

PAPER
VIDEO
PROJECT PAGE
DOI



Geometric Stiffness for Real-time Constrained Multibody Dynamics
 S. Andrews, M. Teichmann, P. G. Kry, Eurographics, 2017
This paper focuses on the stable and efficient simulation of articulated rigid body systems for real-time applications. Specifically, we focus on the use of geometric stiffness, which can dramatically increase simulation stability. We examine several numerical problems with the inclusion of geometric stiffness in the equations of motion, as proposed by previous work, and address these issues by introducing a novel method for efficiently building the linear system. This offers improved tractability and numerical efficiency. Furthermore, geometric stiffness tends to significantly dissipate kinetic energy. We propose an adaptive damping scheme, inspired by the geometric stiffness, that uses a stability criterion based on the numerical integrator to determine the amount of non-constitutive damping required to stabilize the simulation. With this approach, not only is the dynamical behavior better preserved, but the simulation remains stable for mass ratios of 1,000,000-to-1 at time steps up to 0.1 s. We present a number of challenging scenarios to demonstrate that our method improves efficiency, and that it increases stability by orders of magnitude compared to previous work.

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Tunable Robustness: An Artificial Contact Strategy with Virtual Actuator Control for Balance
 D. B. da Silva, R. F. Nunes, C. A. Vidal, J. B. Cavalcante-Neto, P. G. Kry, V. B. Zordan, Computer Graphics Forum, 2017
Physically based characters have not yet received wide adoption in the entertainment industry because control remains both difficult and unreliable. Even with the incorporation of motion capture for reference, which adds believability, characters fail to be convincing in their appearance when the control is not robust. To address these issues, we propose a simple Jacobian transpose torque controller that employs virtual actuators to create a fast and reasonable tracking system for motion capture. We combine this controller with a novel approach we call the topple-free foot (TFF) strategy which conservatively applies artificial torques to the standing foot to produce a character that is capable of performing with arbitrary robustness. The system is both easy to implement and straightforward for the animator to adjust to the desired robustness, by considering the trade off between physical realism and stability. We showcase the benefit of our system with a wide variety of example simulations, including energetic motions with multiple support contact changes, such as capoeira, as well as an extension that highlights the approach coupled with a Simbicon controlled walker. With this work, we aim to advance the state-of-the-art in the practical design for physically based characters that can employ unaltered reference motion (e.g., motion capture data) and directly adapt it to a simulated environment without the need for optimization or inverse dynamics.

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Postural regulation and motion simulation in rock climbing
 F. Quaine, L. Reveret, S. Courtemanche, P. G. Kry, The Science of Climbing and Mountaineering, Chapter 7, 2017
The objective of this chapter is to understand the biomechanics of rock climbing based on the forces applied at each support. The mechanical principles of rock climbing biomechanics are presented first and adapted with different climbing devices used to measure the contact forces. A computational method is presented to overcome the need for a climbing device equipped with three dimensional (3D) force sensors. A simulation method of 3D climbing movements is developed. The first part of this chapter describes the role of limbs in postural regulation during climbing. Notably, supporting forces depend on the posture of the climber, the number of supports and the climbing wall inclination. We discuss the transition between static postures and movement with dynamic motion of the limbs. The second part of the chapter focuses on the kinematics of rock climbing and introduces a modelling technique for estimating the support forces thanks to motion capture analysis.

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Ballistic Shadow Art
 X. Chen, S. Andrews, D. Nowrouzezahrai, P. G. Kry, Graphics Interface, 2017
We present a framework for generating animated shadow art using occluders under ballistic motion. We apply a stochastic optimization to find the parameters of a multi-body physics simulation that produce a desired shadow at a specific instant in time. We perform simulations across many different initial conditions, applying a set of carefully crafted energy functions to evaluate the motion trajectory and multi-body shadows. We select the optimal parameters, resulting in a ballistics simulation that produces ephemeral shadow art. Users can design physically-plausible dynamic artwork that would be extremely challenging if even possible to achieve manually. We present and analyze number of compelling examples.

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Anticipatory balance control and dimension reduction
 A. H. Rabbani, M. van de Panne, P. G. Kry, Computer animation & virtual worlds, 2016
A hallmark of many skilled motions is the anticipatory nature of the balance-related adjustments that happen in preparation for the expected evolution of forces during the motion. This can shape simulated and animated motions in subtle but important ways, help lend physical credence to the motion, and help signal the character's intent. In this article, we investigate how center-of-mass reference trajectories (CMRTs) can be learned so as to achieve anticipatory balance control with a state-of-the-art reactive balancing system. This enables the design of physics-based motion simulations that involve fast pose transitions as well as force-based interactions with the environment, such as punches, pushes, and catching heavy objects. We also show that generating CMRTs in a reduced space may result in faster computation times for similar task motions that deal with environmental interactions. We demonstrate the results on planar human models and show that CMRTs generalize well across parameterized versions of a motion. We illustrate that they are also effective at conveying a mismatch between a character's expectations and reality, for example, thinking that an object is heavier than it is.

WILEY PAGE
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Adaptive semi-implicit integrator for articulated rigid-body systems
 J. Hewlett, L. Kovacs, A. Callejo, P. G. Kry, J. Kövecses, J. Angeles, ASME Journal of Computational and Nonlinear Dynamics, 2017
This paper concerns the dynamic simulation of constrained mechanical systems in the context of real-time applications and stable integrators. The goal is to adaptively find a balance between the stability of an over-damped implicit scheme and the energetic consistency of the symplectic, semi-implicit Euler scheme. As a starting point, we investigate in detail the properties of a recently proposed timestepping scheme, which approximates a full nonlinear implicit solution with a single linear system, without compromising stability. This scheme introduces a geometric stiffness term that improves numerical stability up to a certain time-step size, but it does so at the cost of large mechanical dissipation in comparison to the traditional constrained dynamics formulation. Dissipation is sometimes undesirable from a mechanical point of view, especially if the dissipation is not quantified. In this paper, we propose to use an additional control parameter to regulate “how implicit” the Jacobian matrix is, and change the degree to which the geometric stiffness term contributes. For the selection of this parameter, adaptive schemes are proposed based on the monitoring of energy drift. The proposed adaptive method is verified through the simulation of open-chain systems.

ASME.ORG
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Stippling with aerial robots
B. Galea, E. Kia, N. Aird, P. G. Kry, Computational Aesthetics / Expressive, 2016
BEST PAPER

We describe a method for creating stippled prints using a quadrotor flying robot. At a low level, we use motion capture to measure the position of the robot and the canvas, and a robust control algorithm to command the robot to fly to different stipple positions to make contact with the canvas using an ink soaked sponge. We describe a collection of important details and challenges that must be addressed for successful control in our implementation, including robot model estimation, Kalman filtering for state estimation, latency between motion capture and control, radio communication interference, and control parameter tuning. We use a centroidal Voronoi diagram to generate stipple drawings, and compute a greedy approximation of the traveling salesman problem to draw as many stipples per flight as possible, while accounting for desired stipple size and dynamically adjusting future stipples based on past errors. An exponential function models the natural decay of stipple sizes as ink is used in a flight. We evaluate our dynamic adjustment of stipple locations with synthetic experiments. Stipples per second and variance of stipple placement are presented to evaluate our physical prints and robot control performance.

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DefSense: Computational Design of Customized Deformable Input Devices
 M. Bächer, B. Hepp, F. Pece, P. G. Kry, B. Bickel, B. Thomaszewski, O. Hilliges ACM SIGCHI, 2016

We present a novel optimization-based algorithm for the design and fabrication of customized, deformable input devices, capable of continuously sensing their deformation. We propose to embed piezoresistive sensing elements into flexible 3D printed objects. These sensing elements are then utilized to recover rich and natural user interactions at runtime. Designing such objects manually is a challenging and hard problem for all but the simplest geometries and deformations. Our method simultaneously optimizes the internal routing of the sensing elements and computes a mapping from low-level sensor readings to user-specified outputs in order to minimize reconstruction error. We demonstrate the power and flexibility of the approach by designing and fabricating a set of flexible input devices. Our results indicate that the optimization based design greatly outperforms manual routings in terms of reconstruction accuracy and thus interaction fidelity.

PROJECT PAGE AT DRZ
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PhysIK: Physically plausible and intuitive keyframing
A. H. Rabbani, P. G. Kry, Graphics Interface, 2016

We present an approach for animating characters using inverse kinematics (IK) handles that allows for intuitive keyframing of physically plausible motion. Specifically, we extend traditional IK and keyframing to include center-of-mass (CM) and inertia handles along with physically based templates to help an animator produce trajectories that respect physics during dynamic activities, such as swinging, stepping, and jumping. Animators can easily control both posture and physics-based quantities (inertia shape, CM position, and linear momentum) when building motions from scratch, but also have complete freedom to create exaggerated or impossible motions. We present results for a variety of planar characters of different morphologies.

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Interactive procedural simulation of paper tearing with sound
T. Lejemble, A. Fondevilla, N. Durin, T. Blanc-Beyne, C. Schreck, P.-L. Manteaux, P. G. Kry, M.-P. Cani, Motion in Games, 2015

We present a phenomenological model for the real-time simulation of paper tearing and sound. The model uses as input rotations of the hand along with the index and thumb of left and right hands to drive the position and orientation of two regions of a sheet of paper. The motion of the hands produces a cone shaped deformation of the paper and guides the formation and growth of the tear. We create a model for the direction of the tear based on empirical observation, and add detail to the tear with a directed noise model. Furthermore, we present a procedural sound synthesis method to produce tearing sounds during interaction. We show a variety of paper tearing examples and discuss applications and limitations.

PROJECT PAGE AT INRIA
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Blended linear models for reduced compliant mechanical systems
S. Andrews, M. Teichmann, P. G. Kry, IEEE Transactions on Visualization and Computer Graphics, 2015

We present a method for the simulation of compliant, articulated structures using a plausible approximate model that focuses on modeling endpoint interaction. We approximate the structure's behavior about a reference configuration, resulting in a first order reduced compliant system, or FORKS. Several levels of approximation are available depending on which parts and surfaces we would like to have interactive contact forces, allowing various levels of detail to be selected. Our approach is fast and computation of the full structure's state may be parallelized. Furthermore, we present a method for reducing error by combining multiple FORKS models at different linearization points, through twist blending and matrix interpolation. Our approach is suitable for stiff, articulate grippers, such as those used in robotic simulation, or physics-based characters under static proportional derivative control. We demonstrate that simulations with our method can deal with kinematic chains and loops with non-uniform stiffness across joints, and that it produces plausible effects due to stiffness, damping, and inertia.

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6D Frictional Contact for Rigid Bodies
C. Bouchard, M. Nesme, M. Tournier, B. Wang, F. Faure, P. G. Kry, Graphics Interface, 2015

We present a new approach to modeling contact between rigid objects that augments an individual Coulomb friction point-contact model with rolling and spinning friction constraints. Starting from the intersection volume, we compute a contact normal from the volume gradient. We compute a contact position from the first moment of the intersection volume, and approximate the extent of the contact patch from the second moment of the intersection volume. By incorporating knowledge of the contact patch into a point contact Coulomb friction formulation, we produce a 6D constraint that provides appropriate limits on torques to accommodate displacement of the center of pressure within the contact patch, while also providing a rotational torque due to dry friction to resist spinning. A collection of examples demonstrate the power and benefits of this simple formulation.

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Anticipatory Balance Control
A. H. Rabbani, M. van de Panne, P. G. Kry, ACM SIGGRAPH Conference on Motion in Games, 2014, SELECTED FOR CAVW

A hallmark of many skilled motions is the anticipatory nature of the balance-related adjustments that happen in preparation for the expected evolution of forces during the motion. This can shape simulated and animated motions in subtle-but-important ways, help lend physical credence to the motion, and help signal the character's intent. In this paper, we investigate how center of mass reference trajectories (CMRTs) can be learned in order to achieve anticipatory balance control with a state-of-the-art reactive balancing system. This enables the design of physics-based motion simulations that involve fast pose transitions as well as force-based interactions with the environment, such as punches, pushes, and catching heavy objects. We demonstrate the results on planar human models, and show that CMRTs can generalize across parameterized versions of a motion. We illustrate that they are also effective at conveying a mismatch between a character's expectations and reality, e.g., thinking that an object is heavier than it is.

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Multi-layer skin simulation with adaptive constraints
P. Li, P. G. Kry, ACM SIGGRAPH Conference on Motion in Games, 2014

We present an approach for physics based simulation of the wrinkling of multi-layer skin with heterogeneous material properties. Each layer of skin is simulated with an adaptive mesh, with the different layers coupled via constraints that only permit wrinkle deformation at wavelengths that match the physical properties of the multi-layer model. We use texture maps to define varying elasticity and thickness of the skin layers, and design our constraints as continuous functions, which we discretize at run time to match the changing adaptive mesh topology. In our examples, we use blend shapes to drive the bottom layer, and we present a variety of examples of simulations that demonstrate small wrinkles on top of larger wrinkles, which is a typical pattern seen on human skin. Finally, we show that our physics-based wrinkles can be used in the automatic creation of wrinkle maps, allowing the visual details of our high resolution simulations to be produced at real time speeds.

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FORK-1S: Interactive compliant mechanisms with parallel state computation
 S. Andrews, M. Teichmann, P. G. Kry, ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games, 2014, SELECTED FOR TVCG

We present a method for the simulation of compliant, articulated structures using a plausible approximate model that focuses on modeling endpoint interaction. We approximate the structure's behavior about a reference configuration, resulting in a first order reduced compliant system, or
FORK-1S. Several levels of approximation are available depending on which parts and surfaces we would like to have interactive contact forces, allowing various levels of detail to be selected. Our approach is fast and computation of the full structure's state may be parallelized. Our approach is suitable for stiff, articulate grippers, such as those used in robotic simulation, or physics based characters under static proportional derivative control. We demonstrate that simulations with our method can deal with kinematic chains and loops with non-uniform stiffness across joints, and that it produces plausible effects due to stiffness, damping, and inertia.

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Data-driven Fingertip Appearance for Interactive Hand Simulation
S. Andrews, M. Jarvis, P. G. Kry, ACM SIGGRAPH conference on Motion in Games, 2013

Contact on a finger pad results in deformation that redistributes blood within the fingertip tissue in a manner correlated to the pressure. We build a data-driven model that relates contact information to the visible changes of the finger nail and surrounding tissue on the back of the finger tip. Our data analysis and model construction makes use of the space of hemoglobin concentrations, as opposed to an RGB color space, which permits the model to be transferred across different fingers and different people. We use principal component analysis to build a compact model which maps well to graphics hardware with an efficient fragment program implementation. We provide a validation of our model, and a demonstration of a grasping controller running in a physically based simulation, where grip strength is visible in both hand posture and the appearance of color changes at the fingertips.

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Embedded Thin Shells for Wrinkle Simulation
O. Rémillard, P. G. Kry, ACM Transactions on Graphics (SIGGRAPH), 2013

We present a new technique for simulating high resolution surface wrinkling deformations of composite objects consisting of a soft interior and a harder skin. We combine high resolution thin shells with coarse finite element lattices and define frequency based constraints that allow the formation of wrinkles with properties matching those predicted by the physical parameters of the composite object. Our two-way coupled model produces the expected wrinkling behavior without the computational expense of a large number of volumetric elements to model deformations under the surface. We use C1 quadratic shape functions for the interior deformations, allowing very coarse resolutions to model the overall global deformation efficiently, while avoiding visual artifacts of wrinkling at discretization boundaries. We demonstrate that our model produces wrinkle wavelengths that match both theoretical predictions and high resolution volumetric simulations. We also show example applications in simulating wrinkles on passive objects, such as furniture, and for wrinkles on faces in character animation.

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Goal Directed Multi-Finger Manipulation: Control Policies and Analysis
S. Andrews, P. G. Kry, Computers & Graphics, 2013

We present a method for one-handed, task-based manipulation of objects. Our approach uses a mid-level, multi-phase approach to organize the problem into three phases. This provides an appropriate control strategy for each phase and results in cyclic finger motions that, together, accomplish the task. The exact trajectory of the object is never specified since the goal is defined by the final orientation and position of the object. All motion is physically based and guided by a control policy that is learned through a series of offline simulations. We also discuss practical considerations for our learning method. Variations in the synthesized motions are possible by tuning a scalarized multi-objective optimization. We demonstrate our method with two manipulation tasks, discussing the performance and limitations. Additionally, we provide an analysis of the robustness of the low-level controllers used by our framework.

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Sequential Pose Estimation Using Linearized Rotation Matrices
T. M. Drews, P. G. Kry, J. R. Forbes, C. Verbrugge, In 10th Conference on Computer and Robot Vision (CRV), 2013, BEST PAPER

We present a new formulation for pose estimation using an extended Kalman filter that takes advantage of the Lie group structure of rotations. Using the exponential map along with linearized rotations for updates and errors permits a graceful filter formulation that avoids the awkward representation of Euler angles and the required norm constraint for quaternions. We demonstrate this approach with an implementation that uses sensors commonly found in consumer tablets and mobile phones: a camera and gyroscope, which we use to estimate attitude, position, and gyroscope bias. We use gyroscope measurements for prediction, and vision-based measurements for correction. We show results and discuss the performance of our pose estimation method using ground truth data obtained via a motion capture system.

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Policies for Goal Directed Multi-Finger Manipulation
S. Andrews, P. G. Kry, In 9th Workshop on Virtual Reality Interaction and Physical Simulation (VRIPHYS) 2012, BEST PAPER

We present a method for one-handed task based manipulation of objects. Our approach uses a mid-level multiphase approach to break the problem into three parts, providing an appropriate control strategy for each phase and resulting in cyclic finger motions that accomplish the task. All motion is physically based, and guided by a policy computed for a particular task. The exact trajectory is never specified as the goal of our different tasks are concerned with the final orientation and position of the object. The offline simulations used to learn the policy are effective solutions for the task, but an important aspect of our work is that the policy is general enough to be used online in real time. We present two manipulation tasks and discuss their performance along with limitations.

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Static Pose Reconstruction with an Instrumented Bouldering Wall
R. Aladdin, P. G. Kry, VRST, 2012

This paper describes the design and construction of an instrumented bouldering wall, and a technique for estimating poses by optimizing an objective function involving contact forces. We describe the design and calibration of the wall, which can capture the contact forces and torques during climbing while motion capture (MoCap) records the climber pose, and present a solution for identifying static poses for a given set of holds and forces. We show results of our calibration process and static poses estimated for different measured forces. To estimate poses from forces, we use optimization and start with an inexpensive objective to guide the solver toward the optimal solution. When good candidates are encountered, the full objective function is evaluated with a physics-based simulation to determine physical plausibility while meeting additional constraints. Comparison between our reconstructed poses and MoCap show that our objective function is a good model for human posture.

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Modal Vibrations for Character Animation
P. G. Kry, Motion in Games, 2012

Modal vibrations can be used as a representation for the motion of an elastic system, decoupling the dynamics into a set of independent equations, and providing a good approximation to the system behavior for small displacements from the equilibrium state. In computer animation, elastic joints are commonly used in the simulation and control of articulated characters, which naturally permits a modal representation. This paper revisits the computation of modes for a skeletal character, and surveys recent work on the use of modal vibrations for kinematic animation of locomotion and jumping, and in the creation of physically based locomotion controllers that exhibit a desired style. Examples of other applications are also presented, and possibilities for future work are discussed.

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Inverse Kinodynamics:
Editing and Constraining Kinematic Approximations of Dynamic Motion
 P. G. Kry, C. Rahgoshay, A. H. Rabbani, K. Singh, Computers & Graphics, 2012

We present inverse kinodynamics (IKD), an animator friendly kinematic work flow that both encapsulates short-lived dynamics and allows precise space-time constraints. Kinodynamics (KD), defines the system state at any given time as the result of a kinematic state in the recent past, physically simulated over a short time window to the present. KD is a well suited kinematic approximation to animated characters and other dynamic systems with dominant kinematic motion and short-lived dynamics. Given a dynamic system, we first choose an appropriate kinodynamic window size based on accelerations in the kinematic trajectory and the physical properties of the system. We then present an inverse kinodynamics (IKD) algorithm, where a kinodynamic system can precisely attain a set of animator constraints at specified times. Our approach solves the IKD problem iteratively, and is able to handle full pose or end effector constraints at both position and velocity level, as well as multiple constraints in close temporal proximity. Our approach can also be used to solve position and velocity constraints on passive systems attached to kinematically driven bodies. We describe both manual and automatic procedures for selecting the kinodynamic window size necessary to approximate the dynamic trajectory to a given accuracy. We demonstrate the convergence properties of our IKD approach, and give details of a typical work flow example that an animator would use to create an animation with our system. We show IKD to be a compelling approach to the direct kinematic control of character, with secondary dynamics via examples of skeletal dynamics and facial animation.

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Determining an Aesthetic Inscribed Curve
B. Wyvill, P. G. Kry, R. Seidel, D. Mould, Computational Aesthetics / Expressive, 2012

In this work we propose both implicit and parametric curves to represent aesthetic curves inscribed within Voronoi cells in R2. A user survey was conducted to determine, which class of curves are generally accepted as the more aesthetic. We present the curves, the survey results, and the implications for future work on simulating sponge like volumes.

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Inverse Kinodynamics:
Editing and Constraining Kinematic Approximations of Dynamic Motion
 C. Rahgoshay, A. H. Rabbani, K. Singh, P. G. Kry,Graphics Interface, 2012, BEST PAPER

We present inverse kinodynamics (IKD), an animator friendly kinematic workflow that both encapsulates short-lived dynamics and allows precise space-time constraints. Kinodynamics (KD), defines the system state at any given time as the result of a kinematic state in the recent past, physically simulated over a short temporal window to the present. KD is a well suited kinematic approximation to animated characters and other dynamic systems with dominant kinematic motion and short-lived dynamics. Given a dynamic system, we first choose an appropriate kinodynamic window size based on accelerations in the kinematic trajectory and the physical properties of the system. We then present an inverse kinodynamics (IKD) algorithm, where a kinodynamic system can precisely attain a set of animator constraints at specified times. Our approach solves the IKD problem iteratively, and is able to handle full pose or end effector constraints at both position and velocity level, as well as multiple constraints in close temporal proximity. Our approach can also be used to solve position and velocity constraints on passive systems attached to kinematically driven bodies. We show IKD to be a compelling approach to the direct kinematic control of character, with secondary dynamics via examples of skeletal dynamics and facial animation.

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MOVIE (100 MB)
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Medial Spheres for Shape Approximation
 S. Stolpner, P. Kry, K. Siddiqi,Transactions on Pattern Analysis and Machine Intelligence, 2012

We study the problem of approximating a 3D solid with a union of overlapping spheres. In comparison with a state-of-the-art approach, our method offers more than an order of magnitude speed-up and achieves a tighter approximation in terms of volume difference with the original solid, while using fewer spheres. The spheres generated by our method are internal and tangent to the solid's boundary, which permits an exact error analysis, fast updates under local feature size preserving deformation, and conservative dilation. We show that our dilated spheres offer superior time and error performance in approximate separation distance tests than the state-of-the-art method for sphere set approximation for the class of (sigma,theta)-fat solids. We envision that our sphere-based approximation will also prove useful for a range of other applications, including shape matching and shape segmentation.

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Using Natural Vibrations to Guide Control for Locomotion
 R. Nunes, J. Cavalcante-Neto, C. Vidal, P. G. Kry, V. Zordan, ACM Siggraph Symposium on Interactive 3D Graphics and Games (I3D), 2012

Control for physically based characters presents a challenging task because it requires not only the management of the functional aspects that lead to the successful completion of the desired task, but also the resulting movement must be visually appealing and meet the quality requirements of the application. Crafting controllers to generate desirable behaviors is difficult because the specification of the final outcome is indirect and often at odds with the functional control of the task. This paper presents a method which exploits the natural modal vibrations of a physically based character in order to provide a palette of basis coordinations that animators can use to assemble their desired motion. A visual user interface allows an animator to guide the final outcome by selecting and inhibiting the use of specific modes. Then, an optimization routine applies the user-chosen modes in the tuning of parameters for a fixed locomotion control structure. The result is an animation system that is easy for an animator to drive and is able to produce a wide variety of locomotion styles for varying character morphologies.

PDF (12 MB)
MOVIE [WMV] (56 MB)
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Generalized Helicoids for Modeling Hair Geometry
 E. Piuze, P. G. Kry, K. Siddiqi, Eurographics, 2011

In computer graphics, modeling the geometry of hair and hair-like patterns such as grass and fur remains a significant challenge. Hair strands can exist in an extensive variety of arrangements and the choice of an appropriate representation for tasks such as hair synthesis, fitting, editing, or reconstruction from samples, is non-trivial. To support such applications we present a novel mathematical representation of hair based on a class of minimal surfaces called generalized helicoids. This representation allows us to characterize the geometry of a single hair strand, as well as of those in its vicinity, by three intuitive curvature parameters and an elevation angle. We introduce algorithms for fitting piecewise generalized helicoids to unparameterized hair strands, and for interpolating hair between these fits. We showcase several applications of this representation including the synthesis of different hair geometries, wisp generation, hair interpolation from samples and hair-style parametrization and reconstruction from real hair data.

PDF (12 MB)
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Advances in Modal Analysis Using a Robust and Multiscale Method
 C. Picard, C. Frisson, F. Faure, G. Drettakis, P. G. Kry EURASIP Journal on Advances in Signal Processing, 2010

This paper presents a new approach to modal synthesis for rendering sounds of virtual objects. We propose a generic method that preserves sound variety across the surface of an object at different scales of resolution and for a variety of complex geometries. The technique performs automatic voxelization of a surface model and automatic tuning of the parameters of hexahedral finite elements, based on the distribution of material in each cell. The voxelization is performed using a sparse regular grid embedding of the object, which permits the construction of plausible lower resolution approximations of the modal model. We can compute the audible impulse response of a variety of objects. Our solution is robust and can handle nonmanifold geometries that include both volumetric and surface parts. We present a system which allows us to manipulate and tune sounding objects in an appropriate way for games, training simulations, and other interactive virtual environments.

PAPER LINK
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Volume Contact Constraints at Arbitrary Resolution
 J. Allard, F. Faure, H. Courtecuisse, F. Falipou, C. Duriez, P. G. Kry, SIGGRAPH, 2010

We introduce a new method for simulating frictional contact between volumetric objects using interpenetration volume constraints. When applied to complex geometries, our formulation results in dramatically simpler systems of equations than those of traditional mesh contact models. Contact between highly detailed meshes can be simplified to a single unilateral constraint equation, or accurately processed at arbitrary geometry-independent resolution with simultaneous sticking and sliding across contact patches. We exploit fast GPU methods for computing layered depth images, which provides us with the intersection volumes and gradients necessary to formulate the contact equations as linear complementarity problems. Straightforward and popular numerical methods, such as projected Gauss-Seidel, can be used to solve the system. We demonstrate our method in a number of scenarios and present results involving both rigid and deformable objects at interactive rates.

PDF (12 MB)
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Medial Spheres for Shape Approximation
 S. Stolpner, P. Kry, K. Siddiqi,Symposium on Brain Body and Machine, 2010

We study the problem of approximating a solid with a union of overlapping spheres. We introduce a method based on medial spheres which, when compared to a state-of-the-art approach, offers more than an order of magnitude speedup and achieves a tighter volumetric approximation of the original mesh, while using fewer spheres. The spheres generated by our method are internal to the object, which permits an exact error analysis and comparison with other sphere approximations. We demonstrate that a tight bounding volume hierarchy of our set of spheres may be constructed using rectangle-swept spheres as bounding volumes. Further, once our spheres are dilated, we show that this hierarchy generally offers superior performance in approximate separation distance tests.

PDF (1.8 MB)
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A Robust and Multi-scale Modal Analysis for Sound Synthesis
 C. Picard, F. Faure, G. Drettakis, P. G. Kry, DAFX, 2009

This paper presents a new approach to modal synthesis for rendering sounds of virtual objects. We propose a generic method for modal analysis that preserves sound variety across the surface of an object, at different scales of resolution and for a variety of complex geometries. The technique performs automatic voxelization of a surface model and automatic tuning of the parameters of hexahedral finite elements, based on the distribution of material in each cell. The voxelization is performed using a sparse regular grid embedding of the object, which easily permits the construction of plausible lower resolution approximations of the modal model. With our approach, we can compute the audible impulse response of a variety of objects. Our solution is robust and can handle non-manifold geometries that include both volumetric and surface parts, such as those used in games, training simulations, and other interactive virtual environment.

PDF (2.7 MB)
MOVIE
DOI



Composite Elements on the iPhone
 M. Williams, P. G. Kry, SIGGRAPH Demo, 2009

Use your fingers to squish a 3D model, and let gravity make the model tumble against the walls of its environment. C-FEM is an interactive demonstration that runs on the iPhone and iPod touch. The application is a proof of concept which includes examples demonstrating piecewise interpolation and non homogeneous elastic properties. The demo was made available as a free application in late July 2009.

PROJECT PAGE
C-FEM no longer in app store (email for information)



Preserving Topology and Elasticity for Embedded Deformable Models
 M. Nesme, P. G. Kry, L. Jeřábková, F. Faure, SIGGRAPH, 2009

In this paper we introduce a new approach for the embedding of linear elastic deformable models. Our technique results in significant improvements in the efficient physically based simulation of highly detailed objects. First, our embedding takes into account topological details, that is, disconnected parts that fall into the same coarse element are simulated independently. Second, we account for the varying material properties by computing stiffness and interpolation functions for coarse elements which accurately approximate the behavior of the embedded material. Finally, we also take into account empty space in the coarse embeddings, which provides a better simulation of the boundary. The result is a straightforward approach to simulating complex deformable models with the ease and speed associated with a coarse regular embedding, and with a quality of detail that would only be possible at much finer resolution.

PROJECT PAGE
PDF (5 MB)
MOVIE [DivX AVI] (29.2 MB)
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Modal Locomotion: Animating Virtual Characters with Natural Vibrations
 P. G. Kry, L. Reveret, F. Faure, and M.-P.Cani, Eurographics, 2009

We present a general method to intuitively create a wide range of locomotion controllers for 3D legged characters. The key of our approach is the assumption that efficient locomotion can exploit the natural vibration modes of the body, where these modes are related to morphological parameters such as the shape, size, mass, and joint stiffness. The vibration modes are computed for a mechanical model of any 3D character with rigid bones, elastic joints, and additional constraints as desired. A small number of vibration modes can be selected with respect to their relevance to locomotion patterns and combined into a compact controller driven by very few parameters. We show that these controllers can be used in dynamic simulations of simple creatures, and for kinematic animations of more complex creatures of a variety of shapes and sizes.

PDF (0.7MB)
MOVIE [XVID AVI] (17MB)
DOG TROT [WMV] (1.7MB)
DOG GALLOP [WMV] (1.1MB)
DOI



A Multi-modal Floor-space for Experiencing Material Deformation Underfoot in Virtual Reality
 A. W. Law, B. V. Peck, Y. Visell, P. G. Kry, and J. R. Cooperstock, IEEE International Workshop on Haptic Audio Visual Environments and Games, 2008
We present a floor-space design that provides the impression of walking on various terrains by rendering graphical, audio and haptic stimuli synchronously with low latency. Currently, interactive floors tend to focus on visual and auditory feedback but have neglected to explore the role of haptics. Our design recreates these three modalities in a direct manner where the sensors and reactive cues are located in the same area. The goal of this project is the creation of a realistic and dynamic area of ground that allows multiple, untethered users to engage in intuitive interaction via locomotion in a virtual or augmented reality environment.

PDF (0.8MB)
DOI



HandNavigator: Hands-on Interaction for Desktop Virtual Reality
 P. G. Kry, A. Pihuit, A. Bernhert, and M.-P. Cani, VRST, 2008

This paper presents a novel interaction system, aimed at hands-on manipulation of digital models through natural hand gestures. Our system is composed of a new physical interaction device coupled with a simulated compliant virtual hand model.  The physical interface consists of a SpaceNavigator, augmented with pressure sensors to detect directional forces applied by the user's fingertips. This information controls the position, orientation, and posture of the virtual hand in the same way that the SpaceNavigator (an isometric input device) uses measured forces to animate a virtual frame. In this manner, user control does not involve fatigue due to reaching gestures or holding a desired hand shape. During contact, the user has a realistic visual feedback in the form of plausible interactions between the virtual hand and its environment, while our device provides some passive tactile feedback.  Our device is well suited to any situation where hand gesture, contact, or manipulation tasks need to be performed in virtual.  We demonstrate the device in several simple virtual worlds and evaluate it through a series of user studies.

PDF (4MB)
MOVIE [MOV] (7MB)
DOI



Animating Virtual Character Locomotion and Other Oscillatory Motions
 P. G. Kry, L. Reveret, F. Faure, M.-P.Cani
Cognitive Animation Workshop 2008 / SIGGRAPH Sketches 2007
We present a method for animating locomotion of physically based virtual characters. The key to our approach is based on the observation that efficient locomotion should exploit the natural passive response of the character's dynamical system.  We specifically focus on the natural vibration modes, which are affected by parameters such as shape, size, mass, and joint stiffness. From these modal vibrations we can extract the most promising modes with respect to locomotion, and combine them with different amplitudes, phases, and frequencies to animate various gaits.  To create locomotion controllers, the search for control parameters is reduced since we only need to consider a small number of modes rather than a large number of degrees of freedom.  This can be done by optimization, guided by captured motion analysis, but is also easy enough to do by hand.  Mode shapes are also useful as a low dimensional basis for interactive puppetry, and may lead to simplifications in the higher level control of other movements.

PDF (1MB)



Hands-on Virtual Clay / La sculpture virtuelle à portée de main
 A. Pihuit, P. G. Kry, M.-P.Cani
SMI 2008 / AFRV 2007
This project concerns a new interaction system designed for hands-on 3D shape modeling and deformation through natural hand gestures. Our system is made of a Phantom haptic device coupled with a deformable foam ball that supports pressure sensors. These sensors detect forces exerted by the user's fingertips, and are used to control the configuration of a compliant virtual hand that is modeling soft virtual clay. During interaction, the user is provided both passive tactile feedback through the foam ball, and realistic visual feedback since the virtual hand deforms due to its interaction in the virtual environment. The combination of all these feedbacks provides the artist with a good immersion allowing for effective sculpting in a virtual world.

PDF (0.7MB)
DOI



Grasp Recognition and Manipulation with the Tango
 P. G. Kry and D. K. Pai, ISER, 2006

We describe a novel user interface for natural, whole hand interaction with 3D environments. Our interface uses a graspable device called the Tango, which looks like a ball but measures contact pressures on its surface at 256 tactual elements (taxels) at a high rate (100 Hz). The acceleration of the device is also measured. The key idea is to use this information to recognize the shape and movement of the user’s hand grasping the object. This allows the user to interact with 3D virtual objects using a hand avatar. The interface provides passive force feedback, and is easier to use than interfaces that require wearing gloves or other sensors on the hand. We describe a rotationally invariant matching algorithm for recognizing the hand shape from examples of previous interaction collected with motion capture. We also describe examples of 3D interaction using our system.

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MOVIE [WMV] (12MB)
DOI



Interaction Capture and Synthesis
P. G. Kry and D. K. Pai, ACM Transactions on Graphics, 25:3 (SIGGRAPH), 2006

Modifying motion capture to satisfy the constraints of new animation is difficult when contact is involved, and a critical problem for animation of hands. The compliance with which a character makes contact also reveals important aspects of the movement’s purpose. We present a new technique called interaction capture, for capturing these contact phenomena. We capture contact forces at the same time as motion, at a high rate, and use both to estimate a nominal reference trajectory and joint compliance. Unlike traditional methods, our method estimates joint compliance without the need for motorized perturbation devices. New interactions can then be synthesized by physically based simulation. We describe a novel position-based linear complementarity problem formulation that includes friction, breaking contact, and the compliant coupling between contacts at different fingers. The technique is validated using data from previous work and our own perturbation-based estimates.

PDF (8MB)
BIBTEX
MOVIE [WMV] (7MB)
DOI



Interaction Capture and Synthesis of Human Hands
P. G. Kry, PhD Thesis, 2005

This thesis addresses several issues in modelling interaction with human hands in computer graphics and animation. Modifying motion capture to satisfy the constraints of new animation is difficult when contact is involved because physical interaction involves energy or power transfer between the system of interest and the environment, and is a critical problem for computer animation of hands. Although contact force measurements provide a means of monitoring this transfer, motion capture as currently used for creating animation has largely ignored contact forces. We present a system of capturing synchronized motion and contact forces, called interaction capture. We transform interactions such as grasping into joint compliances and a nominal reference trajectory in an approach inspired by the equilibrium point hypothesis of human motor control. New interactions are synthesized through simulation of a quasi-static compliant articulated model in a dynamic environment that includes friction. This uses a novel position-based linear complementarity problem formulation that includes friction, breaking contact, and coupled compliance between contacts at different fingers. We present methods for reliable interaction capture, addressing calibration, force estimation, and synchronization. Additionally, although joint compliances are traditionally estimated with perturbation-based methods, we introduce a technique that instead produces estimates without perturbation. We validate our results with data from previous work and our own perturbation-based estimates. A complementary goal of this work is hand-based interaction in virtual environments. We present techniques for whole-hand interaction using the Tango, a novel sensor that performs interaction capture by measuring pressure images and accelerations. We approximate grasp hand-shapes from previously observed data through rotationally invariant comparison of pressure measurements. We also introduce methods involving heuristics and thresholds that make reliable drift-free navigation possible with the Tango. Lastly, rendering the skin deformations of articulated characters is a fundamental problem for computer animation of hands. We present a deformation model, called EigenSkin, which provides a means of rendering physically- or example-based deformation models at interactive rates on graphics hardware.

PDF PRINT QUALITY (37.2MB)
PDF WEB (7.1MB)
BIBTEX
MOVIE EXAMPES [WMV] (8MB)
MOVIE CAPTURED GRASP [WMV] (1.7MB)
MOVIE GRASP ON APPLE [WMV] (1.0MB)
MOVIE GRASP ON BULB [WMV] (0.7MB)
MOVIE BULB MANIPULATION [WMV] (7.4MB)
DOI



The Tango: a tangible tangoreceptive whole-hand human interface
D. K. Pai, E. W. VanDerLoo, S. Sadhukhan, and P. G. Kry, World Haptics Symposium, 2005

We describe the Tango, a new passive haptic interface for whole-hand interaction with 3D objects. The Tango is shaped like a ball and can be grasped comfortably in one hand. Its pressure sensitive skin measures the contact pressures exerted by the user's hand, and accelerometers within the device measure its motion and attitude. This information can be used for novel modes of interaction with three dimensional objects. We describe the design of the device, and the software for interpreting the sensor data for user interaction.

PDF (1.2MB)
BIBTEX
DOI



Continuous Contact Simulation for Smooth Surfaces
P. G. Kry, and D. K. Pai, ACM Transactions on Graphics, 22:1, 2003

Dynamics simulation of smooth surfaced rigid bodies in contact is a critical problem in physically based animation and interactive virtual environments. We describe a technique which uses reduced coordinates to evolve a single continuous contact between smooth piece-wise parametric surfaces. The incorporation of friction into our algorithm is straightforward. The dynamics equations, though slightly more complex due to the reduced coordinate formulation, can be integrated easily using explicit integrators without the need for constraint stabilization. Because the reduced coordinates confine integration errors within the constraint manifold, a large choice of step sizes are possible with visually acceptable results. We demonstrate these results using Loop Subdivision surfaces with parametric evaluation.

PDF (1.8MB)
BIBTEX
MOVIE [AVI-MPG4] (10.5MB)
DOI



EigenSkin: Real Time Large Deformation Character Skinning in Graphics Hardware
P. G. Kry, D. L. James, and D. K. Pai, ACM SIGGRAPH Symposium on Computer Animation, 2002

We present a technique which allows subtle nonlinear quasistatic deformations of articulated characters to be compactly approximated by data-dependent eigenbases which are optimized for real time rendering on commodity graphics hardware. The method extends the common Skeletal-Subspace Deformation (SSD) technique to provide efficient approximations of the complex deformation behaviors exhibited in simulated, measured, and artist-drawn characters. Instead of storing displacements for key poses (which may be numerous), we precompute principal components of the deformation influences for individual kinematic joints, and so construct error-optimal eigenbases describing each joint's deformation subspace. Pose-dependent deformations are then expressed in terms of these reduced eigenbases, allowing precomputed coefficients of the eigenbasis to be interpolated at run time. Vertex program hardware can then efficiently render nonlinear skin deformations using a small number of eigendisplacements stored in graphics hardware. We refer to the final resulting character skinning construct as the model's EigenSkin. Animation results are presented for a very large nonlinear finite element model of a human hand rendered in real time at minimal cost to the main CPU.

PDF(5.5MB)
BIBTEX
MOVIE [AVI-MPG4] (18.4MB)
SHADOW PUPPET MOVIE [AVI-MPG4] (23MB)
PROJECT PAGE
DOI



FoleyAutomatic: Physically-based Sound Effects for Interactive Simulation and Animation
K. van den Doel, P. G. Kry, and D. K. Pai, SIGGRAPH 2001

We describe algorithms for real-time synthesis of realistic sound effects for interactive simulations (e.g., games) and animation. These sound effects are produced automatically, from 3D models using dynamic simulation and user interaction. We develop algorithms that are efficient, physically-based, and can be controlled by users in natural ways. We develop effective techniques for producing high quality continuous contact sounds from dynamic simulations running at video rates which are slow relative to audio synthesis. We accomplish this using modal models driven by contact forces modeled at audio rates, which are much higher than the graphics frame rate. The contact forces can be computed from simulations or can be custom designed. We demonstrate the effectiveness with complex realistic simulations.

PDF (1.1MB)
BIBTEX
MOVIE [MPG] (12.7MB)
DOI



Fast Contact Evolution for Piecewise Smooth Surfaces
P. G. Kry, Master's Thesis, 2000

Dynamics simulation of smooth bodies in contact is a critical problem in physically based animation and interactive virtual environments. We describe a technique which uses reduced coordinates to evolve a single continuous contact between Loop subdivision surfaces. The incorporation of both slip and no-slip friction into our algorithm is straightforward. The dynamics equations, though slightly more complex due to the reduced coordinate formulation, can be integrated easily using explicit integrators without the need for constraint stabilization. The use of reduced coordinates also confines integration errors to lie within the constraint manifold which is preferable for visualization. Our algorithm is suitable for piecewise parametric or parameterizable surfaces with polygonal domain boundaries. Because a contact will not always remain in the same patch, we demonstrate how a contact can be evolved across patch boundaries. We also address the issue of non-regular parameterizations occurring in Loop subdivision surfaces through surface replacement with n sided S-patch surfaces. Three simulations show our results. We partially verify our technique first with a frictionless system and then with a blob sliding and rolling inside a bowl. Our third simulation shows that our formulation correctly predicts the spin reversal of a rattleback top. We also present timings of the various components of the algorithm.

SEE TOG PAPER
RATTLEBACK MOVIE [MPG] (1.2MB)



Forward Dynamics Algorithms for Multibody Chains and Contact
D. K. Pai, U. M. Ascher, and P. G. Kry, ICRA 2000

We describe a framework for derivation of several forward dynamics algorithms used in robotics. The framework is based on formulating an augmented system and performing block matrix elimination on this system. Several popular algorithms such as the O(N) Articulated Body method, and Composite Rigid Body method can be easily derived. We also derive an algorithm for simulation of contact between smooth bodies of arbitrary shape, in contact coordinates. Finally, we discuss some potential numerical difficulties that could arise and their solution.

PDF (0.2MB)
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