Many objects and materials around us are of a deformable nature. Relevant examples include clothing, furniture, plants, paper and cardboard, plastic utensils, or even our own skin and hair. Our work aims to develop deformation models that are more computationally efficient or achieve higher realism. We pay special attention to the solution of dynamic deformations under contact, when motion is governed by a combination of internal forces and contact constraints.
The classical way to achieve highly realistic behavior in physically-based simulation of deformations is to design a sufficiently rich constitutive model of the material, and then finely tune the parameters of this model. In the Animetrics project, we propose to largely simplify this complex modeling procedure by capturing several deformation samples, fitting simple material models to the samples, and then modeling non-linear heterogeneous behaviors by interpolating the simple materials. Please see here more information on our research on data-driven simulation methods. Early evidence of our work demonstrates modeling complex elastic deformations by fitting linear deformation models to captured examples (Miguel et al. 2012).
Yarn-Level Cloth Simulation
The large-scale mechanical behavior of cloth is determined by the mechanical properties of the yarns, the weave pattern, and frictional contact between yarns. Standard deformation models use mesh-based continuous approximations of the cloth. There have been some works on yarn-level simulation of knitted cloth. However, the simulation of woven garments at realistic yarn densities, using standard simulation method for elastic rod models and yarn-yarn contact handling, is deemed intractable.
We propose an efficient solution for simulating woven cloth at the yarn level (Cirio et al. 2014). Central to our solution is a novel discretization of interlaced yarns based on yarn crossings and yarn sliding, which allows modeling yarn-yarn contact implicitly, avoiding contact handling at yarn crossings altogether. Combined with a massively parallel solver, we are able to simulate garments with hundreds of thousands of yarn crossings at practical framerates on a desktop machine, showing combinations of large-scale and fine-scale effects induced by yarn-level mechanics. We also provide a solution on the GPU for simultaneous visualization and voxelization of the yarn-level cloth, suitable for both interactive and offline rendering (Lopez et al. 2014). Our method can interactively voxelize millions of polygons into a 3D texture, generating a volume with sub-voxel accuracy which is suitable even for high-density weaving such as linen.
Heterogeneity – Deformation of Medical Images
Many inherently deformable structures, such as human anatomy, are highly heterogeneous. We develop methods to interactively deform heterogeneous volumes, which can be used for medical training and planning applications based on CT and MRI images. This problem involves several challenges on both deformation and visualization of regular volumetric discretizations. Our approach rests on two major components: a massively parallel algorithm for the rasterization of tetrahedral meshes (Gascon et al. 2013) and a method to define a coarse deformable tetrahedral mesh for the homogeneization of a fine heterogeous mesh (Torres et al. 2014). This allows us to simulate the deformation of heterogeneous volume data with over 20 million voxels at interactive rates. Plus, we achieve a level of fidelity close to much finer discretizations with an improvement in performance of several orders of magnitude.
Nonlinear Mechanics – Skin and Virtual Touch
Real-world materials exhibit highly nonlinear mechanical behavior, but computer animation often neglects such nonlinearities. Hyperelasticity, or strain-dependent material stiffness, is one of the clear sources of nonlinearity. Correctly modeling real-world materials would require capturing strain-dependent elasticity, but hyperelasticity induces stiff differential equations that may complicate simulation, in particular for real-time computer animation. We develop novel methods for interactive simulation of hyperelastic materials using strain-limiting constraints (Perez et al. 2013) in a standard constrained dynamics solver. We focus on capturing the anisotropic behavior of materials (Hernandez et al. 2013) and avoiding well-known problem, such as locking, by defining energy constraints (Perez et al. 2013).
Among others, human skin and flesh behave in a way that is highly nonlinear. Our ideas on hyperelastic materials simulation are being applied on the command of haptic devices for rendering direct interaction with the hand. Our approach enables haptic rendering of rich and compelling deformations of the fingertip, which are used in the context of werable haptics, a novel concept for the systematic exploration of haptics in advanced cognitive systems and robotics that will redefine the way humans will cooperate with robots (Wearhap Project).
Related to the previous feature, common deformable objects, such as human flesh, can be aslo modeled as a rigid core surrounded by a layer of soft tissue. Under that assumption, we have optimized the computation of dynamic deformations with contact, using a formulation that exploits a rigid core (Galoppo et al. 2006) or an articulated core (Galoppo et al. 2007). With this definition of deformations in a layer of soft tissue, we can also efficiently compute deformation dynamics on 2D textures in graphics hardware (Galoppo et al. 2006).
Fracture is becoming an increasingly important field within deformation modelling. In particular, animation and videogames industry is demanding higher visual fidelity and more control over the outcomes of a simulation. In that field, we proposed a novel algorithm to simulate brittle fracture (Schvarzman and Otaduy, 2014, a and Schvarzman and Otaduy, 2014, b). It augments previous methods based on Voronoi diagrams, improving their versatility and their ability to adapt fracture patterns automatically to diverse collision scenarios and object properties. We cast brittle fracture as the computation of a high-dimensional Centroidal Voronoi Diagram (CVD), where the distribution of fracture fragments is guided by the deformation field of the fractured object. By formulating the problem in high dimensions, we support robustly object and crack concavities, as well as intuitive artist control. We further accelerate the fracture animation process with example-based learning of the fracture degree, and a highly parallel tessellation algorithm. As a result, we obtain fast animations of detailed and rich fractures, with fracture patterns that adapt to each particular collision scenario.
The increasing importance of simulation on real-time applications is demanding to optimize methods further in order to achieve interactive rates. Another way to optimize the simulation of deformations is to focus on the degrees of freedom only where necessary, using adaptive simulation. We have investigated an approach to adaptive simulation of deformations based on multigrid methods (Otaduy et al. 2007). We have also incorporated adaptivity to geometrically inspired shape-matching deformation methods, which trade some physical realism for increased robustness and efficiency (Steinemann et al. 2008).