Month: June 2017

kDet: Parallel Constant Time Collision Detection for Polygonal Objects

René Weller, Nicole Debowski and Gabriel Zachmann

We define a novel geometric predicate and a class of objects that enables us to prove a linear bound on the number of intersecting polygon pairs for colliding 3D objects in that class. Our predicate is relevant both in theory and in practice: it is easy to check and it needs to consider only the geometric properties of the individual objects – it does not depend on the configuration of a given pair of objects. In addition, it characterizes a practically relevant class of objects: we checked our predicate on a large database of real-world 3D objects and the results show that it holds for all but the most pathological ones. Our proof is constructive in that it is the basis for a novel collision detection algorithm that realizes this linear complexity also in practice. Additionally, we present a parallelization of this algorithm with a worst-case running time that is independent of the number of polygons. Our algorithm is very well suited not only for rigid but also for deformable and even topology-changing objects, because it does not require any complex data structures or pre-processing. We have implemented our algorithm on the GPU and the results show that it is able to find in real-time all colliding polygons for pairs of deformable objects consisting of more than 200k triangles, including self-collisions.

kDet: Parallel Constant Time Collision Detection for Polygonal Objects

Geometric Stiffness for Real-time Constrained Multibody Dynamics

Sheldon Andrews, Marek Teichmann, Paul Kry

This paper focuses on the stable and efficient simulation of articulated rigid body systems for real-time applications. Specifically, we focus on the use of geometric stiffness, which can dramatically increase simulation stability. We examine several numerical problems with the inclusion of geometric stiffness in the equations of motion, as proposed by previous work, and address these issues by introducing a novel method for efficiently building the linear system. This offers improved tractability and numerical efficiency. Furthermore, geometric stiffness tends to significantly dissipate kinetic energy. We propose an adaptive damping scheme, inspired by the geometric stiffness, that uses a stability criterion based on the numerical integrator to determine the amount of non-constitutive damping required to stabilize the simulation. With this approach, not only is the dynamical behavior better preserved, but the simulation remains stable for mass ratios of 1,000,000-to-1 at time steps up to 0.1 s. We present a number of challenging scenarios to demonstrate that our method improves efficiency, and that it increases stability by orders of magnitude compared to previous work.

Geometric Stiffness for Real-time Constrained Multibody Dynamics

Fluxed Animated Boundary Method

Alexey Stomakhin, Andrew Selle

We present a novel approach to guiding physically based particle simulations using boundary conditions. Unlike commonly used ad hoc particle techniques for adding and removing the material from a simulation, our approach is principled by utilizing the concept of volumetric flux. Artists are provided with a simple yet powerful primitive called a fluxed animated boundary (FAB), allowing them to specify a control shape and a material flow field. The system takes care of enforcing the corresponding boundary conditions and necessary particle reseeding. We show how FABs can be used artistically or physically. Finally, we demonstrate production examples that show the efficacy of our method.

Fluxed Animated Boundary Method

Quasi-Newton Methods for Real-time Simulation of Hyperelastic Materials

Tiantian Liu, Sofien Bouaziz, Ladislav Kavan

We present a new method for real-time physics-based simulation supporting many different types of hyperelastic materials. Previous methods such as Position Based or Projective Dynamics are fast, but support only limited selection of materials; even classical materials such as the Neo-Hookean elasticity are not supported. Recently, Xu et al. [2015] introduced new “splinebased materials” which can be easily controlled by artists to achieve desired animation effects. Simulation of these types of materials currently relies on Newton’s method, which is slow, even with only one iteration per timestep. In this paper, we show that Projective Dynamics can be interpreted as a quasi-Newton method. This insight enables very efficient simulation of a large class of hyperelastic materials, including the Neo-Hookean, spline-based materials, and others. The quasi-Newton interpretation also allows us to leverage ideas from numerical optimization. In particular, we show that our solver can be further accelerated using L-BFGS updates (Limitedmemory Broyden-Fletcher-Goldfarb-Shanno algorithm). Our final method is typically more than 10 times faster than one iteration of Newton’s method without compromising quality. In fact, our result is often more accurate than the result obtained with one iteration of Newton’s method. Our method is also easier to implement, implying reduced software development costs.

Quasi-Newton Methods for Real-time Simulation of Hyperelastic Materials