Abstract We introduce affinification, a novel method for accelerating physics‐based animation of elastic solids. During a time‐dependent simulation, our method automatically partitions the space into affine and elastic regions depending on the deformation. As such, we capture localized deformations while significantly reducing computational costs with larger regions of model reduction. We design a new clustering method based on deformation rates to capture affinely deforming regions, and explore multiple heuristics for seeding, pattern generation, and the impact of physical parameters on coarsened regions. We compare our method with the ground truth, showing performance increasing with resolution and recorded simulations up to 17× faster compared to elastic simulations, while retaining similar levels of visual fidelity.

We present an approach for training “agile” character control policies, able to produce a wide variety of motor skills from a single reference motion cycle. Our technique builds off of generative adversarial imitation learning (GAIL), with a key novelty of our approach being to provide modification to the observation map in order to improve agility and robustness. Namely, to support more agile behavior, we adjust the value measurements of the training discriminator through relative features - hence the name ReGAIL. Our state observations include both task relevant relative velocities and poses, as well as relative goal deviation information. In addition, to increase robustness of the resulting gaits, servo gains and damping values are included as part of the policy action to let the controller learn how to best combine tension and relaxation during motion. From a policy informed by a single reference motion, our resulting agent is able to maneuver as needed, at runtime, from walking forward to walking backward or sideways, turning and stepping nimbly. Moreover, thanks to the use of observations in relative frames, the trained controllers are robust to morphological changes of the simulated character, which makes adaptation to new morphologies straightforward. We demonstrate our approach for a humanoid and a quadruped, on both flat and sloped terrains, as well as provide ablation studies to validate the design choices of our framework. In addition, we present an application to prehistoric research, where being able to simulate hominids of specific morphologies on rough terrain is valuable with encouraging results.

We present an approach for training "agile" character control policies, able to produce a wide variety of motor skills from a single reference motion cycle. Our technique builds off of generative adversarial imitation learning (GAIL), with a key novelty of our approach being to provide modification to the observation map in order to improve agility and robustness. Namely, to support more agile behavior, we adjust the value measurements of the training discriminator through relative features - hence the name ReGAIL. Our state observations include both task relevant relative velocities and poses, as well as relative goal deviation information. In addition, to increase robustness of the resulting gaits, servo gains and damping values are included as part of the policy action to let the controller learn how to best combine tension and relaxation during motion. From a policy informed by a single reference motion, our resulting agent is able to maneuver as needed, at runtime, from walking forward to walking backward or sideways, turning and stepping nimbly. We demonstrate our approach for a humanoid and a quadruped, on both flat and sloped terrains, as well as provide ablation studies to validate the design choices of our framework.

Abstract We present a novel multi‐layer method for extended position‐based dynamics that exploits a sequence of reduced models consisting of rigid and elastic parts to speed up convergence. Taking inspiration from concepts like adaptive rigidification and long‐range constraints, we automatically generate different rigid bodies at each layer based on the current strain rate. During the solve, the rigid bodies provide coupling between progressively less distant vertices during layer iterations, and therefore the fully elastic iterations at the final layer start from a lower residual error. Our layered approach likewise helps with the treatment of contact, where the mixed solves of both rigid and elastic in the layers permit fast propagation of impacts. We show several experiments that guide the selection of parameters of the solver, including the number of layers, the iterations per layers, as well as the choice of rigid patterns. Overall, our results show lower compute times for achieving a desired residual reduction across a variety of simulation models and scenarios.

Abstract Traditional mesh‐based methods for cutting deformable bodies rely on modifying the simulation mesh by deleting, duplicating, deforming or subdividing its elements. Unfortunately, such topological changes eventually lead to instability, reduced accuracy, or computational efficiency challenges. Hence, state of the art algorithms favor the extended finite element method (XFEM), which decouples the cut geometry from the simulation mesh, allowing for stable and accurate cuts at an additional computational cost that is local to the cut region. However, in the 3‐dimensional setting, current XFEM frameworks are limited by the cutting configurations that they support. In particular, intersecting cuts are either prohibited or require sophisticated special treatment. Our work presents a general XFEM formulation that is applicable to the 1‐, 2‐, and 3‐dimensional setting without sacrificing the desirable properties of the method. In particular, we propose a generalized enrichment which supports multiple intersecting cuts of various degrees of non‐linearity by leveraging recent advances in robust mesh‐Boolean technology. This novel strategy additionally enables analytic discontinuous integration schemes required to compute mass, force and elastic energy. We highlight the simplicity, expressivity and accuracy of our XFEM implementation across various scenarios in which intersecting cutting patterns are featured.

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 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 - 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.

Abstract 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.

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.

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.

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.

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. Code is available at https://motion-lab.github.io/AdaptNet .

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.

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.

Abstract 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.

Abstract 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 travelling 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.

Abstract 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.

Abstract 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.

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.

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.

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.

Substructuring permits parallelization of physics simulation on multi-core CPUs. We present a new substructuring approach for solving stiff multibody systems containing both bilateral and unilateral constraints. Our approach is based on non-overlapping domain decomposition with the Schur complement method, which we extend to systems involving contact formulated as a mixed bounds linear complementarity problem. At each time step, we alternate between solving the subsystem and interface constraint impulses, which leads to the identification of the active constraints. By using the active constraints to compute the effective mass of subsystems within the interface solve, we obtain an exact solution. We demonstrate that our simulations have preferable behavior compared to standard iterative solvers and substructuring techniques based on the exchange of forces at interface bodies. We observe considerable speedups for structured simulations where a user-defined partitioning can be applied, and moderate speedups for unstructured simulations, such as piles of bodies. In the latter case, we propose an automatic partitioning strategy based on the degree of bodies in the constraint graph. Because our method makes use of direct solvers, we are able to achieve interactive and real-time frame rates for a number of challenging scenarios involving large mass ratios, redundant constraints, and ill-conditioned systems.

Abstract A hallmark of many skilled motions is the anticipatory nature of the balance‐related adjustments that happenin preparation forthe 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.

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, and model the forces and torques produced. We evaluate accuracy of hovering and flight on simple paths, and compare the results to untethered flight.

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.

Abstract 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 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.

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 is a challenging and hard problem if attempted manually 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.

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 (-1) S. 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 FORK (-1)S 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.

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.

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.

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.

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.

This special section presents expanded versions of three of the best papers from the 11th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA 2012), which was held in Lausanne, Switzerland, from 29-31 July 2012. SCA has established itself as the premier conference dedicated specifically to innovations in the software and technology of computer animation. SCA 2012 received 80 submissions and each submission was reviewed by at least three members of the international program committee. After a thorough online discussion, the 72-member international program committee decided on the 27 full papers and nine short presentation papers accepted for the final program. Out of 27 full papers, the symposium's Best Papers Award Committee selected one best paper, two runner-ups, and four honorable mentions. The selection was informed by the original reviews and the conference presentations. We are delighted to present three out of the six very best papers of SCA 2012 invited for this special section. Each of the invited papers contains a minimum of 30 percent new material and received at least three reviews, including one reviewer not among the original SCA reviewers.

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.

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 C 1 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.

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.

Physical simulation is now a robust and common approach to recreating reality in virtual worlds and is almost universally used in the animation of natural phenomena, ballistic objects, and character accessories like clothing and hair. Despite these great strides, the animation of primary characters continues to be dominated by the kinematic techniques of motion capture and above all traditional keyframing. Two aspects of a primary character in particular, skeletal and facial motion, are often laboriously animated using kinematics. There are perhaps three chief reasons for this. First, kinematics, unencumbered by physics, provides the finest level of control necessary for animators to breathe life and personality into their characters. Second, this control is direct and history-free, in that the authored state of the character, set at any point in time is precisely observed upon playback and its impact on the animation is localized to a neighborhood around that time. Third, animator interaction with the time line is WYSIWYG (what-you-see-is-what-you-get), allowing them to scrub to various points in time and observe the character state without having to playback the entire animation. Secondary dynamics can be overlaid on primarily kinematic character motion to enhance the visceral feel of their characters. But unfortunately compromise the second and third reasons animators rely on pure kinematic control.

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.

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 speedup 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 (σ,θ)-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.

Abstract 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.

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.

Abstract 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.

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 behaviour 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.

This paper presents 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.

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 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. 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.

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.

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 that uses reduced coordinates to evolve a single continuous contact between smooth piecewise parametric surfaces. The incorporation of friction into our algorithm is straightforward. The dynamics equations, although slightly more complex due to the reduced coordinate formulation, can be integrated easily using explicit integrators without the need for constraint stabilization. Reduced coordinates confine integration errors to the constraint manifold, thereby permitting a wide choice of step sizes with visually acceptable results. We demonstrate these results using Loop Subdivision surfaces with parametric evaluation.

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.

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 the 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.

This article describes work in progress at the Canadian Space Agency on the design and implementation of haptic devices. Haptic devices are a special class of robotic mechanisms for which structural transparency is a foremost design criterion. Also notable is the fact that often, three or four degrees of freedom, rather than six as in general robotic tasks, are sufficient for many haptic applications. Furthermore, in order to make these devices readily available to many users, it is necessary their kinematic models be sufficiently simple such that they can be controlled by inexpensive means. Various three and four-DOF mechanisms, some of which recently developed by the Canadian Space Agency, are discussed herein in terms of their suitability for haptic applications. For five or six-DOF applications, the concept of the virtual handle is introduced, reducing the problems and complexity usually associated with mechanisms with a high number of degrees of freedom.