Set Coordinate System for 3-D Plots - Maple Programming Help

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Set Coordinate System for 3-D Plots

Description

 • 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.

Examples

 > $\mathrm{plot3d}\left(\mathrm{sin}\left(x\right)+\mathrm{sin}\left(y\right),x=0..2\mathrm{π},y=0..2\mathrm{π},\mathrm{axes}=\mathrm{boxed}\right)$
 > $\mathrm{plot3d}\left(\mathrm{height},\mathrm{angle}=0..2\mathrm{π},\mathrm{height}=-5..5,\mathrm{coords}=\mathrm{cylindrical},\mathrm{title}=\mathrm{CONE}\right)$
 > $\mathrm{plot3d}\left(1,t=0..2\mathrm{π},p=0..\mathrm{π},\mathrm{coords}=\mathrm{spherical},\mathrm{scaling}=\mathrm{constrained}\right)$
 > $\mathrm{plot3d}\left(\mathrm{θ},\mathrm{θ}=0..8\mathrm{π},z=-1..1,\mathrm{coords}=\mathrm{cylindrical}\right)$
 > $\mathrm{plot3d}\left(\mathrm{θ},\mathrm{θ}=0..8\mathrm{π},\mathrm{φ}=0..\mathrm{π},\mathrm{coords}=\mathrm{spherical},\mathrm{style}=\mathrm{wireframe}\right)$
 > $\mathrm{plot3d}\left(\mathrm{θ},\mathrm{θ}=0..8\mathrm{π},\mathrm{φ}=0..\mathrm{π},\mathrm{coords}=\mathrm{toroidal}\left(2\right),\mathrm{style}=\mathrm{wireframe}\right)$

Define a new cylindrical system so $z=z\left(r,\mathrm{\theta }\right)$ instead of $r=r\left(\mathrm{\theta },z\right)$:

 > $\mathrm{addcoords}\left(\mathrm{z_cylindrical},\left[z,r,\mathrm{θ}\right],\left[r\mathrm{cos}\left(\mathrm{θ}\right),r\mathrm{sin}\left(\mathrm{θ}\right),z\right]\right)$
 > $\mathrm{plot3d}\left(r\mathrm{cos}\left(\mathrm{θ}\right),r=0..10,\mathrm{θ}=0..2\mathrm{π},\mathrm{coords}=\mathrm{z_cylindrical},\mathrm{title}=\mathrm{z_cylindrical},\mathrm{orientation}=\left[-132,71\right],\mathrm{axes}=\mathrm{boxed}\right)$

The command to create the plot from the Plotting Guide is

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