We recover plane curves from their branch points under projection onto a line. Our focus lies on cubics and quartics. These have 6 and 12 branch points respectively. The plane Hurwitz numbers 40 and 120 count the orbits of solutions. We determine the numbers of real solutions, and we present exact algorithms for recovery. Our approach relies on 150 years of beautiful algebraic geometry, from Clebsch to Vakil and beyond.

翻译：我们从他们投射到直线的分支点回收飞机曲线。 我们的注意力集中在立方体和石刻上。 它们分别有6个和12个分支点。 Hurwitz 飞机编号为 40 和 120 计算解决方案的轨道。 我们确定实际解决方案的数量,并提出精确的恢复算法。 我们的方法依靠150年的优美代数几何,从克莱布希到瓦基尔,等等。