Category: Rigid bodies

Two-way Coupling of Rigid and Deformable Bodies

We propose a framework for the full two-way coupling of rigid and deformable bodies, which is achieved with both a unified time integration scheme as well as individual two-way coupled algorithms at each point of that scheme. As our algorithm is two-way coupled in every fashion, we do not require ad hoc methods for dealing with stability issues or interleaving parts of the simulation. We maintain the ability to treat the key desirable aspects of rigid bodies (e.g. contact, collision, stacking, and friction) and deformable bodies (e.g. arbitrary constitutive models, thin shells, and self-collisions). In addition, our simulation framework supports more advanced features such as proportional derivative controlled articulation between rigid bodies. This not only allows for the robust simulation of a number of new phenomena, but also directly lends itself to the design of deformable creatures with proportional derivative controlled articulated rigid skeletons that interact in a life-like way with their environment.

Two-way Coupling of Rigid and Deformable Bodies

Image-based Collision Detection and Response between Arbitrary Volume Objects

We present a new image-based method to process contacts between objects bounded by triangular surfaces. Unlike previous methods, it relies on image-based volume minimization, which eliminates complex geometrical computations and robustly handles deep intersections.  The surfaces are rasterized in three orthogonal directions, and intersections are detected based on pixel depth and normal orientation. Per-pixel contact forces are computed and accumulated at the vertices. We show how to compute pressure forces which serve to minimize the intersection volume, as well as friction forces. No geometrical precomputation is required, which makes the method efficient for both deformable and rigid objects. We demonstrate it on rigid, skinned, and particle-based physical models with detailed surfaces in contacts at interactive frame rates.

Image-based Collision Detection and Response between Arbitrary Volume Objects

Spline Joints for Multibody Dynamics

Spline joints are a novel class of joints that can model general scleronomic constraints for multibody dynamics based on the minimalcoordinates formulation. The main idea is to introduce spline curves and surfaces in the modeling of joints: We model 1-DOF joints using splines on SE(3), and construct multi-DOF joints as the product of exponentials of splines in Euclidean space. We present efficient recursive algorithms to compute the derivatives of the spline joint, as well as geometric algorithms to determine optimal parameters in order to achieve the desired joint motion. Our spline joints can be used to create interesting new simulated mechanisms for computer animation and they can more accurately model complex biomechanical joints such as the knee and shoulder.

Spline Joints for Multibody Dynamics

GDC Physics Tutorial

The slides for Erwin Coumans’ Game Developers Conference Physics Tutorial on parallel SPU physics are available for download and on-line here:

http://www.bulletphysics.com/Bullet/wordpress/uncategorized/gdc-2008-physics-tutorial-on-parallel-game-physics-for-spu

They cover parallelizing a typical collision detection and rigid body dynamics pipeline and provide links for further reading.

Thanks for Erwin for the link.

A Fast and Stable Penalty Method for Rigid Body Simulation

Two methods have been used extensively to model resting contact for rigid body simulation. The first approach, the penalty method, applies virtual springs to surfaces in contact to minimize interpenetration. This method, as typically implemented, results in oscillatory behavior and considerable penetration. The second approach, based on formulating resting contact as a linear complementarity problem, determines the resting contact forces analytically to prevent interpenetration. The analytical method exhibits expected-case polynomial complexity in the number of contact points, and may fail to find a solution in polynomial time when friction is modeled. We present a fast penalty method that minimizes oscillatory behavior and leads to little penetration during resting contact; our method compares favorably to the analytical method with regard to these two measures, while exhibiting much faster performance both asymptotically and empirically.

A Fast and Stable Penalty Method for Rigid Body Simulation

Some Theses…

Frank Losasso’s PhD thesis on fluid simulation, which contains previously unpublished work on coupling together SPH and level set based fluid simulations:

Algorithms for Increasing the Efficiency and Fidelity of Fluid Simulation

Eftychios Sifakis’ PhD thesis on face, muscle, speech, and surgery simulation:

Algorithmic Aspects of the Simulation and Control of Computer Generated Human Anatomy Models

Geoffrey Irving’s PhD thesis on a variety of physics simulation topics:

Methods for the Physically-Based Simulation of Solids and Fluids

Update: While I’m doing the thesis thing, here’s a couple slightly older ones that are probably worth a look.

Adam Bargteil’s PhD thesis on liquid surface tracking.

Surface Tracking and Texturing

Bart Adams PhD thesis on point-based graphics:

Point-Based Modeling, Animation and Rendering of Dynamic Objects

Animating Corrosion and Erosion

In this paper, we present a simple method for animating natural phenomena such as erosion, sedimentation, and acidic corrosion. We discretize the appropriate physical or chemical equations using finite differences, and we use the results to modify the shape of a solid body. We remove mass from an object by treating its surface as a level set and advecting it inward, and we deposit the chemical and physical byproducts into simulated fluid. Similarly, our technique deposits sediment onto a surface by advecting the level set outward. Our idea can be used for off-line high quality animations as well as interactive applications such as games, and we demonstrate both in this paper.

Animating Corrosion and Erosion