Another way to represent coordinate transformations in Cartesian coordinates is through affine transformations. A point in 4-dimensional space with Cartesian coordinates may be represented by a quaternion . Euler's formula provides a means of conversion between cartesian coordinates and polar coordinates. Formulas involving homogeneous coordinates are often simpler and more symmetric than their Cartesian counterparts. The relation of Cartesian and spherical polars is given in Spherical coordinate system. The transformation between geodetic and Cartesian coordinates may be found in Geographic coordinate conversion. Consider two-dimensional plane flow within a Cartesian coordinate system. Nomograms use a parallel coordinate system invented by d'Ocagne rather than standard Cartesian coordinates. Some authors use different notations for homogeneous coordinates which help distinguish them from Cartesian coordinates. These definitions are equivalent when using Cartesian coordinates. Unit vectors may be used to represent the axes of a Cartesian coordinate system. Using and , one can derive a relationship between derivatives in Cartesian and polar coordinates. The relation of Cartesian and ellipsoidal coordinates is discussed in Torge. The user must know the points of the polygon in a Cartesian plane. Spinors can be exhibited as concrete objects using a choice of Cartesian coordinates.