Large steps in cloth simulation

The bottle-neck in most cloth simulation systems is that time steps must be small to avoid numerical instability. This paper describes a cloth simulation system that can stably take large time steps. The simulation system couples a new technique for enforcing constraints on individual cloth particles with an implicit integration method. The simulator models cloth as a triangular mesh, with internal cloth forces derived using a simple continuum formulation that supports modeling operations such as local anisotropic stretch or compression; a unified treatment of damping forces is included as well. The implicit integration method generates a large, unbanded sparse linear system at each time step which is solved using a modified conjugate gradient method that simultaneously enforces particles ’ constraints. The constraints are always maintained exactly, independent of the number of conjugate gradient iterations, which is typically small. The resulting simulation system is significantly faster than previous accounts of cloth simulation systems in the literature. Keywords—Cloth, simulation, constraints, implicit integration, physically-based modeling.

Why Some Interfaces Cannot be Sharp

A central goal of modern materials physics and nanoscience is control of materials and their interfaces to atomic dimensions. For interfaces between polar and non-polar layers, this goal is thwarted by a polar catastrophe that forces an interfacial reconstruction. In traditional semiconductors this reconstruction is achieved by an atomic disordering and stoichiometry change at the interface, but in multivalent oxides a new option is available: if the electrons can move, the atoms don`t have to. Using atomic-scale electron energy loss spectroscopy we find that there is a fundamental asymmetry between ionically and electronically compensated interfaces, both in interfacial sharpness and carrier density. This suggests a general strategy to design sharp interfaces, remove interfacial screening charges, control the band offset, and hence dramatically improving the performance of oxide devices.Comment: 12 pages of text, 6 figure

Atomic structure of dislocation kinks in silicon

We investigate the physics of the core reconstruction and associated structural excitations (reconstruction defects and kinks) of dislocations in silicon, using a linear-scaling density-matrix technique. The two predominant dislocations (the 90-degree and 30-degree partials) are examined, focusing for the 90-degree case on the single-period core reconstruction. In both cases, we observe strongly reconstructed bonds at the dislocation cores, as suggested in previous studies. As a consequence, relatively low formation energies and high migration barriers are generally associated with reconstructed (dangling-bond-free) kinks. Complexes formed of a kink plus a reconstruction defect are found to be strongly bound in the 30-degree partial, while the opposite is true in the case of 90-degree partial, where such complexes are found to be only marginally stable at zero temperature with very low dissociation barriers. For the 30-degree partial, our calculated formation energies and migration barriers of kinks are seen to compare favorably with experiment. Our results for the kink energies on the 90-degree partial are consistent with a recently proposed alternative double-period structure for the core of this dislocation.Comment: 12 pages, two-column style with 8 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#rn_di

Linear-time dynamics using lagrange multipliers

Current linear-time simulation methods for articulated figures are based exclusively on reduced-coordinate formulations. This paper describes a general, non-iterative linear-time simulation method based instead on Lagrange multipliers. Lagrange multiplier methods are important for computer graphics applications because they bypass the difficult (and often intractable) problem of parameterizing a system’s degrees of freedom. Given a loop-free set of n equality constraints acting between pairs of bodies, the method takes O(n) time to compute the system’s dynamics. The method does not rely on matrix bandwidth, so no assumptions about the constraints’ topology are needed. Bodies need not be rigid, constraints can be of various dimensions, and unlike reduced-coordinate approaches, nonholonomic (e.g. velocity-dependent) constraints are allowed. An additional set of k one-dimensional constraints which induce loops and/or handle inequalities can be accommodated with cost O(kn). This makes it practical to simulate complicated, closedloop articulated figures with joint-limits and contact at interactive rates. A complete description of a sample implementation is provided in pseudocode.

Fast Contact Force Computation for Nonpenetrating Rigid Bodies

A new algorithm for computing contact forces between solid objects with friction is presented. The algorithm allows a mix of contact points with static and dynamic friction. In contrast to previous approaches, the problem of computing contact forces is not transformed into an optimization problem. Because of this, the need for sophisticated optimization software packages is eliminated. For both systems with and without friction, the algorithm has proven to be considerably faster, simpler, and more reliable than previous approaches to the problem. In particular, implementation of the algorithm by nonspecialists in numerical programming is quite feasible

Analytical methods for dynamic simulation of non-penetrating rigid bodies

A method for analytically calculating the forces between systems of rigid bodies in resting (non-colliding) contact is presented. The systems of bodies may either be in motion or static equilibrium and adjacent bodies may touch at multiple points. The analytic formulation of the forces between bodies in non-colliding contact can be modified to deal with colliding bodies. Accordingly, an improved method for analytically calculating the forces between systems of rigid bodies in colliding contact is also presented. Both methods can be applied to systems with arbitrary holonomic geometric constraints, such as linked figures. The analytical formulations used treat both holonomic and non-holonomic constraints in a consistent manner

Determining Frictional Inconsistency for Rigid Bodies is NP-Complete

The computational complexity of computing the forces between bodies in contact is presented. The bodies are restricted to be perfectly rigid bodies that contact at finitely many points. It has been known for some time that under the Coulomb model of friction, some configurations of bodies are inconsistent; that is, no contact forces satisfying the constraints of the Coulomb friction model exist for the configuration. The main result of this paper is a proof that determining if a configuration is inconsistent is an NP-complete problem. An immediate corollary of this proof is that computing the contact forces for a configuration of bodies is NP-hard. Computing contact forces remains NP-hard even if configurations are restricted to be consistent