The transform command generates a procedure that can be used to change plot data structures by applying the procedure f to all the points in the plot structure.

The procedure f represents a mapping

where m and n can take values 2 or 3. The procedure must take as input m arguments and output a list of n components.

Examples of the use of this command include embedding two-dimensional plots into three-dimensional space, changing coordinate systems or transforming curves in the complex plane into the Riemann Sphere.

The result of a call to transform is a procedure that takes a 2-D or 3-D plot data structure as parameter. You can assign the procedure to a variable, and apply the procedure to various plots.  For more information about plot data structures, see plot/structure.

The transform command is usually used with [m, n] equal to [2, 2], [2, 3], or [3, 3].  It returns a transformation procedure in the case where m is 3 and n is 2.  However, this procedure works only on those 3-D plot objects that have 2-D counterparts.

Several commands in the plottools package can transform plots. For a list, see the plottools help page.  The plots[changecoords] and plots[display] commands can also be used to transform plots.

If the transform command is applied to a shape, such as an arrow, the polygons that make up the shape may not render correctly when all of the points in a plot structure are transformed. To create a shape based on transformed coordinates, it is recommended that you transform the coordinates and then generate the shape from those coordinates.