Position Based Dynamics posBasedDyn
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3
rd
Workshop in Virtual Reality Interactions and Physical Simulation "VRIPHYS" (2006)
C. Mendoza, I. Navazo (Editors)
Position Based Dynamics
Matthias Müller Bruno Heidelberger Marcus Hennix John Ratcliff
AGEIA
Abstract
The most popular approaches for the simulation of dynamic systems in computer graphics are force based. Internal
and external forces are accumulated from which accelerations are computed based on Newton’s second law of
motion. A time integration method is then used to update the velocities and finally the positions of the object.
A few simulation methods (most rigid body simulators) use impulse based dynamics and directly manipulate
velocities. In this paper we present an approach which omits the velocity layer as well and immediately works
on the positions. The main advantage of a position based approach is its controllability. Overshooting problems
of explicit integration schemes in force based systems can be avoided. In addition, collision constraints can be
handled easily and penetrations can be resolved completely by projecting points to valid locations. We have used
the approach to build a real time cloth simulator which is part of a physics software library for games. This
application demonstrates the strengths and benefits of the method.
Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry
and Object ModelingPhysically Based Modeling; I.3.7 [Computer Graphics]: Three-Dimensional Graphics and
RealismAnimation and Virtual Reality
1. Introduction
Research in the field of physically based animation in com-
puter graphics is concerned with finding new methods for
the simulation of physical phenomena such as the dynamics
of rigid bodies, deformable objects or fluid flow. In contrast
to computational sciences where the main focus is on accu-
racy, the main issues here are stability, robustness and speed
while the results should remain visually plausible. There-
fore, existing methods from computational sciences can not
be adopted one to one. In fact, the main justification for
doing research on physically based simulation in computer
graphics is to come up with specialized methods, tailored to
the particular needs in the field. The method we present falls
into this category.
The traditional approach to simulating dynamic objects
has been to work with forces. At the beginning of each time
step, internal and external forces are accumulated. Examples
of internal forces are elastic forces in deformable objects or
viscosity and pressure forces in fluids. Gravity and collision
forces are examples of external forces. Newton’s second law
of motion relates forces to accelerations via the mass. So us-
ing the density or lumped masses of vertices, the forces are
transformed into accelerations. Any time integration scheme
can then be used to first compute the velocities from the ac-
celerations and then the positions from the velocities. Some
approaches use impulses instead of forces to control the an-
imation. Because impulses directly change velocities, one
level of integration can be skipped.
In computer graphics and especially in computer games
it is often desirable to have direct control over positions of
objects or vertices of a mesh. The user might want to attach
a vertex to a kinematic object or make sure the vertex always
stays outside a colliding object. The method we propose here
works directly on positions which makes such manipula-
tions easy. In addition, with the position based approach it is
possible to control the integration directly thereby avoiding
overshooting and energy gain problems in connection with
explicit integration. So the main features and advantages of
position based dynamics are
• Position based simulation gives control over explicit inte-
gration and removes the typical instability problems.
c
° The Eurographics Association 2006.
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