The changecoords function transforms a plot structure to one that uses a new coordinate system.

The input p must be a two or three dimensional plot data structure, while coord must be one of the accepted set of coordinate types available. At present these include:

In three dimensions - bipolarcylindrical, bispherical, cardioidal, cardioidcylindrical, casscylindrical, confocalellip, confocalparab, conical, cylindrical, ellcylindrical, ellipsoidal, hypercylindrical, invcasscylindrical, invellcylindrical, invoblspheroidal, invprospheroidal, logcoshcylindrical, logcylindrical, maxwellcylindrical, oblatespheroidal, paraboloidal, paraboloidal2, paracylindrical, prolatespheroidal, rosecylindrical, sixsphere, spherical, spherical_math, spherical_phsycis, tangentcylindrical, tangentsphere, and toroidal.

In two dimensions - bipolar, cardioid, cassinian, elliptic, hyperbolic, invcassinian, invelliptic, logarithmic, logcosh, maxwell, parabolic, polar, rose, and tangent.

The conversions from the various coordinate systems to Cartesian coordinates can be found in the coords help page.

The result of a call to changecoords is a PLOT or PLOT3D data structure containing information to render the plot. You can assign the data structure to a variable, save it in a file, then read it back in for redisplay.  For more information about plot data structures, see plot/structure.

There are other functions available to transform plot data structures. A number of these are in the plottools package and are listed on the plottools help page.  The plots[display] function can also be used to transform plots.

The command with(plots,changecoords) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{plots}\right)\:$

$p≔\mathrm{plot}\left(\left[\sin \left(x\right)\,x\,x=0..2\mathrm{\pi }\right]\right)\:$

$\mathrm{changecoords}\left(p\,\mathrm{polar}\right)$

$p≔\mathrm{plot3d}\left(\left[{1.3}^x\sin \left(y\right)\,x\,y\right]\,x=-1..2\mathrm{\pi }\,y=0..\mathrm{\pi }\right)\:$

$\mathrm{changecoords}\left(p\,\mathrm{spherical}\right)$

$\mathrm{changecoords}\left(p\,\mathrm{paraboloidal}\right)$

$\mathrm{changecoords}\left(p\,\mathrm{conical}\left(2\,3\right)\right)$

$p≔\mathrm{plot3d}\left(\left[x+y\,x\,y\right]\,x=-\mathrm{\pi }..\mathrm{\pi }\,y=-\mathrm{\pi }..\mathrm{\pi }\right)\:$

$\mathrm{changecoords}\left(p\,\mathrm{bipolarcylindrical}\right)$

$\mathrm{changecoords}\left(p\,\mathrm{bipolarcylindrical}\left(3\right)\right)$