Spectral-Based Group Formation Control

Given a pair of keyframe formations for a group consisting of multiple individuals, we present a spectral-based approach to smoothly transforming a source group formation into a target formation while respecting the clusters of the involved individuals. The proposed method provides an effective means for controlling the macroscopic spatiotemporal arrangement of individuals for applications such as expressive formations in mass performances and tactical formations in team sports. Our main idea is to formulate this problem as rotation interpolation of the eigenbases for the Laplacian matrices, each of which represents how the individuals are clustered in a given keyframe formation. A stream of time-varying formations is controlled by editing the underlying adjacency relationships among individuals as well as their spatial positions at each keyframe, and interpolating the keyframe formations while producing plausible collective behaviors over a period of time. An interactive system of editing existing group behaviors in a hierarchical fashion has been implemented to provide flexible formation control of large crowds.