5.1 Cartesian Transformations

**GMT** Cartesian coordinate transformations come in three flavors:

- Linear coordinate transformation
- Log coordinate transformation
- Power (exponential) coordinate transformation

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

- 5.1.1 Cartesian Linear Transformation (
**-Jx****-JX**)- 5.1.1.1 Regular floating point coordinates
- 5.1.1.2 Geographic coordinates
- 5.1.1.3 Calendar time coordinates

- 5.1.2 Cartesian Logarithmic projection
- 5.1.3 Cartesian Power projection