Translation surface (differential geometry)

In differential geometry a translation surface is a surface that is generated by translations: For two space curves c 1 , c 2 {\displaystyle c_{1},c_{2}} with a common point P {\displaystyle P} , the curve c 1 {\displaystyle c_{1}} is shifted such that point P {\displaystyle P} is moving on c 2 {\displaystyle c_{2}} . Through this procedure, curve c 1 {\displaystyle c_{1}} generates a surface: the translation surface.

Source: Wikipedia — Translation surface (differential geometry) (CC BY-SA 4.0)