5.1 Cartesian Transformations

GMT Cartesian coordinate transformations come in three flavors:

• Linear coordinate transformation
• Log$_{10}$ coordinate transformation
• Power (exponential) coordinate transformation

These transformations convert input coordinates $(x,y)$ to locations $(x', y')$ on a plot. There is no coupling between $x$ and $y$ (i.e., $x' = f(x)$ and $y' = f(y)$); it is a one-dimensional projection. Hence, we may use separate transformations for the $x$- and $y$-axes (and $z$-axes for 3-D plots). Below, we will use the expression $u' = f(u)$, where $u$ is either $x$ or $y$ (or $z$ for 3-D plots). The coefficients in $f(u)$ depend on the desired plot size (or scale), the chosen $(x,y)$ domain, and the nature of $f$ itself.

Two subsets of linear will be discussed separately; these are a polar (cylindrical) projection and a linear projection applied to geographic coordinates (with a 360$^{o}$ periodicity in the $x$-coordinate). We will show examples of all of these projections using dummy data sets created with gmtmath, a ``Reverse Polish Notation'' (RPN) calculator that operates on or creates table data:

gmtmath -T0/100/1  T SQRT = sqrt.d
gmtmath -T0/100/10 T SQRT = sqrt.d10