一种四边形网格上的Midedge细分格式

提出了一种逼近型细分格式，通过初始网格的边插入边点，再去除初始点、边，连接所插入边点的方式生成新的网格。 该细分格式是对PETERS 等提出的Midedge格式的拓展，其分离因子为1-2，意味着每通过1次细分，便将1个矩形分离成2个。 通过分析对应细分矩阵的性质，证明了此细分格式具有至少C1的连续性这一性质。

A new Midedge scheme of quadrilateral mesh

This paper presents an approximating subdivision scheme which can generate a new mesh by connecting the midpoint of every edge to the midpoints of its neighboring edge. When all the midpoints are linked, the old mesh is discarded. The subdivision scheme is a new continuation of the traditional Midedge scheme presented by PETERS et al. The splitting factor is 1-2 that means a quadrangle would be splited to two quadrangles through each subdivision step. The refinement rule yields a regular surface proved by analyzing the property of the corresponding subdivision matrix.