Complex fans are sets of complex numbers whose magnitudes and angles range in closed intervals. The fact that the sum of two fans is a disordered shape gives rise to the need for computational methods to find the minimal enclosing fan. Cases where the sum of two fans contains the origin of the complex plane as a boundary point are of special interest. The result of the addition is then enclosed by circles in current methods, but under certain circumstances this turns out to be an overestimate. The focus of this article is the diagnosis and treatment of such cases.

中文翻译：

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改进的复数扇形算法

复数扇形是复数的集合，其大小和角度在闭合区间内变化。两个扇形之和是无序形状的事实导致需要计算方法来找到最小的封闭扇形。两个扇形之和包含复平面的原点作为边界点的情况特别令人感兴趣。然后在当前方法中将加法的结果用圆圈括起来，但在某些情况下，这被证明是高估的。本文的重点是此类病例的诊断和治疗。