Given any $\epsilon >0$ and any planar region $\Omega$ bounded by a simple n-gon $P$ we construct a ($1 + \epsilon)$-quasiconformal map between $\Omega$ and the unit disk in time $C(\epsilon)n$. One can take $ C(\epsilon) = C + C \log (1/\epsilon) \log \log (1/\epsilon)$.

中文翻译：

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线性时间的共形映射

给定任何 $\epsilon >0$ 和任何平面区域 $\Omega$ 以简单的 n-gon $P$ 为界，我们在 $\Omega$ 和单位圆盘之间构造一个 ($1 + \epsilon)$-准共形映射$C(\epsilon)n$。可以取 $ C(\epsilon) = C + C \log (1/\epsilon) \log \log (1/\epsilon)$。