Research
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Projective Dynamics: Fusing Constraint Projections for Fast Simulation
Sofien Bouaziz, Sebastian Martin, Tiantian Liu, Ladislav Kavan, Mark Pauly
ACM Transactions on Graphics (Proc. ACM SIGGRAPH 2014)
ACM Transactions on Graphics (Proc. ACM SIGGRAPH 2014)
We present a new method for implicit time integration of physical
systems. Our approach builds a bridge between nodal Finite Element methods and Position Based Dynamics, leading to a simple, efficient, robust, yet accurate solver that supports many different types of constraints. We propose specially designed energy potentials that can be solved efficiently using an alternating optimization approach. Inspired by continuum mechanics, we derive a set of continuumbased potentials that can be efficiently incorporated within our solver. We demonstrate the generality and robustness of our approach in many different applications ranging from the simulation of solids, cloths, and shells, to example-based simulation. Comparisons to Newton-based and Position Based Dynamics solvers highlight the benefits of our formulation. Video Youtube Binaries |
Rig-Space Physics
Fabian Hahn, Sebastian Martin, Bernhard Thomaszewski, Robert Sumner, Stelian Coros, Markus Gross
ACM Transactions on Graphics (Proc. ACM SIGGRAPH 2012)
ACM Transactions on Graphics (Proc. ACM SIGGRAPH 2012)
We present a method that brings the benefits of physics-based simulations to traditional animation pipelines. We formulate the equations of motions in the subspace of deformations defined by ananimator’s rig. Our framework fits seamlessly into the workflow
typically employed by artists, as our output consists of animation curves that are identical in nature to the result of manual keyframing. Artists can therefore explore the full spectrum between handcrafted animation and unrestricted physical simulation. To enhance the artist’s control, we provide a method that transforms stiffness values defined on rig parameters to a non-homogeneous distribution of material parameters for the underlying FEM model. In addition, we use automatically extracted high-level rig parameters to intuitively edit the results of our simulations, and also to speed up computation. To demonstrate the effectiveness of our method, we create compelling results by adding rich physical motions to coarse input animations. In the absence of artist input, we create realistic passive motion directly in rig space. Video |
Deformable Objects Alive!
Stelian Coros, Sebastian Martin, Bernhard Thomaszewski, Christian Schumacher, Robert Sumner, Markus Gross
ACM Transactions on Graphics (Proc. ACM SIGGRAPH 2012)
ACM Transactions on Graphics (Proc. ACM SIGGRAPH 2012)
We present a method for controlling the motions of active deformablecharacters. As an underlying principle, we require thatall motions be driven by internal deformations. We achieve this bydynamically adapting rest shapes in order to induce deformations
that, together with environment interactions, result in purposeful and physically-plausible motions. Rest shape adaptation is a powerful concept and we show that by restricting shapes to suitable subspaces, it is possible to explicitly control the motion styles of deformable characters. Our formulation is general and can be combined with arbitrary elastic models and locomotion controllers. We demonstrate the efficiency of our method by animating curve, shell, and solid-based characters whose motion repertoires range from simple hopping to complex walking behaviors. Video |
Efficient Simulation of Example-Based Materials
Christian Schumacher, Bernhard Thomaszewski, Stelian Coros, Sebastian Martin, Robert Sumner, Markus Gross
ACM/Eurographics Symposium on Computer Animation (SCA), 2012
ACM/Eurographics Symposium on Computer Animation (SCA), 2012
We present a new method for efficiently simulating art-directable deformable materials. We use example poses todefine subspaces of desirable deformations via linear interpolation. As a central aspect of our approach, we use
an incompatible representation for input and interpolated poses that allows us to interpolate between elements individually. This enables us to bypass costly reconstruction steps and we thus achieve significant performance improvements compared to previous work. As a natural continuation, we furthermore present a formulation of example-based plasticity. Finally, we extend the directability of example-based materials and explore a number of powerful control mechanisms. We demonstrate these novel concepts on a number of solid and shell animations including artistic deformation behaviors, cartoon physics, and example-based pose space dynamics. Video |
Example-Based Elastic Materials
Sebastian Martin, Bernhard Thomaszewski, Eitan Grinspun, Markus Gross
ACM Transactions on Graphics (Proc. ACM SIGGRAPH 2011)
ACM Transactions on Graphics (Proc. ACM SIGGRAPH 2011)
We propose an example-based approach for simulating complex
elastic material behavior. Supplied with a few poses that characterize a given object, our system starts by constructing a space of prefered deformations by means of interpolation. During simulation, this example manifold then acts as an additional elastic attractor that guides the object towards its space of prefered shapes. Added on top of existing solid simulation codes, this example potential effectively allows us to implement inhomogeneous and anisotropic materials in a direct and intuitive way. Due to its example-based interface, our method promotes an art-directed approach to solid simulation, which we exemplify on a set of practical examples. Video |
Unified Simulation of Elastic Rods, Shells, and Solids
Sebastian Martin, Peter Kaufmann, Mario Botsch, Eitan Grinspun, Markus Gross
ACM Transactions on Graphics (Proc. ACM SIGGRAPH 2010)
ACM Transactions on Graphics (Proc. ACM SIGGRAPH 2010)
We develop an accurate, unified treatment of elastica. Following the method of resultant-based formulation to its logical extreme, we derive a higher-order integration rule, or elaston, measuring stretching, shearing, bending, and twisting along any axis. The theory and accompanying implementation do not distinguish between forms of different dimension (solids, shells, rods), nor between manifold regions and non-manifold junctions. Consequently, a single code accurately models a diverse range of elastoplastic behaviors, including buckling, writhing, cutting and merging. Emphasis on convergence to the continuum sets us apart from early unification efforts.
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Shape-Preserving Animation of Deformable Objects
Sebastian Martin, Christoph Huber, Peter Kaufmann, Markus Gross
Proceedings of Vision, Modeling, and Visualization (VMV) 2009
Proceedings of Vision, Modeling, and Visualization (VMV) 2009
We present a novel approach for animating elastically deformable solids in a shape-preserving manner. Standard approaches to animate this kind of objects are based on classic FEM discretizations of the elasticity theory, combined with embedding techniques to deform highly-detailed object geometries. However, these approaches are usually not able to preserve fine geometric features at sub-element scales, showing visually disturbing deformations. We propose to use Green Coordinates (GC) for the representation of the deformation field to get shapepreservation by construction and describe how to discretize the elastic energy using these cage-based coordinates. By linearizing the deformation field we arrive at a simple approach which leads to just a few additional terms compared to classic FEM discretizations.
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Enrichment Textures for Detailed Cutting of Shells
Peter Kaufmann, Sebastian Martin, Mario Botsch, Eitan Grinspun, Markus Gross
ACM Transactions on Graphics (Proc. ACM SIGGRAPH 2009)
ACM Transactions on Graphics (Proc. ACM SIGGRAPH 2009)
We present a method for simulating highly detailed cutting and fracturing of thin shells using low-resolution simulation meshes. Instead of refining or remeshing the underlying simulation domain to resolve complex cut paths, we adapt the extended finite element method (XFEM) and enrich our approximation by customdesigned basis functions, while keeping the simulation mesh unchanged. The enrichment functions are stored in enrichment textures, which allows for fracture and cutting discontinuities at a resolution much finer than the underlying mesh, similar to image textures for increased visual resolution. Furthermore, we propose harmonic enrichment functions to handle multiple, intersecting, arbitrarily shaped, progressive cuts per element in a simple and unified framework. Our underlying shell simulation is based on discontinuous Galerkin (DG) FEM, which relaxes the restrictive requirement of C1 continuous basis functions and thus allows for simpler, C0 continuous XFEM enrichment functions.
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Flexible Simulation of Deformable Models Using Discontinuous Galerkin FEM
Peter Kaufmann, Sebastian Martin, Mario Botsch, Markus Gross
Journal of Graphical Models, 2009, Special Issue of ACM SIGGRAPH / Eurographics Symposium on Computer Animation 2008
Journal of Graphical Models, 2009, Special Issue of ACM SIGGRAPH / Eurographics Symposium on Computer Animation 2008
We propose a simulation technique for elastically deformable objects based on the discontinuous Galerkin finite element method (DG FEM). In contrast to traditional FEM, it overcomes the restrictions of conforming basis functions by allowing for discontinuous elements with weakly enforced continuity constraints. This added exibility enables the simulation of arbitrarily shaped, convex and non-convex polyhedral elements, while still using simple polynomial basis functions. For the accurate strain integration over these elements we propose an analytic technique based on the divergence theorem. Being able to handle arbitrary elements eventually allows us to derive simple and efficient techniques for volumetric mesh generation, adaptive mesh refinement, and robust cutting. Furthermore, we show DG FEM not to suer from locking artifacts even for nearly incompressible materials, a problem that in standard FEM requires special handling.
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Polyhedral Finite Elements Using Harmonic Basis Functions
Sebastian Martin, Peter Kaufmann, Martin Wicke, Mario Botsch, Markus Gross
Proceedings of Eurographics Symposium on Geometry Processing 2008, Computer Graphics Forum 2008, (Best Student Paper Award)
Proceedings of Eurographics Symposium on Geometry Processing 2008, Computer Graphics Forum 2008, (Best Student Paper Award)
Finite element simulations in computer graphics are typically based on tetrahedral or hexahedral elements, which enables simple and efficient implementations, but in turn requires complicated remeshing in case of topological changes or adaptive refinement. We propose a flexible finite element method for arbitrary polyhedral elements, thereby effectively avoiding the need for remeshing. Our polyhedral finite elements are based on harmonic basis functions, which satisfy all necessary conditions for FEM simulations and seamlessly generalize both linear tetrahedral and trilinear hexahedral elements. We discretize harmonic basis functions using the method of fundamental solutions, which enables their flexible computation and efficient evaluation. The versatility of our approach is demonstrated on cutting and adaptive refinement within a simulation framework for corotated linear elasticity.
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