We present a fully automatic method to generate detailed and accurate artistic shadows from pairs of line drawing sketches and lighting directions. We also contribute a new dataset of one thousand examples of pairs of line drawings and shadows that are tagged with lighting directions. Remarkably, the generated shadows quickly communicate the underlying 3D structure of the sketched scene. Consequently, the shadows generated by our approach can be used directly or as an excellent starting point for artists. We demonstrate that the deep learning network we propose takes a hand-drawn sketch, builds a 3D model in latent space, and renders the resulting shadows. The generated shadows respect the hand-drawn lines and underlying 3D space and contain sophisticated and accurate details, such as self-shadowing effects. Moreover, the generated shadows contain artistic effects, such as rim lighting or halos appearing from backlighting, that would be achievable with traditional 3D rendering methods.

Clustered shape matching is an approach for physics-based animation of deformable objects, which breaks an object into overlapping clusters of particles. At each timestep, it computes a best-fit rigid transformation between a cluster’s rest state and current particle configuration and Hookean springs are used to pull particles toward desired goal positions. In this paper, we present multi-resolution clustering as an extension to clustered shape matching. We iteratively construct fine-to-coarse sets of clusters and weights over the set of particles and compute dynamics in a single coarse-to-fine pass. We demonstrate that our approach enhances the possible elastic behavior available to artists and provides an intuitive parameterization to blend between stiffness and deformation richness, which are in contention in the traditional clustered shape matching approach that operates at a single spatial scale. We can specify a different stiffness value for each resolution level, where a greater weight at coarser levels result in a stiffer object while a greater weight at finer levels yield richer deformation; we evaluate a number of approaches for choosing these stiffness values and demonstrate the differences in the accompanying video.

Position-based dynamics has emerged as an exceedingly popular approach for animating soft body dynamics. Unfortunately, the basic approach suffers from artificial loss of angular momentum. We propose a simple approach to preserve global linear and angular momenta of bodies by directly tracking these quantities and adjusting velocities to ensure they are preserved. This approach entails negligible computational cost, requires less than 25 lines of code, and exactly preserves global linear and angular momenta.

Since the introduction of the conjugate gradient method to computer graphics, researchers have largely treated it as a black box. In particular, an arbitrary small value is chosen for the tolerance and the method is run to convergence. In the context of soft body animation, this approach results in significant wasted computation and has led researchers to consider alternative, more complex, and less versatile approaches. In this paper we argue that in the context of corotational finite elements, less than 10 iterations can give a good enough solution and substantial savings of computational cost. We examine the use of different preconditioners for conjugate gradient including the mass and Jacobi matrices, as well as the use of different initial guesses. We show that for our examples an initial guess of the previous velocity and the Jacobi preconditioner works best.

In this paper, we revisit the problem online reclustering in clustered shape matching simulations and propose an approach that employs two nonlinear optimizations to create new clusters. The first optimization finds the embedding of particles and clusters into three-dimensional space that minimizes elastic energy. The second finds the optimal location for the new cluster, working in this embedded space. The result is an approach that is more robust in the presence of elastic deformation. We also experimentally verify that our clustered shape matching approach converges as the number of clusters increases, suggesting that our reclustering approach does not change the underlying material properties. Further, we demonstrate that particle resampling is not strictly necessary in our framework allowing us to trivially conserve volume. Finally, we highlight an error in estimating rotations in the original shape-matching work [Müller et al. 2005] that has been repeated in much of the follow up work.

We introduce a new collision proxy for example-based deformable bodies. Specifically, we approximate the deforming geometry as a union of spheres. During pre-computation we perform a sphere packing on the input, undeformed geometry. Then, for each example pose, we move and resize the spheres to approximate the example. During runtime we blend together these positions and radii, using the same skinning weights we use for the geometry. We demonstrate the method on a car crash example, where we achieve an overall speedup of 5--20 times, depending on the resolution of the collision proxy geometry.

In this paper, we incorporate ductile fracture into the clustered shape matching simulation framework for deformable bodies, thus filling a gap in the shape matching literature. Our plasticity and fracture models are inspired by the finite element literature on deformable bodies, but are adapted to the clustered shape matching framework. The resulting approach is fast, versatile, and simple to implement.

Physics-based animation is often used to animate scenes containing destruction of near-rigid, man-made materials. For these applications, the most important visual features are plastic deformation and fracture. Methods based on continuum mechanics model these materials as elastoplastic, and must perform expensive elasticity computations even though elastic deformations are imperceptibly small for rigid materials. We introduce an example-based plasticity model based on linear blend skinning that allows artists to author simulation objects using familiar tools. Dynamics are computed using an unmodified rigid body simulator, making our method computationally efficient and easy to integrate into existing pipelines. We introduce a flexible technique for mapping impulses computed by the rigid body solver to local, example-based deformations. For completeness, our method also supports prescoring based fracture. We demonstrate the practicality of our method by animating a variety of destructive scenes.

In this paper, we address clustering and collision detection in the clustered shape matching simulation framework for deformable bodies. Our clustering algorithm is "fuzzy," meaning that it gives particles weighted membership in clusters. These weights are a significant extension to the basic clustered shape matching framework as they are used to divide particle mass among the clusters. We explore several weighting schemes and demonstrate that the choice of weighting scheme gives artists additional control over material behavior. Furthermore, by design our clustering algorithm yields spherical clusters, which not only results in sparse weight vectors, but also exceptionally efficient collision geometry. We further enhance this simple collision proxy by intersecting with half-spaces to allow for even better, yet still simple and computationally efficient, collision proxies. The resulting approach is fast, versatile, and simple to implement.

Abstract We present several enhancements to model‐reduced fluid simulation that allow improved simulation bases and two‐way solid–fluid coupling. Specifically, we present a basis enrichment scheme that allows us to combine data‐driven or artistically derived bases with more general analytic bases derived from Laplacian eigenfunctions. We handle two‐way solid–fluid coupling in a time‐splitting fashion—we alternately timestep the fluid and rigid body simulators, while taking into account the effects of the fluid on the rigid bodies and vice versa. We employ the vortex panel method to handle solid–fluid coupling and use dynamic pressure to compute the effect of the fluid on rigid bodies. Copyright © 2014 John Wiley & Sons, Ltd.

Abstract Traditional methods for creating dynamic objects and characters from static drawings involve careful tweaking of animation curves and/or simulation parameters. Sprite sheets offer a more drawing‐centric solution, but they do not encode timing information or the logic that determines how objects should transition between poses and cannot generalize outside the given drawings. We present an approach for creating dynamic sprites that leverages sprite sheets while addressing these limitations. In our system, artists create a drawing, deform it to specify a small number of example poses, and indicate which poses can be interpolated. To make the object move, we design a procedural simulation to navigate the pose manifold in response to external or user‐controlled forces. Powerful artistic control is achieved by allowing the artist to specify both the pose manifold and how it is navigated, while physics is leveraged to provide timing and generality. We used our method to create sprites with a range of different dynamic properties. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we present a straightforward, easy to implement method for particle skinning-generating surfaces from animated particle data. We cast the problem in terms of constrained optimization and solve the optimization using a level-set approach. The optimization seeks to minimize the thin-plate energy of the surface, while staying between surfaces defined by the union of spheres centered at the particles. Our approach skins each frame independently while preserving the temporal coherence of the underlying particle animation. Thus, it is well-suited for environments where particle skinning is treated as a post-process, with each frame generated in parallel. Moreover, our approach is integrated with the OpenVDB library and the underlying partial differential equation is amenable to implicit time integration. We demonstrate our method on data generated by a variety of fluid simulation techniques and simple particle systems.

In this paper, we advocate explicit symplectic Euler integration and strain limiting in a shape matching simulation framework. The resulting approach resembles not only previous work on shape matching and strain limiting, but also the recently popular position-based dynamics. However, unlike this previous work, our approach reduces to explicit integration under small strains, but remains stable in the presence of non-linearities.

In this article, we investigate the use of quadratic finite elements for graphical animation of deformable bodies. We consider both integrating quadratic elements with conventional linear elements to achieve a computationally efficient adaptive-degree simulation framework as well as wholly quadratic elements for the simulation of nonlinear rest shapes. In both cases, we adopt the Bézier basis functions and employ a co-rotational linear strain formulation. As with linear elements, the co-rotational formulation allows us to precompute per-element stiffness matrices, resulting in substantial computational savings. We present several examples that demonstrate the advantages of quadratic elements in general and our adaptive-degree system in particular. Furthermore, we demonstrate, for the first time in computer graphics, animations of volumetric deformable bodies with nonlinear rest shapes.

We present a straightforward, easy-to-implement, point-based approach for animating elastoplastic materials. The core idea of our approach is the introduction of embedded space —the least-squares best fit of the material's rest state into three dimensions. Nearest-neighbor queries in the embedded space efficiently update particle neighborhoods to account for plastic flow. These queries are simpler and more efficient than remeshing strategies employed in mesh-based finite element methods. We also introduce a new estimate for the volume of a particle, allowing particle masses to vary spatially and temporally with fixed density. Our approach can handle simultaneous extreme elastic and plastic deformations. We demonstrate our approach on a variety of examples that exhibit a wide range of material behaviors.

In this paper, we present a method for animating multiphase flow of immiscible fluids using unstructured moving meshes. Our underlying discretization is an unstructured tetrahedral mesh, the deformable simplicial complex (DSC), that moves with the flow in a Lagrangian manner. Mesh optimization operations improve element quality and avoid element inversion. In the context of multiphase flow, we guarantee that every element is occupied by a single fluid and, consequently, the interface between fluids is represented by a set of faces in the simplicial complex. This approach ensures that the underlying discretization matches the physics and avoids the additional book-keeping required in grid-based methods where multiple fluids may occupy the same cell. Our Lagrangian approach naturally leads us to adopt a finite element approach to simulation, in contrast to the finite volume approaches adopted by a majority of fluid simulation techniques that use tetrahedral meshes. We characterize fluid simulation as an optimization problem allowing for full coupling of the pressure and velocity fields and the incorporation of a second-order surface energy. We introduce a preconditioner based on the diagonal Schur complement and solve our optimization on the GPU. We provide the results of parameter studies as well as a performance analysis of our method, together with suggestions for performance optimization.

We present several enhancements to model-reduced fluid simulation that allow improved simulation bases and two-way solid-fluid coupling. Specifically, we present a basis enrichment scheme that allows us to combine data driven or artistically derived bases with more general analytic bases derived from Laplacian Eigenfunctions. We handle two-way solid-fluid coupling in a time-splitting fashion---we alternately timestep the fluid and rigid body simulators, while taking into account the effects of the fluid on the rigid bodies and vice versa. We employ the vortex panel method to handle solid-fluid coupling and use dynamic pressure to compute the effect of the fluid on rigid bodies.

Traditional methods for creating dynamic objects and characters from static drawings involve careful tweaking of animation curves and/or simulation parameters. Sprite sheets offer a more drawing-centric solution, but they do not encode timing information or the logic that determines how objects should transition between poses and cannot generalize outside the given drawings. We present an approach for creating dynamic sprites that leverages sprite sheets while addressing these limitations. In our system, artists create a drawing, deform it to specify a small number of example poses, and indicate which poses can be interpolated. To make the object move, we design a procedural simulation to navigate the pose manifold in response to external or user-controlled forces. Powerful artistic control is achieved by allowing the artist to specify both the pose manifold and how it is navigated, while physics is leveraged to provide timing and generality. We used our method to create sprites with a range of different dynamic properties.

Embedding high-resolution surface geometry in coarse control meshes is a standard approach to achieving high-quality computer animation at low computational expense. In this paper we present an effective, automatic method for generating such control meshes. The resulting high-quality, tetrahedral meshes enclose and approximate an input surface mesh, avoiding extrapolation artifacts and ensuring that the resulting coarse volumetric meshes are adequate collision proxies. Our approach comprises three steps: we begin with a tetrahedral mesh built from the body-centered cubic lattice that tessellates the bounding box of the input surface; we then perform a sculpting phase that carefully removes elements from the lattice; and finally a variational vertex adjustment phase iteratively adjusts vertex positions to more closely approximate the surface geometry. Our approach provides explicit trade-offs between mesh quality, resolution, and surface approximation. Our experiments demonstrate the technique can be used to build high-quality meshes appropriate for simulations within games.

Fluid simulation has been one of the greatest successes of physics-based animation, generating hundreds of research papers and a great many special effects over the last fifteen years. However, the animation of large-scale, splashing liquids remains challenging. In this paper, we show that a novel combination of unilateral incompressibility, mass-full FLIP, and blurred boundaries is extremely well-suited to the animation of large-scale, violent, splashing liquids.

We describe a scheme for time integration of mass-spring systems that makes use of a solver based on block coordinate descent. This scheme provides a fast solution for classical linear (Hookean) springs. We express the widely used implicit Euler method as an energy minimization problem and introduce spring directions as auxiliary unknown variables. The system is globally linear in the node positions, and the non-linear terms involving the directions are strictly local. Because the global linear system does not depend on run-time state, the matrix can be pre-factored, allowing for very fast iterations. Our method converges to the same final result as would be obtained by solving the standard form of implicit Euler using Newton's method. Although the asymptotic convergence of Newton's method is faster than ours, the initial ratio of work to error reduction with our method is much faster than Newton's. For real-time visual applications, where speed and stability are more important than precision, we obtain visually acceptable results at a total cost per timestep that is only a fraction of that required for a single Newton iteration. When higher accuracy is required, our algorithm can be used to compute a good starting point for subsequent Newton's iteration.

The articles in this special section consist of selected papers from the 10th annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation that was held 5-7 August 2011.

Abstract We investigate the representation of signals defined on triangle meshes using linearly interpolated vertex attributes. Compared to texture mapping, storing data only at vertices yields significantly lower memory overhead and less expensive runtime reconstruction. However, standard approaches to determine vertex values such as point sampling or averaging triangle samples lead to suboptimal approximations. We discuss how an optimal solution can be efficiently calculated using continuous least‐squares. In addition, we propose a regularization term that allows us to minimize gradient discontinuities and mach banding artifacts while staying close to the optimum. Our method has been integrated in a game production lighting tool and we present examples of representing signals such as ambient occlusion and precomputed radiance transfer in real game scenes, where vertex baking was used to free up resources for other game components.

We propose a method for learning linear upsampling operators for physically-based cloth simulation, allowing us to enrich coarse meshes with mid-scale details in minimal time and memory budgets, as required in computer games. In contrast to classical subdivision schemes, our operators adapt to a specific context (e.g. a flag flapping in the wind or a skirt worn by a character), which allows them to achieve higher detail. Our method starts by pre-computing a pair of coarse and fine training simulations aligned with tracking constraints using harmonic test functions. Next, we train the upsampling operators with a new regularization method that enables us to learn mid-scale details without overfitting. We demonstrate generalizability to unseen conditions such as different wind velocities or novel character motions. Finally, we discuss how to re-introduce high frequency details not explainable by the coarse mesh alone using oscillatory modes .

In this paper we present a visually compelling and informative cartoon rendering style for liquid animations. Our style is inspired by animations such as Futurama,1 The Little Mermaid,2 and Bambi2. We take as input a liquid surface obtained from a three-dimensional physically based liquid simulation system and output animations that evoke a cartoon style and convey liquid movement. Our method is based on four cues that emphasize properties of the liquid's shape and motion. We use bold outlines to emphasize depth discontinuities, patches of constant color to highlight near-silhouettes and areas of thinness, and, optionally place temporally coherent oriented textures on the liquid surface to help convey motion.

We present an extension to Lagrangian finite element methods to allow for large plastic deformations of solid materials. These behaviors are seen in such everyday materials as shampoo, dough, and clay as well as in fantastic gooey and blobby creatures in special effects scenes. To account for plastic deformation, we explicitly update the linear basis functions defined over the finite elements during each simulation step. When these updates cause the basis functions to become ill-conditioned, we remesh the simulation domain to produce a new high-quality finite-element mesh, taking care to preserve the original boundary. We also introduce an enhanced plasticity model that preserves volume and includes creep and work hardening/softening. We demonstrate our approach with simulations of synthetic objects that squish, dent, and flow. To validate our methods, we compare simulation results to videos of real materials.

In this article, we present a semi-Lagrangian surface tracking method for use with fluid simulations. Our method maintains an explicit polygonal mesh that defines the surface, and an octree data structure that provides both a spatial index for the mesh and a means for efficiently approximating the signed distance to the surface. At each timestep, a new surface is constructed by extracting the zero set of an advected signed-distance function. Semi-Lagrangian backward path tracing is used to advect the signed-distance function. One of the primary advantages of this formulation is that it enables tracking of surface characteristics, such as color or texture coordinates, at negligible additional cost. We include several examples demonstrating that the method can be effectively used as part of a fluid simulation to animate complex and interesting fluid behaviors.

This paper describes a technique for animating the behavior of viscoelastic fluids, such as mucus, liquid soap, pudding, toothpaste, or clay, that exhibit a combination of both fluid and solid characteristics. The technique builds upon prior Eulerian methods for animating incompressible fluids with free surfaces by including additional elastic terms in the basic Navier-Stokes equations. The elastic terms are computed by integrating and advecting strain-rate throughout the fluid. Transition from elastic resistance to viscous flow is controlled by von Mises's yield condition, and subsequent behavior is then governed by a quasi-linear plasticity model.

In this paper, we describe a method for realistically animating ductile fracture in common solid materials such as plastics and metals. The effects that characterize ductile fracture occur due to interaction between plastic yielding and the fracture process. By modeling this interaction, our ductile fracture method can generate realistic motion for a much wider range of materials than could be realized with a purely brittle model. This method directly extends our prior work on brittle fracture [O'Brien and Hodgins, SIGGRAPH 99]. We show that adapting that method to ductile as well as brittle materials requires only a simple to implement modification that is computationally inexpensive. This paper describes this modification and presents results demonstrating some of the effects that may be realized with it.