A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles intersect with an intersection angle in (0, π). Two sequences of circle patterns are employed to approximate a given conformal map g and its first derivative. For the domain of g we use embedded circle patterns where all circles have the same radius decreasing to 0 and with uniformly bounded intersection angles. The image circle pattern has the same combinatorics and intersection angles and is determined from boundary conditions (radii or angles) according to the values of g (|g| or arg g). For quasicrystallic circle patterns the convergence result is strengthened to C∞-convergence on compact subsets.
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机译：圆形图案是平面中圆的配置，其组合由平面图G给出，使得G的每个顶点对应一个圆。如果两个顶点通过G中的一条边连接，则相应的圆以（0，π）中的相交角相交。使用两个圆形图案序列来逼近给定的共形图g及其一阶导数。对于g的域，我们使用嵌入的圆型，其中所有圆的半径均减小到0，并且交点角均匀一致。像圈图案具有相同的组合角和相交角，并且根据g（| g |或arg g）的值根据边界条件（半径或角度）确定。对于准晶圆图案，在紧子集上，收敛结果增强到C∞收敛。
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