Category: Rods

Cable Joints

Matthias Müller, Nuttapong Chentanez, Stefan Jeschke, Miles Macklin

Robustly and efficiently simulating cables and ropes that are part of a larger system such as cable driven machines, cable cars or tendons in a human or robot is a challenging task. To be able to adapt to the environment, cables are typically modeled as a large number of small segments that are connected via joints. The two main difficulties with this approach are to satisfy the inextensibility constraint and to handle the typically large mass ratio between the small segments and the larger objects they connect. In this paper we present a new approach which solves these problems in a simple and effective way. Our method is based on the idea to simulate the effect of the cables instead of the cables themselves. To this end we propose a new special type of distance constraint we call cable joint that changes both its attachment points and its rest length dynamically. A cable connecting a series of objects is then modeled as a sequence of cable joints which reduces the complexity of the simulation from the order of the number of segments to just the number of connected objects. This makes simulations both faster and more robust as we will demonstrate on a variety of examples.

Cable Joints

Cosserat Rods with Projective Dynamics

Carlota Soler, Tobias Martin, Olga Sorkine-Hornung

We present a novel method to simulate Cosserat rods with Projective Dynamics (PD). The proposed method is both numerically robust and accurate with respect to the underlying physics, making it suitable for a variety of applications in computer graphics and related disciplines. Cosserat theory assigns an orientation frame to each point and is thus able to realistically simulate stretching and shearing effects, in addition to bending and twisting. Within the PD framework, it is possible to obtain accurate simulations given the implicit integration over time and its decoupling of the local-global solve. In the proposed method, we start from the continuous formulation of the Cosserat theory and derive the constraints for the PD solver. We extend the standard definition of PD and add body orientations as system variables. Thus, we include the preservation of angular momentum, so tha twisting and bending can be accurately simulated. Our formulation allows the simulation of different bending behaviors with respect to a user-defined Young’s modulus, the radius of the rod’s cross-section, and material density. We show how different material specifications in our simulations converge within a few iterations to a reference solution, generated with a high-precision finite element method. Furthermore, we demonstrate mesh independence of our formulation: Refining the simulation mesh still results in the same characteristic motion, which is in contrast to previous position based method.

Comparison of Mixed Linear Complementarity Problem Solvers for Multibody Simulations with Contact

Andreas Enzenhofer, Sheldon Andrews, Marek Teichmann, Jozsef Kövecses

The trade-off between accuracy and computational performance is one of the central conflicts in real-time multibody simulations, much of which can be attributed to the method used to solve the constrained multibody equations. This paper examines four mixed linear complementarity problem (MLCP) algorithms when they are applied to physical problems involving frictional contact. We consider several different, and challenging, test cases such as grasping, stability of static models, closed loops, and long chains of bodies. The solver parameters are tuned for these simulations and the results are evaluated in terms of numerical accuracy and computational performance. The objective of this paper is to determine the accuracy properties of each solver, find the appropriate method for a defined task, and thus draw conclusions regarding the applicability of each method

Comparison of Mixed Linear Complementarity Problem Solvers for Multibody Simulations with Contact

Direct Position-Based Solver for Stiff Rods

Crispin Deul, Tassilo Kugelstadt, Marcel Weiler, Jan Bender

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 ten-thousand segments. In summary, our method allows the efficient simulation of stiff rods in the Position-Based Dynamics framework with a speedup of two orders of magnitude compared to the original XPBD approach.

Direct Position-Based Solver for Stiff Rods

A Multi-Scale Model for Simulating Liquid-Hair Interactions

Yun (Raymond) Fei, Henrique Teles Maia, Christopher Batty, Changxi Zheng, Eitan Grinspun

The diverse interactions between hair and liquid are complex and span multiple length scales, yet are central to the appearance of humans and animals in many situations. We therefore propose a novel multi-component simulation framework that treats many of the key physical mechanisms governing the dynamics of wet hair. The foundations of our approach are a discrete rod model for hair and a particle-in-cell model for fluids. To treat the thin layer of liquid that clings to the hair, we augment each hair strand with a height field representation. Our contribution is to develop the necessary physical and numerical models to evolve this new system and the interactions among its components. We develop a new reduced-dimensional liquid model to solve the motion of the liquid along the length of each hair, while accounting for its moving reference frame and influence on the hair dynamics. We derive a faithful model for surface tension-induced cohesion effects between adjacent hairs, based on the geometry of the liquid bridges that connect them. We adopt an empirically-validated drag model to treat the effects of coarse-scale interactions between hair and surrounding fluid, and propose new volume-conserving dripping and absorption strategies to transfer liquid between the reduced and particle-in-cell liquid representations. The synthesis of these techniques yields an effective wet hair simulator, which we use to animate hair flipping, an animal shaking itself dry, a spinning car wash roller brush dunked in liquid, and intricate hair coalescence effects, among several additional scenarios.

A Multi-Scale Model for Simulating Liquid-Hair Interactions

Position and Orientation Based Cosserat Rods

Tassilo Kugelstadt, Elmar Schoemer

We present a novel method to simulate bending and torsion of elastic rods within the position-based dynamics (PBD) framework. The main challenge is that torsion effects of Cosserat rods are described in terms of material frames which are attached to the centerline of the rod. But frames or orientations do not fit into the classical position-based dynamics formulation. To solve this problem we introduce new types of constraints to couple orientations which are represented by unit quaternions. For constraint projection quaternions are treated in the exact same way as positions. Unit length is enforced with an additional constraint. This allows us to use the strain measures form Cosserat theory directly as constraints in PBD. It leads to very simple  algebraic expressions for the correction displacements which only contain quaternion products and additions. Our results show that our method is very robust and accurately produces the complex bending and torsion effects of rods. Due to its simplicity our method is very efficient and more than one order of magnitude faster than existing position-based rod simulation methods. It even achieves the same performance as position-based simulations without torsion effects.

Position and Orientation Based Cosserat Rods

Wetbrush: GPU-based 3D painting simulation at the bristle level

Zhili Chen, Byungmoon Kim, Daichi Ito, Huamin Wang

We present a real-time painting system that simulates the interactions among brush, paint, and canvas at the bristle level. The key challenge is how to model and simulate sub-pixel paint details, given the limited computational resource in each time step. To achieve this goal, we propose to define paint liquid in a hybrid fashion: the liquid close to the brush is modeled by particles, and the liquid away from the brush is modeled by a density field. Based on this representation, we develop a variety of techniques to ensure the performance and robustness of our simulator under large time steps, including brush and particle simulations in non-inertial frames, a fixed-point method for accelerating Jacobi iterations, and a new Eulerian-Lagrangian approach for simulating detailed liquid effects. The resulting system can realistically simulate not only the motions of brush bristles and paint liquid, but also the liquid transfer processes among different representations. We implement the whole system on GPU by CUDA. Our experiment shows that artists can use the system to draw realistic and vivid digital paintings, by applying the painting techniques that they are familiar with but not offered by many existing systems.

Wetbrush: GPU-based 3D painting simulation at the bristle level

Yarn-Level Simulation of Woven Cloth

Gabriel Cirio, Jorge Lopez-Moreno, David Miraut, Miguel A. Otaduy

The large-scale mechanical behavior of woven cloth is determined by the mechanical properties of the yarns, the weave pattern, and frictional contact between yarns. Using standard simulation methods for elastic rod models and yarn-yarn contact handling, the simulation of woven garments at realistic yarn densities is deemed intractable. This paper introduces an efficient solution for simulating woven cloth at the yarn level. 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 models for internal yarn forces and inter-yarn frictional contact, as well as 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.

Yarn-Level Simulation of Woven Cloth

Coupling Hair with Smoothed Particle Hydrodynamics Fluids

Wei-Chin Lin

We present a two-way coupling technique for simulating the complex interaction between hair and fluids. In our approach, the motion of hair and fluids is simulated by evaluating the hydrodynamic forces among them based on boundary handling techniques used in SPH (Smoothed Particle Hydrodynamics) fluids. When hair makes contact with fluids, water absorption inside the hair volume can be simulated with a diffusion process by treating the hair volume as porous media with anisotropic permeability. The saturation of each hair strand is then used to derive the adhesive force between wet hair strands. This enables us to simulate the formation of hair clumps dynamically without the need to employ post clumping processes. The proposed method can be easily applied to any SPH fluid solvers as well as various hair models.

Coupling Hair with Smoothed Particle Hydrodynamics Fluids

Adaptive Nonlinearity for Collisions in Complex Rod Assemblies

Danny M. Kaufman, Rasmus Tamstorf, Breannan Smith, Jean-Marie Aubry, Eitan Grinspun

We develop an algorithm for the efficient and stable simulation of large-scale elastic rod assemblies. We observe that the time-integration step is severely restricted by a strong nonlinearity in the response of stretching modes to transversal impact, the degree of this nonlinearity varying greatly with the shape of the rod. Building on these observations, we propose the ADONIS collision response algorithm that adapts the degree of nonlinearity in impact solves. We illustrate the advantages of the ADONIS algorithm by analyzing simulations involving elastic rod assemblies of varying density and scale, with up to 1.7 million individual contacts per time step.

Adaptive Nonlinearity for Collisions in Complex Rod Assemblies