The default coordinate system for all three dimensional plotting commands is the Cartesian coordinate system.  The coords option allows the user to alter this coordinate system.  The alternate choices are: bipolarcylindrical, bispherical, cardioidal, cardioidcylindrical, casscylindrical, confocalellip, confocalparab, conical, cylindrical, ellcylindrical, ellipsoidal, hypercylindrical, invcasscylindrical, invellcylindrical, invoblspheroidal, invprospheroidal, logcoshcylindrical, logcylindrical, maxwellcylindrical, oblatespheroidal, paraboloidal, paracylindrical, prolatespheroidal, rosecylindrical, sixsphere, spherical, tangentcylindrical, tangentsphere, and toroidal.

For a description of each of the above coordinate systems, see the coords help page.

When using Cartesian coordinates, z, the vertical coordinate, is expressed as a function of x and y: $\mathrm{plot3d}\left(z\left(x\,y\right)\,x=a..b\,y=c..d\right)$.

For alternate coordinate systems this is interpreted differently. For example, when using cylindrical coordinates, Maple expects the command to be of the following form: $\mathrm{plot3d}\left(r\left(\mathrm{\theta }\,z\right)\,\mathrm{\theta }=a..b\,z=c..d\,\mathrm{coords}=\mathrm{cylindrical}\right)$.

r, the distance to the projection of the point in the x-y plane from the origin, is a function of theta, the counterclockwise angle from the positive x-axis, and of z, the height above the x-y plane. For spherical coordinates the interpretation is: $\mathrm{plot3d}\left(r\left(\mathrm{\theta }\,\mathrm{\phi }\right)\,\mathrm{\theta }=a..b\,\mathrm{\phi }=c..d\,\mathrm{coords}=\mathrm{spherical}\right)$.

where theta is the counterclockwise angle measured from the x-axis in the x-y plane.  phi is the angle measured from the positive z-axis, or the colatitude.  These angles determine the direction from the origin while the distance from the origin, r, is a function of phi and theta. Other coordinate systems have similar interpretations.

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

All coordinate systems are also valid for parametrically defined 3-D plots with the same interpretations of the coordinate system transformations.

$\mathrm{plot3d}\left(\sin \left(x\right)+\sin \left(y\right)\,x=0..2\mathrm{\pi }\,y=0..2\mathrm{\pi }\,\mathrm{axes}=\mathrm{boxed}\right)$

$\mathrm{plot3d}\left(\mathrm{height}\,\mathrm{angle}=0..2\mathrm{\pi }\,\mathrm{height}=-5..5\,\mathrm{coords}=\mathrm{cylindrical}\,\mathrm{title}=\mathrm{CONE}\right)$

$\mathrm{plot3d}\left(1\,t=0..2\mathrm{\pi }\,p=0..\mathrm{\pi }\,\mathrm{coords}=\mathrm{spherical}\,\mathrm{scaling}=\mathrm{constrained}\right)$

$\mathrm{plot3d}\left(\mathrm{\theta }\,\mathrm{\theta }=0..8\mathrm{\pi }\,z=-1..1\,\mathrm{coords}=\mathrm{cylindrical}\right)$

$\mathrm{plot3d}\left(\mathrm{\theta }\,\mathrm{\theta }=0..8\mathrm{\pi }\,\mathrm{\phi }=0..\mathrm{\pi }\,\mathrm{coords}=\mathrm{spherical}\,\mathrm{style}=\mathrm{wireframe}\right)$

$\mathrm{plot3d}\left(\mathrm{\theta }\,\mathrm{\theta }=0..8\mathrm{\pi }\,\mathrm{\phi }=0..\mathrm{\pi }\,\mathrm{coords}=\mathrm{toroidal}\left(2\right)\,\mathrm{style}=\mathrm{wireframe}\right)$

$\mathrm{addcoords}\left(\mathrm{z\_cylindrical}\,\left[z\,r\,\mathrm{\theta }\right]\,\left[r\cos \left(\mathrm{\theta }\right)\,r\sin \left(\mathrm{\theta }\right)\,z\right]\right)$

$\mathrm{plot3d}\left(r\cos \left(\mathrm{\theta }\right)\,r=0..10\,\mathrm{\theta }=0..2\mathrm{\pi }\,\mathrm{coords}=\mathrm{z\_cylindrical}\,\mathrm{title}=\mathrm{z\_cylindrical}\,\mathrm{orientation}=\left[-132\,71\right]\,\mathrm{axes}=\mathrm{boxed}\right)$

$\mathrm{plot3d}\left(r\cos \left(\mathrm{\theta }\right)\,r=0..10\,\mathrm{\theta }=0..2\mathrm{\pi }\,\mathrm{coords}=\mathrm{cylindrical}\,\mathrm{orientation}=\left[100\,71\right]\right)$