Game Development Reference
In-Depth Information
Particle-Based Simulation
Using Verlet Integration
Thomas Jakobsen
This pearl explains a technique that I developed in 1999 for the Hitman game
series to simulate falling (and usually very dead) people, a method of animation
now colloquially known as the ragdoll effect. The algorithm is also useful for
simulating cloth, hair, rigid objects, soft bodies, etc.
At the heart of the algorithm lies the so-called Verlet 1 technique for numeri-
cal integration coupled with a particle-based body representation and the use of
relaxation to solve systems of equations. Together with a nice square root op-
timization, the combined method has several advantages, most notably speed of
execution, stability, and simplicity.
While today's much-faster hardware platforms allow for more advanced and
more realistic approaches to physics simulation, there are still situations where a
particle-based Verlet approach, like the one presented here, is preferable, either
due to speed of execution or because of its simplicity. Verlet-based schemes are
especially useful for real-time cloth simulation, for use on low-spec hardware, for
two-dimensional games, and as an easy introduction to the world of physically
based animation. The mathematics behind the technique is fairly easy to under-
stand, and once you reach the limits of the technique, the underlying ideas of
semi-implicit integration and relaxation carry over to more advanced state repre-
sentations, constraints, and interactions. As such, Verlet integration is not only a
good starting point for the beginner, but it also forms the basis for physics simula-
tion in many existing commercial games, and it is a good stepping-stone to more
advanced approaches.
1 French, pronounced with a silent t :
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