The emergence of geometric order in proliferating metazoan epithelia

The predominantly hexagonal cell pattern of simple epithelia was noted in the earliest microscopic analyses of animal tissues, a topology commonly thought to reflect cell sorting into optimally packed honeycomb arrays. Here we use a discrete Markov model validated by time-lapse microscopy and clonal analysis to demonstrate that the distribution of polygonal cell types in epithelia is not a result of cell packing, but rather a direct mathematical consequence of cell proliferation. On the basis of in vivo analysis of mitotic cell junction dynamics in Drosophila imaginal discs, we mathematically predict the convergence of epithelial topology to a fixed equilibrium distribution of cellular polygons. This distribution is empirically confirmed in tissue samples from vertebrate, arthropod and cnidarian organisms, suggesting that a similar proliferation-dependent cell pattern underlies pattern formation and morphogenesis throughout the metazoa.     

基于视点变化的徒手作图输入变形

提出了一种直观,高效地用于概念设计作用图的等手输入,进行几何变形的方法,采用此方法可以徒手输入两笔曲线（参考曲线和目标曲线）,并据此二曲线来移动多边形模型的顶点,从而达到变形三维模型的目的,解决了大曲率变形时产生的自相关问题,另外,还可用来定义变形影响区域。     

采用网格再划分技术的网格推延造型

提出了一种对自由多边形物体直观高效的三维网格推延造型方法,采用这种造型方法,用户可以在已有的三维物体上勾勒两笔二维轮廓,从而推延了新的空间网格曲面,阐述了两种网格再划分技术,网格优化和网格细分,在此基础上,详细介绍了网格推延造型的方法,该方法能广泛地应用于多边形物体的自由造型。