Physically based rigging for deformable characters

In this paper, we introduce a framework for instrumenting (rigging) characters that are modeled as dynamic elastic bodies, so that their shapes can be controlled by an animator. Because the shape of such a character is determined by physical dynamics, the rigging system cannot simply dictate the shape as in traditional animation. For this reason, we introduce forces as the building blocks of rigging. Rigging forces guide the shape of the character, but are combined with other forces during simulation. Forces have other desirable features: they can be combined easily and simulated at any resolution, and since they are not tightly coupled with the surface geometry, they can be more easily transferred from one model to another. Our framework includes a new pose-dependent linearization scheme for elastic dynamics, which ensures a correspondence between forces and deformations, and at the same time produces plausible results at interactive speeds. We also introduce a novel method of handling collisions around creases.     

Incremental Deformation Subspace Reconstruction

Recalculating the subspace basis of a deformable body is a mandatory procedure for subspace simulation, after the body gets modified by interactive applications. However, using linear modal analysis to calculate the basis from scratch is known to be computationally expensive. In the paper, we show that the subspace of a modified body can be efficiently obtained from the subspace of its original version, if mesh changes are small. Our basic idea is to approximate the stiffness matrix by its low‐frequency component, so we can calculate new linear deformation modes by solving an incremental eigenvalue decomposition problem. To further handle nonlinear deformations in the subspace, we present a hybrid approach to calculate modal derivatives from both new and original linear modes. Finally, we demonstrate that the cubature samples trained for the original mesh can be reused in fast reduced force and stiffness matrix evaluation, and we explore the use of our techniques in various simulation problems. Our experiment shows that the updated subspace basis still allows a simulator to generate visual plausible deformation effects. The whole system is efficient and it is compatible with other subspace construction approaches.     

Fluid Simulation with Articulated Bodies

We present an algorithm for creating realistic animations of characters that are swimming through fluids. Our approach combines dynamic simulation with data-driven kinematic motions (motion capture data) to produce realistic animation in a fluid. The interaction of the articulated body with the fluid is performed by incorporating joint constraints with rigid animation and by extending a solid/fluid coupling method to handle articulated chains. Our solver takes as input the current state of the simulation and calculates the angular and linear accelerations of the connected bodies needed to match a particular motion sequence for the articulated body. These accelerations are used to estimate the forces and torques that are then applied to each joint. Based on this approach, we demonstrate simulated swimming results for a variety of different strokes, including crawl, backstroke, breaststroke, and butterfly. The ability to have articulated bodies interact with fluids also allows us to generate simulations of simple water creatures that are driven by simple controllers.     

Efficient Dynamic Constraints for Animating Articulated Figures

This paper presents an efficient dynamics-based computer animation system for simulating and controlling the motion of articulated figures. A non-trivial extension of Featherstone's O(n) recursive forward dynamics algorithm is derived which allows enforcing one or more constraints on the animated figures. We demonstrate how the constraint force evaluation algorithm we have developed makes it possible to simulate collisions between articulated figures, to compute the results of impulsive forces, to enforce joint limits, to model closed kinematic loops, and to robustly control motion at interactive rates. Particular care has been taken to make the algorithm not only fast, but also easy to implement and use. To better illustrate how the constraint force evaluation algorithm works, we provide pseudocode for its major components. Additionally, we analyze its computational complexity and finally we present examples demonstrating how our system has been used to generate interactive, physically correct complex motion with small user effort.     

Nonlinear Deformation Synthesis via Sparse Principal Geodesic Analysis

This paper introduces the construction of a low-dimensional nonlinear space capturing the variability of a non-rigid shape from a data set of example poses. The core of the approach is a Sparse Principal Geodesic Analysis (SPGA) on the Riemannian manifold of discrete shells, in which a pose of a non-rigid shape is a point. The SPGA is invariant to rigid body motions of the poses and supports large deformation. Since the Riemannian metric measures the membrane and bending distortions of the shells, the sparsity term forces the modes to describe largely decoupled and localized deformations. This property facilitates the analysis of articulated shapes. The modes often represent characteristic articulations of the shape and usually come with a decomposing of the spanned subspace into low-dimensional widely decoupled subspaces. For example, for human models, one expects distinct, localized modes for the bending of elbow or knee whereas some more modes are required to represent shoulder articulation. The decoupling property can be used to construct useful starting points for the computation of the nonlinear deformations via a superposition of shape submanifolds resulting from the decoupling. In a preprocessing stage, samples of the individual subspaces are computed, and, in an online phase, these are interpolated multilinearly. This accelerates the construction of nonlinear deformations and makes the method applicable for interactive applications. The method is compared to alternative approaches and the benefits are demonstrated on different kinds of input data.     

Real time falling animation with active and protective responses

Combined with motion capture and dynamic simulation, characters in animation have realistic motion details and can respond to unexpected contact forces. This paper proposes a novel and real-time character motion generation approach which introduces a parallel process, and uses an approximate nearest neighbor optimization search method. Besides, we employ a support vector machine (SVM), which is trained on a set of samples and predicts a subset of our ‘return-to’ motion capture (mocap) database in order to reduce the search time. In the dynamic simulation process, we focus on designing a biomechanics based controller which detects the balance of the characters in locomotion and drives them to take several active and protective responses when they fall to the ground in order to reduce the injuries to their bodies. Finally, we show the time costs in synthesis and the visual results of our approach. The experimental results indicate that our motion generation approach is suitable for interactive games or other real-time applications.     

Soft Articulated Characters with Fast Contact Handling

Fast contact handling of soft articulated characters is a computationally challenging problem, in part due to complex interplay between skeletal and surface deformation. We present a fast, novel algorithm based on a layered representation for articulated bodies that enables physically-plausible simulation of animated characters with a high-resolution deformable skin in real time. Our algorithm gracefully captures the dynamic skeleton-skin interplay through a novel formulation of elastic deformation in the pose space of the skinned surface. The algorithm also overcomes the computational challenges by robustly decoupling skeleton and skin computations using careful approximations of Schur complements, and efficiently performing collision queries by exploiting the layered representation. With this approach, we can simultaneously handle large contact areas, produce rich surface deformations, and capture the collision response of a character/s skeleton.     

Volume preserving viscoelastic fluids with large deformations using position-based velocity corrections

We propose a particle-based hybrid method for simulating volume preserving viscoelastic fluids with large deformations. Our method combines smoothed particle hydrodynamics (SPH) and position-based dynamics (PBD) to approximate the dynamics of viscoelastic fluids. While preserving their volumes using SPH, we exploit an idea of PBD and correct particle velocities for viscoelastic effects not to negatively affect volume preservation of materials. To correct particle velocities and simulate viscoelastic fluids, we use connections between particles which are adaptively generated and deleted based on the positional relations of the particles. Additionally, we weaken the effect of velocity corrections to address plastic deformations of materials. For one-way and two-way fluid-solid coupling, we incorporate solid boundary particles into our algorithm. Several examples demonstrate that our hybrid method can sufficiently preserve fluid volumes and robustly and plausibly generate a variety of viscoelastic behaviors, such as splitting and merging, large deformations, and Barus effect.     

The application of interactive dynamic virtual surgical simulation visualization method

In this paper, an interactive dynamic simulation method is proposed to solve computational models of soft tissue undergoing large deformation, collision detection, and volume conservation in medical surgical simulation visualization. During the process of implementation of the interactive dynamic simulation method, the point-based method is used to simulate the elastic solids undergoing large deformations and the position-based method is used to simulate the objects collision, friction and volume conservation. Numerical results demonstrate that the proposed method improves the efficiency and stability of the response of heterogeneous soft tissue undergoing contact or even the multi-organs interactions, and it can be extended to interactive biopsy and cutting simulation.

     

Haptic‐constraint modeling based on interactive metaballs

Adding interactive haptic‐constraint sensations is important in interactive computer gaming and 3D shape design. Usually constraints are set on vertices of the object to drive the deformation. How to simulate dynamic force constraints in interactive design is still a challenging task. In this paper, we propose a novel haptic‐constraint modeling method based on interactive metaballs, during which the haptic‐constraint tools are attracted to the target location and then control the touch‐enabled deformation within the constrained areas. The interactive force feedbacks facilitate designers to accurately deform the target regions and fine carve the details as their intention on the objects. Our work studies how to apply touch sensation in such constrained deformations using interactive metaballs, thus users can truly feel and control the soft‐touch objects during the deforming interactions. Experimental results show that the dynamic sense of touch during the haptic manipulation is intuitively simulated to users, via the interacting interface we have developed. Copyright © 2010 John Wiley & Sons, Ltd.     

A generalized framework for interactive dynamic simulation for multirigid bodies

This paper presents a generalized framework for dynamic simulation realized in a prototype simulator called the Interactive Generalized Motion Simulator (I-GMS), which can simulate motions of multirigid-body systems with contact interaction in virtual environments. I-GMS is designed to meet two important goals: generality and interactivity. By generality, we mean a dynamic simulator which can easily support various systems of rigid bodies, ranging from a single free-flying rigid object to complex linkages such as those needed for robotic systems or human body simulation. To provide this generality, we have developed I-GMS in an object-oriented framework. The user interactivity is supported through a haptic interface for articulated bodies, introducing interactive dynamic simulation schemes. This user-interaction is achieved by performing push and pull operations via the PHANToM haptic device, which runs as an integrated part of I-GMS. Also, a hybrid scheme was used for simulating internal contacts (between bodies in the multirigid-body system) in the presence of friction, which could avoid the nonexistent solution problem often faced when solving contact problems with Coulomb friction. In our hybrid scheme, two impulse-based methods are exploited so that different methods are applied adaptively, depending on whether the current contact situation is characterized as "bouncing" or "steady." We demonstrate the user-interaction capability of I-GMS through on-line editing of trajectories of a 6-degree of freedom (dof) articulated structure.     

Visual Exploration of High‐Dimensional Data through Subspace Analysis and Dynamic Projections

We introduce a novel interactive framework for visualizing and exploring high‐dimensional datasets based on subspace analysis and dynamic projections. We assume the high‐dimensional dataset can be represented by a mixture of low‐dimensional linear subspaces with mixed dimensions, and provide a method to reliably estimate the intrinsic dimension and linear basis of each subspace extracted from the subspace clustering. Subsequently, we use these bases to define unique 2D linear projections as viewpoints from which to visualize the data. To understand the relationships among the different projections and to discover hidden patterns, we connect these projections through dynamic projections that create smooth animated transitions between pairs of projections. We introduce the view transition graph, which provides flexible navigation among these projections to facilitate an intuitive exploration. Finally, we provide detailed comparisons with related systems, and use real‐world examples to demonstrate the novelty and usability of our proposed framework.     

A Novel Plastic Phase-Field Method for Ductile Fracture with GPU Optimization

In this paper, we articulate a novel plastic phase-field (PPF) method that can tightly couple the phase-field with plastic treatment to efficiently simulate ductile fracture with GPU optimization. At the theoretical level of physically-based modeling and simulation, our PPF approach assumes the fracture sensitivity of the material increases with the plastic strain accumulation. As a result, we first develop a hardening-related fracture toughness function towards phase-field evolution. Second, we follow the associative flow rule and adopt a novel degraded von Mises yield criterion. In this way, we establish the tight coupling of the phase-field and plastic treatment, with which our PPF method can present distinct elastoplasticity, necking, and fracture characteristics during ductile fracture simulation. At the numerical level towards GPU optimization, we further devise an advanced parallel framework, which takes the full advantages of hierarchical architecture. Our strategy dramatically enhances the computational efficiency of preprocessing and phase-field evolution for our PPF with the material point method (MPM). Based on our extensive experiments on a variety of benchmarks, our novel method's performance gain can reach 1.56× speedup of the primary GPU MPM. Finally, our comprehensive simulation results have confirmed that this new PPF method can efficiently and realistically simulate complex ductile fracture phenomena in 3D interactive graphics and animation.     

The Impulse Graph: A New Dynamic Structure For Global Collisions

In interactive virtual environments and dynamic simulations, collisions between complex objects and articulated bodies may occur simultaneously at multiple points or regions of interference. Many solutions to the collision response problem are formulated based on the local pair-wise contact dynamics. In this article, we present a new solution to the global interactions and dynamic response between multiple structures in a three-dimensional environment. This is based on a new dynamic impulse graph that tracks the reaction forces through the entire system and gives a global view of all the interactions in a multibody system.     

Robust and Efficient Wave Simulations on Deforming Meshes

The goal of this paper is to enable the interactive simulation of phenomena such as animated fluid characters. While full 3D fluid solvers achieve this with control algorithms, these 3D simulations are usually too costly for real‐time environments. In order to achieve our goal, we reduce the problem from a three‐ to a two‐dimensional one, and make use of the shallow water equations to simulate surface waves that can be solved very efficiently. In addition to a low runtime cost, stability is likewise crucial for interactive applications. Hence, we make use of an implicit time integration scheme to obtain a robust solver. To ensure a low energy dissipation, we apply an Implicit Newmark time integration scheme. We propose a general formulation of the underlying equations that is tailored towards the use with an Implicit Newmark integrator. Furthermore, we gain efficiency by making use of a direct solver. Due to the generality of our formulation, the fluid simulation can be coupled interactively with arbitrary external forces, such as forces caused by inertia or collisions. We will discuss the properties of our algorithm, and demonstrate its robustness with simulations on strongly deforming meshes.     

Velocity-based modeling of physical interactions in dense crowds

We present an interactive algorithm to model physics-based interactions in dense crowds. Our approach is capable of modeling both physical forces and interactions between agents and obstacles, while also allowing the agents to anticipate and avoid upcoming collisions during local navigation. We combine velocity-based collision-avoidance algorithms with external physical forces. The overall formulation produces various effects of forces acting on agents and crowds, including balance recovery motion and force propagation through the crowd. We further extend our method to model more complex behaviors involving social and cultural rules. We use finite-state machines to specify a series of behaviors and demonstrate our approach on many complex scenarios. Our algorithm can simulate a few thousand agents at interactive rates and can generate many emergent behaviors.     

An interactive virtual prototyping platform considering environment effect described by fluid dynamics

Virtual prototyping (VP) technology has been regarded as a cost-effective way of envisaging real circumstances that enhance effective communication of designs and ideas, without manufacturing physical samples. Different from recent interactive VPs that are only based on multi-body systems, our VP platform is based on a multi-body coupled with fluid system, that is, the performance and functions of a VP will not be independent of environment factors or disturbances but interact with each other and constitute a whole system. Using this platform designers can simulate a robot through vacuum, air, water environments, etc., so it can provide a better support to the generality and quality of a VP. As for interactive manipulation, designers can modify the constraints between bodies, apply force/torque to interested bodies and change the parameters of forces/torques. Corresponding to user interaction, the platform automatically updates the dynamic behavior of the VP under current condition in the simulation loop. Furthermore, we implemented a virtual MiniBaja vehicle to verify the interactivity and effectiveness of this platform.     

Physically based modeling and simulation with dynamic spherical volumetric simplex splines

In this paper, we present a novel computational modeling and simulation framework based on dynamic spherical volumetric simplex splines. The framework can handle the modeling and simulation of genus-zero objects with real physical properties. In this framework, we first develop an accurate and efficient algorithm to reconstruct the high-fidelity digital model of a real-world object with spherical volumetric simplex splines which can represent with accuracy geometric, material, and other properties of the object simultaneously. With the tight coupling of Lagrangian mechanics, the dynamic volumetric simplex splines representing the object can accurately simulate its physical behavior because it can unify the geometric and material properties in the simulation. The visualization can be directly computed from the object’s geometric or physical representation based on the dynamic spherical volumetric simplex splines during simulation without interpolation or resampling. We have applied the framework for biomechanic simulation of brain deformations, such as the brain shifting during surgery and brain injury under blunt impact. We have compared our simulation results with the ground truth obtained through intra-operative magnetic resonance imaging and real biomechanic experiments. The evaluations demonstrate the excellent performance of our new technique.     

Interactive Construction and Animation of Layered Elastically Deformable Characters

An interactive system is described for creating and animating deformable 3D characters. By using a hybrid layered model of kinematic and physics-based components together with an immersive 3D direct manipulation interface, it is possible to quickly construct characters that deform naturally when animated and whose behavior can be controlled interactively using intuitive parameters. In this layered construction technique, called the elastic surface layer model, a simulated elastically deformable skin surface is wrapped around a kinematic articulated figure. Unlike previous layered models, the skin is free to slide along the underlying surface layers constrained by geometric constraints which push the surface out and spring forces which pull the surface in to the underlying layers. By tuning the parameters of the physics-based model, a variety of surface shapes and behaviors can be obtained such as more realistic-looking skin deformation at the joints, skin sliding over muscles, and dynamic effects such as squash-and-stretch and follow-through. Since the elastic model derives all of its input forces from the underlying articulated figure, the animator may specify all of the physical properties of the character once, during the initial character design process, after which a complete animation sequence can be created using a traditional skeleton animation technique. Character construction and animation are done using a 3D user interface based on two-handed manipulation registered with head-tracked stereo viewing. In our configuration, a six degree-of-freedom head-tracker and CrystalEyes shutter glasses are used to display stereo images on a workstation monitor that dynamically follow the user head motion. 3D virtual objects can be made to appear at a fixed location in physical space which the user may view from different angles by moving his head. To construct 3D animated characters, the user interacts with the simulated environment using both hands simultaneously: the left hand, controlling a Spaceball, is used for 3D navigation and object movement, while the right hand, holding a 3D mouse, is used to manipulate through a virtual tool metaphor the objects appearing in front of the screen. Hand-eye coordination is made possible by registering virtual space to physical space, allowing a variety of complex 3D tasks necessary for constructing 3D animated characters to be performed more easily and more rapidly than is possible using traditional interactive techniques.     

Model predictive control for fast reaching in clutter

A key challenge for haptically reaching in dense clutter is the frequent contact that can occur between the robot’s arm and the environment. We have previously used single-time-step model predictive control (MPC) to enable a robot to slowly reach into dense clutter using a quasistatic mechanical model. Rapid reaching in clutter would be desirable, but entails additional challenges due to dynamic phenomena that can lead to higher forces from impacts and other types of contact. In this paper, we present a multi-time-step MPC formulation that enables a robot to rapidly reach a target position in dense clutter, while regulating whole-body contact forces to be below a given threshold. Our controller models the dynamics of the arm in contact with the environment in order to predict how contact forces will change and how the robot’s end effector will move. It also models how joint velocities will influence potential impact forces. At each time step, our controller uses linear models to generate a convex optimization problem that it can solve efficiently. Through tens of thousands of trials in simulation, we show that with our dynamic MPC a simulated robot can, on average, reach goals 1.4 to 2 times faster than our previous controller, while attaining comparable success rates and fewer occurrences of high forces. We also conducted trials using a real 7 degree-of-freedom (DoF) humanoid robot arm with whole-arm tactile sensing. Our controller enabled the robot to rapidly reach target positions in dense artificial foliage while keeping contact forces low.