A geometric transformation that scales, rotates, or translates images or coordinates between any two Euclidean spaces. It is commonly used in GIS to transform maps between coordinate systems. In a Helmert transformation, parallel lines remain parallel. The midpoint of a line segment remains a midpoint, and all points on a straight line remain on a straight line. The Helmert transformation is named for the German mathematician and geodesist Friedrich Robert Helmert (1843-1917).