Geometry-constrained crowd formation animation

Formation control technology can exhibit the collective flock behaviors of a crowd for simulation and animation purpose, and thus, can be applied in various fields. In this paper, an innovative geometry-constrained framework for smooth formation animation of regulated crowds is proposed. We employ the morphing method to generate a series of in-between constrained shapes as key frames to impose process control and ensure smoothness of formation transformations. We also introduce centroidal Voronoi tessellation (CVT) to calculate optimal distribution of agents, and present an improved Lloyd descent method to perform path planning by utilizing its fixed point iteration feature. As extensions, the proposed framework can handle environmental obstacles avoiding problems for the whole crowd to preserve certain formation extremely by utilizing a domain modification method, and can also be adapted to 3D spaces and density-based domains. Experimental results show that the proposed method can generate stable, smooth, orderly, regular and elegant crowd formation animations.