We introduce a novel framework for interactive landscape authoring that supports bi-directional feedback between erosion and vegetation simulation. Vegetation and terrain erosion have strong mutual impact and their interplay influences the overall realism of virtual scenes. Despite their importance, these complex interactions have been neglected in computer graphics. Our framework overcomes this by simulating the effect of a variety of geomorphological agents and the mutual interaction between different material and vegetation layers, including rock, sand, humus, grass, shrubs, and trees. Users are able to exploit these interactions with an authoring interface that consistently shapes the terrain and populates it with details. Our method, validated through side-by-side comparison with real terrains, can be used not only to generate realistic static landscapes, but also to follow the temporal evolution of a landscape over a few centuries.

Authoring Landscapes by Combining Ecosystem and Terrain Erosion Simulation

]]>Data driven models of human poses and soft-tissue deformations can produce very realistic results, but they only model the visible surface of the human body and cannot create skin deformation due to interactions with the environment. Physical simulations can generalize to external forces, but their parameters are difficult to control. In this paper, we present a layered volumetric human body model learned from data. Our model is composed of a data-driven inner layer and a physics-based external layer. The inner layer is driven with a volumetric statistical body model (VSMPL). The soft tissue layer consists of a tetrahedral mesh that is driven using the finite element method (FEM). Model parameters, namely the segmentation of the body into layers and the soft tissue elasticity, are learned directly from 4D registrations of humans exhibiting soft tissue deformations. The learned two layer model is a realistic full-body avatar that generalizes to novel motions and external forces. Experiments show that the resulting avatars produce realistic results on held out sequences and react to external forces. Moreover, the model supports the retargeting of physical properties from one avatar when they share the same topology.

]]>We introduce a new technique for real-time physically based volume sculpting of virtual elastic materials. Our formulation is based on the elastic response to localized force distributions associated with common modeling primitives such as grab, scale, twist, and pinch. The resulting brush-like displacements correspond to the regularization of fundamental solutions of linear elasticity in infinite 2D and 3D media. These deformations thus provide the realism and plausibility of volumetric elasticity, and the interactivity of closed-form analytical solutions. To finely control our elastic deformations, we also construct compound brushes with arbitrarily fast spatial decay. Furthermore, pointwise constraints can be imposed on the displacement field and its derivatives via a single linear solve. We demonstrate the versatility and efficiency of our method with multiple examples of volume sculpting and image editing.

Regularized Kelvinlets: Sculpting Brushes based on Fundamental Solutions of Elasticity

]]>We present a novel method to enrich standard rigid-body impact models with a spatially varying coefficient of restitution map, or Bounce Map. Even state-of-the art methods in computer graphics assume that for a single rigid body, post- and pre-impact dynamics are related with a single global, constant, namely the coefficient of restitution. We first demonstrate that this assumption is highly inaccurate, even for simple objects. We then present a technique to efficiently and automatically generate a function which maps locations on the object’s surface along with impact normals, to a scalar coefficient of restitution value. Furthermore, we propose a method for two-body restitution analysis, and, based on numerical experiments, estimate a practical model for combining one-body Bounce Map values to approximate the two-body coefficient of restitution. We show that our method not only improves accuracy, but also enables visually richer rigid-body simulations

Bounce Maps: An Improved Restitution Model for Real-Time Rigid-Body Impact

]]>In this paper we introduce a novel method to adaptive incompressible SPH simulations. Instead of using a scheme with a number of fixed particle sizes or levels, our approach allows continuous particle sizes. This enables us to define optimal particle masses with respect to, e.g., the distance to the fluid’s surface. A required change in mass due to the dynamics of the fluid is properly and stably handled by our scheme of mass redistribution. This includes temporally smooth changes in particle masses as well as sudden mass variations in regions of high flow dynamics. Our approach guarantees low spatial variations in particle size, which is a core property in order to achieve large adaptivity ratios for incompressible fluid simulations. Conceptually, our approach allows for infinite continuous adaptivity, practically we achieved adaptivity ratios up to 5 orders of magnitude, while still being mass preserving and numerically stable, yielding unprecedented vivid surface detail at comparably low computational cost and moderate particle counts.

]]>We present a new integration algorithm for the accurate and efficient solution of stiff elastodynamic problems governed by the second-order ordinary differential equations of structural mechanics. Current methods have the shortcoming that their performance is highly dependent on the numerical stiffness of the underlying system that often leads to unrealistic behavior or a significant loss of efficiency. To overcome these limitations, we present a new integration method which is based on a mathematical reformulation of the underlying differential equations, an exponential treatment of the full nonlinear forcing operator as opposed to more standard partially implicit or exponential approaches, and the utilization of the concept of stiff accuracy which ensures that the efficiency of the simulations is significantly less sensitive to increased stiffness. As a consequence, we are able to tremendously accelerate the simulation of stiff systems compared to established integrators and significantly increase the overall accuracy. The advantageous behavior of this approach is demonstrated on a broad spectrum of complex examples like deformable bodies, textiles, bristles, and human hair. Our easily parallelizable integrator enables more complex and realistic models to be explored in visual computing without compromising efficiency.

]]>Botanical simulation plays an important role in many fields including visual effects, games and virtual reality. Previous plant simulation research has focused on computing physically based motion, under the assumption that the material properties are known. It is too tedious and impractical to manually set the spatially-varying material properties of complex trees. In this paper, we give a method to set the mass density, stiffness and damping properties of individual tree components (branches and leaves) using a small number of intuitive parameters. Our method is rooted in plant biomechanics literature and builds upon power laws observed in real botanical systems. We demonstrate our materials by simulating them using offline and model-reduced FEM simulators. Our parameters can be tuned directly by artists; but we also give a technique to infer the parameters from ground truth videos of real trees. Our materials produce tree animations that look much more similar to real trees than previous methods, as evidenced by our user study and experiments.

]]>We present a novel physics-based approach to facial animation. Contrary to commonly used generative methods, our solution computes facial expressions by minimizing a set of non-linear potential energies that model the physical interaction of passive flesh, active muscles, and rigid bone structures. By integrating collision and contact handling into the simulation, our algorithm avoids inconsistent poses commonly observed in generative methods such as blendshape rigs. A novel muscle activation model leads to a robust optimization that faithfully reproduces complex facial articulations. We show how person-specific simulation models can be built from a few expression scans with a minimal data acquisition process and an almost entirely automated processing pipeline. Our method supports temporal dynamics due to inertia or external forces, incorporates skin sliding to avoid unnatural stretching, and offers full control of the simulation parameters, which enables a variety of advanced animation effects. For example, slimming or fattening the face is achieved by simply scaling the volume of the soft tissue elements. We show a series of application demos, including artistic editing of the animation model, simulation of corrective facial surgery, or dynamic interaction with external forces and objects.

]]>To date, material modeling in physically based computer animation has largely focused on mass and stiffness material properties. However, deformation dynamics is largely affected also by the damping properties. In this paper, we propose an interactive design method for nonlinear isotropic and anisotropic damping of complex three-dimensional solids simulated using the Finite Element Method (FEM). We first give a damping design method and interface whereby the user can set the damping properties so that motion aligned with each of a few chosen example deformations is damped by an independently prescribed amount, whereas the rest of the deformation space follows standard Rayleigh damping, or any viscous damping. Next, we demonstrate how to design nonlinear damping that depends on the magnitude of the deformation along each example deformation, by editing a single spline curve for each example deformation. Our user interface enables an art-directed and intuitive approach to controlling damping in solid simulations. We mathematically prove that our nonlinear anisotropic damping generalizes the frequency-dependent Caughey damping model, when starting from the Rayleigh damping. Finally, we give an inverse design method whereby the damping curve parameters can be inferred automatically from high-level user input, such as the amount of amplitude loss in one oscillation cycle along each of the chosen example deformations. To minimize numerical damping for implicit integration, we introduce an accurate and stable implicit integrator, which removes spurious high-frequency oscillations while only introducing a minimal amount of numerical damping. Our damping can generate effects not possible with previous methods, such as controllable nonlinear decaying envelopes whereby large deformations are damped faster or slower than small deformations, and damping anisotropic effects. We also fit our damping to videos of real-world objects undergoing large deformations, capturing their nonlinear and anisotropic damping dynamics.

]]>This paper proposes a novel framework to evaluate fluid simulation methods based on crowd-sourced user studies in order to robustly gather large numbers of opinions. The key idea for a robust and reliable evaluation is to use a reference video from a carefully selected real-world setup in the user study. By conducting a series of controlled user studies and comparing their evaluation results, we observe various factors that affect the perceptual evaluation. Our data show that the availability of a reference video makes the evaluation consistent. We introduce this approach for computing scores of simulation methods as visual accuracy metric. As an application of the proposed framework, a variety of popular simulation methods are evaluated.

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