The 3 × 3 local mass matrix fully characterizes a pair of colliding “rigid” bodies for many purposes. We prove here that arbitrary 3 × 3, symmetric positive definite matrices have physical realizations as local mass matrices for collisions of two bodies with finite dimensions and inertia. General collision models thus must be able to handle all such matrices.

The main purpose of SiLVIA is to supply procedures for simulating the dynamics of colliding rigid bodies and the interactive manipulation of these bodies in virtual environments. Detecting collisions between virtual objects and calculating their reaction to these collisions play an important role in VR applications such as ergonomy studies or virtual assembly simulations.

Several physical systems in condensed matter have been modeled approximating their constituent particles as hard objects. The hard spheres model has been indeed one of the cornerstones of the computational and theoretical description in condensed matter. The next level of description is to consider particles as rigid objects of generic shape, which would enrich the possible phenomenology enormo...

We apply the alternating direction method of multipliers (ADMM) optimization algorithm to implicit time integration of elastic bodies, and show that the resulting method closely relates to the recently proposed projective dynamics algorithm. However, as ADMM is a general-purpose optimization algorithm applicable to a broad range of objective functions, it permits the use of nonlinear constituti...

We present an e cient algorithm for simulation of non-penetrating exible bodies with nonlinear elasticity. We use nite element methods to discretize the continuum model of non-rigid objects and the fast marching level set method to precompute a distance eld for each undeformed body. As the objects deform, the distance elds are deformed accordingly to estimate penetration depth, allowing enforce...

We present an eecient algorithm for simulation of non-penetrating exible bodies with nonlinear elasticity. We use nite element methods to discretize the continuum model of non-rigid objects and the fast marching level set method to precompute a distance eld for each un-deformed body. As the objects deform, the distance elds are deformed accordingly to estimate penetration depth, allowing enforc...

The property that the stream cipher RC4 can generate the same keystream outputs under two different secret keys has been discovered recently. The principle that how the two different keys can achieve a collision is well known by investigating the key scheduling algorithm of RC4. However, how to find those colliding key pairs is a different story, which has been largely remained unexploited. Pre...

The paper deals with a set of algorithms including path planning, trajectory planning, and path tracking for a tricycle type wheeled mobile robot. Path planning is carried out with parametric polynomial interpolation using an optimization algorithm based on robot geometric constraints. Trajec-tory characteristics are then derived from the planned geometric path with time varying parameters. A s...

global optimization methods play an important role to solve many real-world problems. flower pollination algorithm (fp) is a new nature-inspired algorithm, based on the characteristics of flowering plants. in this paper, a new hybrid optimization method called hybrid flower pollination algorithm (fppso) is proposed. the method combines the standard flower pollination algorithm (fp) with the par...

Abstract Three typical elastic problems, including beam bending, truss extension and compression, two-rings collision are simulated with smoothed particle hydrodynamics (SPH) using Lagrangian Eulerian algorithms. A contact-force model for collisions equation of state pressure arising in colliding bodies also analytically derived. Numerical validations, on the corresponding theoretical models, c...