Animation of Deformable Bodies with Quadratic Bézier Finite Elements

Adam W. Bargteil, Elaine Cohen

In this paper, 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 non-linear 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 non-linear rest shapes.

Animation of Deformable Bodies with Quadratic Bezier Finite Elements

Vriphys 2014

I’ve been slow in getting this list together, so without further ado:

  • Continuous Collision Detection Between Points and Signed Distance Fields
  • Massively Parallel Batch Neural Gas for Bounding Volume Hierarchy Construction
  • Massively-Parallel Proximity Queries for Point Clouds
  • Efficient Transfer of Contact-Point Local Deformations in Data-Driven Simulations Using Hermitian Moments
  • A unified topological-physical model for adaptive refinement
  • A p-Multigrid Algorithm using Cubic Finite Elements for Efficient Deformation Simulation
  • Mechanical modelling of three-dimensional plant tissue indented by a probe
  • Controlling the Shape and Motion of Plumes in Explosion Simulations
  • SutureHap: a Suture Simulator with Haptic Feedback
  • Information Fusion for Real-time Motion Estimation in Image-guided Breast Biopsy Navigation
  • Virtual Fitting Pipeline: Body Dimension Recognition, Cloth Modelling, and On-Body Simulation
  • Coupling Hair with Smoothed Particle Hydrodynamics Fluids
  • A Parallel Architecture for IISPH Fluids
  • An Improved Jacobi Solver for Particle Simulation
  • Parallel Particles: A Parallel Position Based Approach for Fast and Stable Simulation of Granular Materials
  • Laplacian Cut-Maps for Real-Time Deformables
  • Variable stiffness haptic interface controlled through Inverse simulation

If anyone has links to the associated papers for the (many) missing ones, please let me know!

Continuous Collision Detection Between Points and Signed Distance Fields

Hongyi Xu, Jernej Barbic

We present an algorithm for fast continuous collision detection between points and signed distance fields. Such robust queries are often needed in computer animation, haptics and virtual reality applications, but have so far only been investigated for polygon (triangular) geometry representations. We demonstrate how to use an octree subdivision of the distance field for fast traversal of distance field cells. We also give a method to combine octree subdivision with points organized into a tree hierarchy, for efficient culling of continuous collision detection tests. We apply our method to multibody rigid simulations, and demonstrate that our method accelerates continuous collision detection between points and distance fields by an order of magnitude.

Continuous Collision Detection Between Points and Signed Distance Fields

Fast and Exact Continuous Collision Detection with Bernstein Sign Classification

Min Tang, Ruofeng Tong, Zhendong Wang, Dinesh Manocha

We present fast algorithms to perform accurate CCD queries between triangulated models. Our formulation uses properties of the Bernstein basis and Bezier curves and reduces the problem to evaluating signs of polynomials. We present a geometrically exact CCD algorithm based on the exact geometric computation paradigm to perform reliable Boolean collision queries. This algorithm is more than an order of magnitude faster than prior exact algorithms. We evaluate its performance for cloth and FEM simulations on CPUs and GPUs, and highlight the benefits.

Fast and Exact Continuous Collision Detection with Bernstein Sign Classification

Subspace Clothing Simulation Using Adaptive Bases

Fabian Hahn, Bernhard Thomaszewski, Stelian Coros, Robert W. Sumner, Forrester Cole, Mark Meyer, Tony DeRose, and Markus Gross

We present a new approach to clothing simulation using low-dimensional linear subspaces with temporally adaptive bases. Our method exploits full-space simulation training data in order to construct a pool of low-dimensional bases distributed across pose space. For this purpose, we interpret the simulation data as offsets from a kinematic deformation model that captures the global shape of clothing due to body pose. During subspace simulation, we select low-dimensional sets of basis vectors according to the current pose of the character and the state of its clothing. Thanks to this adaptive basis selection scheme, our method is able to reproduce diverse and detailed folding patterns with only a few basis vectors. Our experiments demonstrate the feasibility of subspace clothing simulation and indicate its potential in terms of quality and computational efficiency.

Subspace Clothing Simulation Using Adaptive Bases

Coupling 3D Eulerian, Height Field and Particle Methods for the Simulation of Large Scale Liquid Phenomena

Nuttapong Chentanez, Matthias Mueller, Tae-Yong Kim

We propose a new method to simulate large scale water phenomena by combining particle, 3D grid and height field methods. In contrast to most hybrid approaches that use particles to simulate foam and spray only, we also represent the bulk of water near the surface with both particles and a grid depending on the regions of interest and switch between those two representations during the course of the simulation. For the coupling we leverage the recent idea of tracking the water surface with a density field in grid based methods. Combining particles and a grid simulation then amounts to adding the density field of the particles and the one stored on the grid. For open scenes, we simulate the water outside of the 3D grid domain by solving the Shallow Water Equations on a height field. We propose new methods to couple these two domains such that waves travel naturally across the border. We demonstrate the effectiveness of our approach in various scenarios including a whale breaching simulation, all running in real-time or at interactive rates.

Coupling 3D Eulerian, Height Field and Particle Methods for the Simulation of Large Scale Liquid Phenomena

An Adaptive Virtual Node Algorithm with Robust Mesh Cutting

Yuting Wang, Chenfanfu Jiang, Craig Schroeder, Joseph Teran

We present a novel virtual node algorithm (VNA) for changing tetrahedron mesh topology to represent arbitrary cutting triangulated surfaces. Our approach addresses a number of shortcomings in the original VNA of [MBF04]. First, we generalize the VNA so that cuts can pass through tetrahedron mesh vertices and lie on mesh edges and faces. The original algorithm did not make sense for these cases and required often ambiguous perturbation of the cutting surface to avoid them. Second, we develop an adaptive approach to the definition of embedded material used for element duplication. The original algorithm could only handle a limited number of configurations which restricted cut surfaces to have curvature at the scale of the tetrahedron elements. Our adaptive approach allows for cut surfaces with curvatures independent of the embedding tetrahedron mesh resolution. Finally, we present a novel, provably-robust floating point mesh intersection routine that accurately registers triangulated surface cuts against the background tetrahedron mesh without the need for exact arithmetic.

An Adaptive Virtual Node Algorithm with Robust Mesh Cutting

Augmented MPM for phase-change and varied materials

Alexey Stomakhin, Craig Schroeder, Chenfanfu Jiang, Lawrence Chai, Joseph Teran, Andrew Selle

In this paper, we introduce a novel material point method for heat transport, melting and solidifying materials. This brings a wider range of material behaviors into reach of the already versatile material point method. This is in contrast to best-of-breed fluid, solid or rigid body solvers that are difficult to adapt to a wide range of materials. Extending the material point method requires several contributions. We introduce a dilational/deviatoric splitting of the constitutive model and show that an implicit treatment of the Eulerian evolution of the dilational part can be used to simulate arbitrarily incompressible materials. Furthermore, we show that this treatment reduces to a parabolic equation for moderate compressibility and an elliptic, Chorin-style projection at the incompressible limit. Since projections are naturally done on marker and cell (MAC) grids, we devise a staggered grid MPM method. Lastly, to generate varying material parameters, we adapt a heat-equation solver to a material point framework.

Augmented MPM for phase-change and varied materials

Optimization Integrator for Large Time Steps

Theodore F. Gast, Craig Schroeder

Practical time steps in today’s state-of-the-art simulators typically rely on Newton’s method to solve large systems of nonlinear equations. In practice, this works well for small time steps but is unreliable at large time steps at or near the frame rate, particularly for difficult or stiff simulations. We show that recasting backward Euler as a minimization problem allows Newton’s method to be stabilized by standard optimization techniques with some novel improvements of our own. The resulting solver is capable of solving even the toughest simulations at the 24Hz frame rate and beyond. We show how simple collisions can be incorporated directly into the solver through constrained minimization without sacrificing efficiency. We also present novel penalty collision formulations for self collisions and collisions against scripted bodies designed for the unique demands of this solver.

Optimization Integrator for Large Time Steps

Sensitivity-optimized Rigging for Example-based Real-Time Clothing Synthesis

Weiwei Xu, Noboyuki Umetani, Qianwen Chao, Jie Mao, Xiaogang Jin, Xin Tong

We present a real-time solution for generating detailed clothing deformations from pre-computed clothing shape examples. Given an input pose, it synthesizes a clothing deformation by blending skinned clothing deformations of nearby examples controlled by the body skeleton. Observing that cloth deformation can be well modeled with sensitivity analysis driven by the underlying skeleton, we introduce a sensitivity based method to construct a pose-dependent rigging solution from sparse examples. We also develop a sensitivity based blending scheme to find nearby examples for the input pose and evaluate their contributions to the result. Finally, we propose a stochastic optimization based greedy scheme for sampling the pose space and generating example clothing shapes. Our solution is fast, compact and can generate realistic clothing animation results for various kinds of clothes in real time.

Sensitivity-optimized Rigging for Example-based Real-Time Clothing Synthesis