37-Issue 6

Permanent URI for this collection

https://diglib.eg.org/handle/10.2312/2632656

Browse

Browsing 37-Issue 6 by Subject "animation"

Now showing 1 - 2 of 2
  • No Thumbnail Available
    Item
    Direct Position‐Based Solver for Stiff Rods
    (© 2018 The Eurographics Association and John Wiley & Sons Ltd., 2018) Deul, Crispin; Kugelstadt, Tassilo; Weiler, Marcel; Bender, Jan; Chen, Min and Benes, Bedrich
    In this paper, we present a novel direct solver for the efficient simulation of stiff, inextensible elastic rods within the position‐based dynamics (PBD) framework. It is based on the XPBD algorithm, which extends PBD to simulate elastic objects with physically meaningful material parameters. XPBD approximates an implicit Euler integration and solves the system of non‐linear equations using a non‐linear Gauss–Seidel solver. However, this solver requires many iterations to converge for complex models and if convergence is not reached, the material becomes too soft. In contrast, we use Newton iterations in combination with our direct solver to solve the non‐linear equations which significantly improves convergence by solving all constraints of an acyclic structure (tree), simultaneously. Our solver only requires a few Newton iterations to achieve high stiffness and inextensibility. We model inextensible rods and trees using rigid segments connected by constraints. Bending and twisting constraints are derived from the well‐established Cosserat model. The high performance of our solver is demonstrated in highly realistic simulations of rods consisting of multiple 10 000 segments. In summary, our method allows the efficient simulation of stiff rods in the PBD framework with a speedup of two orders of magnitude compared to the original XPBD approach.We present a novel direct solver for the efficient simulation of stiff, inextensible elastic rods. It is based on the XPBD algorithm, which extends Position‐Based Dynamics to simulate elastic objects with physically meaningful material parameters. However, the non‐linear Gauss‐Seidel solver of XPBD requires many iterations to converge for complex models and if convergence is not reached, the material becomes too soft. In contrast, we use Newton iterations in combination with our direct solver which significantly improves convergence by solving all constraints of an acyclic structure simultaneously. We model rods using rigid segments connected by constraints. Bending and twisting constraints are derived from the Cosserat model. The high performance of our solver allows the simulation of rods consisting of multiple 10 000 segments with a speedup of two orders of magnitude compared to the original XPBD approach.
  • No Thumbnail Available
    Item
    An Implicit SPH Formulation for Incompressible Linearly Elastic Solids
    (© 2018 The Eurographics Association and John Wiley & Sons Ltd., 2018) Peer, Andreas; Gissler, Christoph; Band, Stefan; Teschner, Matthias; Chen, Min and Benes, Bedrich
    We propose a novel smoothed particle hydrodynamics (SPH) formulation for deformable solids. Key aspects of our method are implicit elastic forces and an adapted SPH formulation for the deformation gradient that—in contrast to previous work—allows a rotation extraction directly from the SPH deformation gradient. The proposed implicit concept is entirely based on linear formulations. As a linear strain tensor is used, a rotation‐aware computation of the deformation gradient is required. In contrast to existing work, the respective rotation estimation is entirely realized within the SPH concept using a novel formulation with incorporated kernel gradient correction for first‐order consistency. The proposed implicit formulation and the adapted rotation estimation allow for significantly larger time steps and higher stiffness compared to explicit forms. Performance gain factors of up to one hundred are presented. Incompressibility of deformable solids is accounted for with an ISPH pressure solver. This further allows for a pressure‐based boundary handling and a unified processing of deformables interacting with SPH fluids and rigids. Self‐collisions are implicitly handled by the pressure solver.We propose a novel smoothed particle hydrodynamics (SPH) formulation for deformable solids. We propose a novel smoothed particle hydrodynamics (SPH) formulation for deformable solids. Key aspects of our method are implicit elastic forces and an adapted SPH formulation for the deformation gradient that—in contrast to previous work—allows a rotation extraction directly from the SPH deformation gradient. The proposed implicit concept is entirely based on linear formulations. As a linear strain tensor is used, a rotation‐aware computation of the deformation gradient is required. In contrast to existing work, the respective rotation estimation is entirely realized within the SPH concept using a novel formulation with incorporated kernel gradient correction for first‐order consistency.