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Chapter 7
Simulator
This chapter is devoted to a brief description of concept abstractions in the simulator and an
overview of the simulator implementation — the goal is to provide the reader with a global view
of the simulator but not to pursue the implementation details. The details are nicely documented
in the Reference Guide, that comes with this thesis. We will also attempt to avoid the repetition
of various topics already discussed in the previous chapters where appropriate (such as notes on
computational/numerical issues), because the discussions can be found there, as well as in the
Reference Guide.
The simulator implementation is more or less based on the notes from the previous chapters,
but as one could expect, many concepts have to be implemented in a more sophisticated way
and smart algorithms have to be used in order to achieve an interactive performance (yet the
notes should be sufficient to implement a functional simulator). Although these aspects can be
characterized as “implementation details”, insignificant from the point of the rigid body dynamics
theory, this is what makes the implementation quite involved and distinguishes a practical
simulator from a toy. Certain implementation tricks were adopted from [22].
For example, conditions on λ multipliers due to constraints were formulated in terms of dense
matrix A from equation (6.8), but equation (6.9) needs be exploited in the practice. As another
example, all bodies were simulated in terms of a single equation of motion, but it might be
desirable to partition bodies to distinct simulation groups so that each group could be handled
separately (so that when a particular group was being advanced the other groups could remain
idle and would not have to be updated). For example, its ODE might be integrated with a
different time step, using a different integration method or precision. If all bodies in the group
are “at rest”, the simulation group could be skipped while advancing the simulation state, which
could significantly decrease the processing time when handling complex scenes, etc.
We will now present the main simulator components, outline the way the components collaborate
and describe the improvements over the notes from previous chapters, noting that details
can be found in the Reference Guide.
7.1 Overview
The rigid body simulation is represented by Simulator class that maintains a list of registered
bodies, their separation to disjoint simulation groups simulated in terms of their own equations of
motion and a list of force objects representing explicit interactions among bodies. The idea is to
keep bodies that might influence each other in a common simulation group while bodies that can
not influence each other in distinct groups so that the groups could be simulated independently
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