Center for Human Modeling and Simulation

Document Type

Conference Paper

Date of this Version


Publication Source

Proceedings of the 18th meeting of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games (I3D '14)

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I3D 2014, March 14-16, 2014, San Francisco, California, USA.


Crowd activities are often randomized to create the appearance of heterogeneity. However, the parameters that control randomization are frequently hard to tune because it is unclear how changes at the character level affect the high-level appearance of the crowd. We propose a method for computing randomization parameters that supports direct animator control. Given details about the environment, available activities, timing information and the desired highlevel appearance of the crowd, we model the problem as a graph, formulate a convex optimization problem, and solve for a set of stochastic transition rates which satisfy the constraints. Unlike the use of heuristics for adding randomness to crowd activities, our approach provides guarantees on convergence to the desired result, allows for decentralized simulation, and supports a variety of constraints. In addition, because the rates can be pre-computed, no additional runtime processing is needed during simulation.

Copyright/Permission Statement

© ACM 2014. This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in Interactive 3D Graphics and Games,


stochastic modeling, crowd authoring, optimization



Date Posted: 13 January 2016

This document has been peer reviewed.