中文摘要：

大型团体演出，如团体操，往往涉及到快速、平滑、流畅、整齐的群体队形变换问题．基于虚拟人群仿真技术，通过引入几何约束方法，结合Morphing，CVT和Lloyd技术，从团体操队形约束、个体分布布局、个体配对、个体运动路径规划、群体碰撞避免等方面，综合提出一种新颖的团体操群体队形变换解决方案．首先采用Morphing生成从源队形到目标体操队形的一系列中间约束形状，保证变化的平滑性；然后利用CVT技术实现群体在约束形状中的分布布局；由于约束形状变化，个体的运动路径规划和碰撞避免均采用改进的Lloyd下降法，即变空间域下的Lloyd下降法来实现；最终搭建系统平台，有效地提高了团体操队形设计质量和效率．

英文摘要：

Massive sports, such as group calisthenics, often involve rapid, smooth, fluent, and regular formation deformation. The paper introduces a novel geometric constraint method, which is combined with morphing, centroidal Voronoi tessellation （CVT） and Lloyd techniques, and puts forward a new group formation control solution for formation constrain, individual distribution layout, individual matching, motion path planning, and collision avoidance. In order to ensure the smoothness of deformation, morphing technology is used to generate a series of shapes between source formation and target formation as constrains. CVT methodology is utilized to compute the uniform layout of Agents in the constrained shape. Also due to the change of constraint shapes, improved Lloyd descent method, namely variable domain Lloyd descent, is applied to perform path planning and collision avoidance for the crowd. Finally, the computer aided system is built to effectively improve the design quality and efficiency of group calisthenics and other massive team sports.