Large-Strain Surface Modeling Using Plasticity.

Modeling arbitrarily large deformations of surfaces smoothly embedded in three-dimensional space is challenging. We give a new method to represent surfaces undergoing large spatially varying rotations and strains, based on differential geometry, and surface first and second fundamental forms. Methods that penalize the difference between the current shape and the rest shape produce sharp spikes under large strains, and variational methods produce wiggles, whereas our method naturally supports large strains and rotations without any special treatment. For stable and smooth results, we demonstrate that the deformed surface has to locally satisfy compatibility conditions (Gauss-Codazzi equations) on the first and second fundamental forms. We then give a method to locally modify the surface first and second fundamental forms in a compatible way. We use those fundamental forms to define surface plastic deformations, and finally recover output surface vertex positions by minimizing the surface elastic energy under the plastic deformations. We demonstrate that our method makes it possible to smoothly deform triangle meshes to large spatially varying strains and rotations, while meeting user constraints.

ERGOBOSS: Ergonomic Optimization of Body-Supporting Surfaces.

Humans routinely sit or lean against supporting surfaces and it is important to shape these surfaces to be comfortable and ergonomic. We give a method to design the geometric shape of rigid supporting surfaces to maximize the ergonomics of physically based contact between the surface and a deformable human. We model the soft deformable human using a layer of FEM deformable tissue surrounding a rigid core, with measured realistic elastic material properties, and large-deformation nonlinear analysis. We define a novel cost function to measure the ergonomics of contact between the human and the supporting surface. We give a stable and computationally efficient contact model that is differentiable with respect to the supporting surface shape. This makes it possible to optimize our ergonomic cost function using gradient-based optimizers. Our optimizer produces supporting surfaces superior to prior work on ergonomic shape design. Our examples include furniture, apparel and tools. We also validate our results by scanning a real human subject's foot and optimizing a shoe sole shape to maximize foot contact ergonomics. We 3D-print the optimized shoe sole, measure contact pressure using pressure sensors, and demonstrate that the real unoptimized and optimized pressure distributions qualitatively match those predicted by our simulation.

Evaluating the Efficiency of Six-DoF Haptic Rendering-Based Virtual Assembly Training.

Haptics plays an important role in training users to assemble mechanical components, such as airplane or car parts. Because mechanical components are often geometrically complex, efficient collision detection and six-DoF haptic rendering of contact are required for virtual assembly, and this has been extensively explored in prior work. However, as this article shows, this alone is not sufficient for efficient virtual assembly training. This article asks how to augment six-DoF haptic rendering of contact to maximize virtual assembly training efficiency, and proposes and measures several visual and haptic guidance strategies. Our visual strategies consist of displaying animations of the correct assembly path, motion indicator cues, and close-ups on difficult assembly path sections. Our haptic guidance consists of forces and torques that correct the trainee's deviation from the path. We investigate several haptic guidance strategies, including continuous forces and torques, force/torque nudging and anti-forces/torques. We designed a user study to evaluate the training efficiency of our proposed strategies quantitatively, using ANOVA and Tukey statistics. Our main finding is that the most efficient training approach is to use haptic rendering of contact in combination with visual animation-based guidance. Continuous forces, nudging, anti-forces and motion indicator cues were measured to be less effective.

6-DoF Haptic Rendering of Static Coulomb Friction Using Linear Programming.

Simulating frictional contact between objects with complex geometry is important for 6-DoF haptic rendering applications. For example, friction determines whether components can be navigated past narrow clearances in virtual assembly. State-of-the-art haptic rendering of frictional contact either augments penalty contact with frictional penalty springs, which do not prevent sliding and cannot render correct static friction, or uses constraint-based methods that are difficult to meet the stringent haptic loop computation time requirements for complex geometry. We give a 6-DoF Coulomb friction haptic rendering algorithm for distributed contact between rigid objects with complex geometry. Our algorithm is compatible with the fast point vs implicit function penalty-based contact method such as the Voxmap-PointShell method. Our algorithm incorporates the maximal dissipation principle and produces correct static friction, all the while inheriting the speed of penalty-based methods. We demonstrate our algorithm on several challenging 6-DoF haptic rendering examples.

6-DoF Haptic Rendering Using Continuous Collision Detection between Points and Signed Distance Fields.

We present an algorithm for fast continuous collision detection between points and signed distance fields, and demonstrate how to robustly use it for 6-DoF haptic rendering of contact between objects with complex geometry. Continuous collision detection is often needed in computer animation, haptics, and virtual reality applications, but has so far only been investigated for polygon (triangular) geometry representations. We demonstrate how to robustly and continuously detect intersections between points and level sets of the signed distance field. We suggest using an octree subdivision of the distance field for fast traversal of distance field cells. We also give a method to resolve continuous collisions between point clouds organized into a tree hierarchy and a signed distance field, enabling rendering of contact between rigid objects with complex geometry. We investigate and compare two 6-DoF haptic rendering methods now applicable to point-versus-distance field contact for the first time: continuous integration of penalty forces, and a constraint-based method. An experimental comparison to discrete collision detection demonstrates that the continuous method is more robust and can correctly resolve collisions even under high velocities and during complex contact.

Enriching Triangle Mesh Animations with Physically Based Simulation.

We present a system to combine arbitrary triangle mesh animations with physically based Finite Element Method (FEM) simulation, enabling control over the combination both in space and time. The input is a triangle mesh animation obtained using any method, such as keyframed animation, character rigging, 3D scanning, or geometric shape modeling. The input may be non-physical, crude or even incomplete. The user provides weights, specified using a minimal user interface, for how much physically based simulation should be allowed to modify the animation in any region of the model, and in time. Our system then computes a physically-based animation that is constrained to the input animation to the amount prescribed by these weights. This permits smoothly turning physics on and off over space and time, making it possible for the output to strictly follow the input, to evolve purely based on physically based simulation, and anything in between. Achieving such results requires a careful combination of several system components. We propose and analyze these components, including proper automatic creation of simulation meshes (even for non-manifold and self-colliding undeformed triangle meshes), converting triangle mesh animations into animations of the simulation mesh, and resolving collisions and self-collisions while following the input.

Adaptive 6-DoF Haptic Contact Stiffness Using the Gauss Map.

The penalty method is a popular approach to resolving contact in haptic rendering. In simulations involving complex distributed contact, there are, however, many simultaneous individual contacts. These contacts have normals pointing in several directions, many of which may be parallel, causing the stiffness effectively to add up in a temporally highly-varying and unpredictable way. Consequently, penalty-based simulation suffers from stability problems. Previous methods tackled this problem using implicit integration, or simply by scaling the stiffness down globally by the number of contacts. Although this provides some control over the net stiffness, it leads to large penetrations, as small contacts are effectively ignored when compared to larger contacts. We propose an adaptive stiffness method that employs the Gauss map of the normal distribution to ensure a spatially uniform and controllable stiffness in all the contact directions. Combined with virtual coupling saturation, the penetration can be kept shallow all the while haptic simulation remains stable, even for large-scale complex geometry with complex distributed 6-DoF contact scenarios. Our method is fast and can be applied to any penalty-based formulation between rigid objects. While used primarily for rigid objects, we also apply our method to reduced deformable objects. We demonstrate the effectiveness of our approach on several challenging 6-DoF haptic rendering scenarios, such as car engine and landing gear virtual assembly.

Stable Anisotropic Materials.

The Finite Element Method (FEM) is commonly used to simulate isotropic deformable objects in computer graphics. Several applications (wood, plants, muscles) require modeling the directional dependence of the material elastic properties in three orthogonal directions. We investigate linear orthotropic materials, a special class of linear anisotropic materials where the shear stresses are decoupled from normal stresses, as well as general linear (non-orthotropic) anisotropic materials. Orthotropic materials generalize transversely isotropic materials, by exhibiting different stiffness in three orthogonal directions. Orthotropic materials are, however, parameterized by nine values that are difficult to tune in practice, as poorly adjusted settings easily lead to simulation instabilities. We present a user-friendly approach to setting these parameters that is guaranteed to be stable. Our approach is intuitive as it extends the familiar intuition known from isotropic materials. Similarly to linear orthotropic materials, we also derive a stability condition for a subset of general linear anisotropic materials, and give intuitive approaches to tuning them. In order to simulate large deformations, we augment linear corotational FEM simulations with our orthotropic and general anisotropic materials.

Implicit Multibody Penalty-BasedDistributed Contact.

The penalty method is a simple and popular approach to resolving contact in computer graphics and robotics. Penalty-based contact, however, suffers from stability problems due to the highly variable and unpredictable net stiffness, and this is particularly pronounced in simulations with time-varying distributed geometrically complex contact. We employ semi-implicit integration, exact analytical contact gradients, symbolic Gaussian elimination and a SVD solver to simulate stable penalty-based frictional contact with large, time-varying contact areas, involving many rigid objects and articulated rigid objects in complex conforming contact and self-contact. We also derive implicit proportional-derivative control forces for real-time control of articulated structures with loops. We present challenging contact scenarios such as screwing a hexbolt into a hole, bowls stacked in perfectly conforming configurations, and manipulating many objects using actively controlled articulated mechanisms in real time.