Implicit-Explicit Schemes for Fast Animation
with Particle Systems
Universität Tübingen, Germany
Particle systems have been widely employed to animate deformable objects. In
order to achieve real time capable systems often simplifications have been made
to reduce the computational costs for solving the ODE at the expense of numer-
ical and physical correctness. Implicit-Explicit (IMEX) methods provide a way
to solve partly stiff systems efficiently, if the system meets some requirements.
These methods allow the solution of the differential equation for particle systems
to be computed both correctly and very quickly. Here we use an IMEX method
to simulate draping textiles. In particular, our approach does not require any post-
correction and works for very stiff materials.
Since the mid of the 80’s the animation of deformable models has attracted more and
more attention in computer graphics. Terzopoulos and Fleischer  proposed a con-
tinuous model for deformable objects and solved the resulting PDEs with finite dif-
ferences. Later on, particle systems became a very common model, in particular for
two-dimensional deformable objects like textiles [3, 6, 9, 2]. All approaches require an
ordinary differential equation to be solved.
Although Terzopoulos and Fleischer used a semi-implicit numerical method, i.e.
explicit in space and implicit in time, later on explicit methods became popular. These
require considerably less work per step, because there are no systems of equations to
Unfortunately explicit methods allow only small time steps for stiff particle sys-
tems. With the work of Baraff and Witkin , implicit time stepping underwent a
renaissance in animation, because these implicit methods allow large time steps with-
out loss of stability. Traditionally in computer graphics realistic behaviour is more
important than short computation time, whereas in virt