Shape transformation for polyhedral objects
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
2-D shape blending: an intrinsic solution to the vertex path problem
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Constrained animation of flocks
Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation
Shape-constrained flock animation
Computer Animation and Virtual Worlds - CASA'2008 Special Issue
On centroidal voronoi tessellation—energy smoothness and fast computation
ACM Transactions on Graphics (TOG)
Situation agents: agent-based externalized steering logic
Computer Animation and Virtual Worlds - CASA' 2010 Special Issue
Simulating formations of non-holonomic systems with control limits along curvilinear coordinates
MIG'10 Proceedings of the Third international conference on Motion in games
Autonomous multi-agents in flexible flock formation
MIG'10 Proceedings of the Third international conference on Motion in games
Formation sketching: an approach to stylize groups in crowd simulation
Proceedings of Graphics Interface 2011
Animation of flocks flying in line formations
Artificial Life
Least squares quantization in PCM
IEEE Transactions on Information Theory
Environment-aware real-time crowd control
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
FAME, soft flock formation control for collective behavior studies and rapid games development
SEAL'12 Proceedings of the 9th international conference on Simulated Evolution and Learning
Generating Freestyle Group Formations in Agent-Based Crowd Simulations
IEEE Computer Graphics and Applications
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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.