A new constructive method, called optimized advance front method (OAFM), for ellipse packing is proposed. The OAFM allows particle rotation at several angles and movement along a local advance front. Combined with the ellipse approximated by four connected arcs and a series of sequential coordinate transformations, the OAFM generates dense ellipse packing with any imposed size, aspect ratio, and orientation distribution at a fastpacking speed, and the generated ellipse packing can satisfy an imposed spatial arrangement. Based on the approximation of ellipses by multicircles, Laguerre Voronoi Tessellation method constructs initial cells. The initial cells are then merged to create the convex polygon with the same size, aspect ratio, orientation, and location as that of the obtained ellipse. Three examples of ellipse packing and convex polygon demonstrate that the convex polygon generated can be statistically equivalent with the real material and satisfy an imposed spatial arrangement.

提出了一种用于椭圆包装的新型构造方法，称为优化超前锋方法（OAFM）。OAFM允许粒子旋转几个角度并沿着局部超前运动。结合由四个连接的圆弧近似的椭圆和一系列顺序的坐标变换，OAFM以快速的包装速度生成具有任何强加的大小，长宽比和方向分布的密集椭圆形填充，并且生成的椭圆形填充可以满足强加的空间布置。基于多圆的椭圆近似，Laguerre Voronoi Tessellation方法构造了初始细胞。然后合并初始单元，以创建具有与所获得椭圆相同的大小，纵横比，方向和位置的凸多边形。