Continuous conformal transformation minimizes the conformal energy. The convergence of minimizing discrete conformal energy when the discrete mesh size tends to zero is an open problem. This paper addresses this problem via a careful error analysis of the discrete conformal energy. Under a weak condition on triangulation, the discrete function minimizing the discrete conformal energy converges to the continuous conformal mapping as the mesh size tends to zero.

翻译：连续相容转换会最小化同质能量。 当离散网格大小趋向为零时, 最小化离散相符合能量的趋同是一个尚未解决的问题。 本文通过对离散相符合能量进行仔细的错误分析来解决这个问题。 在三角测量条件薄弱的情况下, 离散功能会最小化离散相符合能量, 与连续的相符合绘图相融合, 因为网格大小往往为零 。