The modeling of virtual crowds has been widely investigated in recent years. Two fundamental approaches are used to model human crowds. The first employs microcosmic methods and mainly includes agent-based

force-based

and rule-based models. In these models

each agent perceives environmental information and responses to static or dynamic obstacles on their own. Microscopic models are suitable for small crowds and provide flexibility. The second is applicable in large-crowd simulations

treats the crowd as a whole

uses macroscopic methods

and mainly includes fluid dynamics

continuum models

and potential fields. However

very few algorithms combine the two aforementioned models to simulate dynamic group behavior. Group dynamics

which has been extensively studied in social psychology

attempts to find the general rule of crowd movement by a dynamic analysis of group phenomenon. The founder of this concept

Kurt Lewin

considers that individual behavior is the result of personality characteristics and environmental influence. Recent researchers have proposed different theories to explain group behavior

but current simulation methods cannot generate believable and heterogeneous crowd simulation because of the separation of global planning and local motion. This study proposes a new method that combines global path planning and local motion control to simulate diverse group behavior. In particular

group dynamics is introduced into continuum crowd simulation to model the following behavior of intra-group and the avoidance behavior of inter-group. First

the environment is divided into a series of 2D grids

the target and obstacle grids are specified

the individuals are converted into unit density fields

and crowd flow constraint is introduced to calculate the maximum speed field. Second

the unit cost field is computed by minimizing a linear combination of the length of path

amount of time to the destination and discomfort degree per unit time along the path. Second

three lists

namely

known

unknown

and candidate lists

are established

and the target grid is stored into the known list. Finally

fast marching method and upwind difference scheme are used to approximate the gradient for constructing a global potential field and providing each individual with an initial velocity. In the second phase

individuals are assigned into groups depending on their walking speeds

moving directions

and locations. Then

the divide-and-conquer algorithm is employed to construct group convex hull

and the group position is the average position of its edge members. Finally

the convex hull edge is expanded to a limited extent and local potential field is constructed by its swept space during a time step. In the local motion control phase

the global potential and local fields are integrated to generate group avoidance behavior and the individual local motion is adjusted to produce following behavior on the basis of following acceleration. After updating the global potential information at each time step

the crowd simulation results in different scale numbers of individuals and grid resolution are compared. Experimental results show that the proposed method can model large-scale crowd simulation in an efficient and diverse manner. For example

when simulating 5 000 individuals walking in a scenario with the grid resolution of 80×80

the average frame rate is 35.7 ms

which is approximately 28 frames per second. Compared with continuum model

the proposed method can produce more group behavior and in the high density area as individuals can dynamically avoid one another because they follow the leader to solve the local interaction. When constructing the global potential field

the fast marching method is influenced by the grid resolution but the coarse grid resolution can be used to compute smooth trajectories. At the same time

the proposed algorithm can generate considerable group behavior on the basis of group dynamics. Existing group behavior models employ additional collision avoidance methods to realize the local movement of a small crowd and thus may sometimes consider several special circumstances. This condition leads to unnecessary computations. Our proposed method integrates local motion control into global path planning and is thus suitable for large-scale diverse crowd simulation. During the simulation process

the method can produce the following behavior of intra-group and the avoidance behavior of inter-group when using the continuum model. Therefore

the diverse crowd motion simulation algorithm is efficient.