Set Coordinate System for 3-D Plots - Maple Help

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Set Coordinate System for 3-D Plots

Description

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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.

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

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When using Cartesian coordinates, z, the vertical coordinate, is expressed as a function of x and y: plot3dzx,y,x=a..b,y=c..d.

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For alternate coordinate systems this is interpreted differently. For example, when using cylindrical coordinates, Maple expects the command to be of the following form: plot3drθ,z,θ=a..b,z=c..d,coords=cylindrical.

  

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: plot3drθ,φ,θ=a..b,φ=c..d,coords=spherical.

  

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.

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

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

Examples

plot3dsinx+siny,x=0..2π,y=0..2π,axes=boxed

plot3dheight,angle=0..2π,height=5..5,coords=cylindrical,title=CONE

plot3d1,t=0..2π,p=0..π,coords=spherical,scaling=constrained

plot3dθ,θ=0..8π,z=1..1,coords=cylindrical

plot3dθ,θ=0..8π,φ=0..π,coords=spherical,style=wireframe

plot3dθ,θ=0..8π,φ=0..π,coords=toroidal2,style=wireframe

Define a new cylindrical system so z=zr,θ instead of r=rθ,z:

addcoordsz_cylindrical,z,r,θ,rcosθ,rsinθ,z

plot3drcosθ,r=0..10,θ=0..2π,coords=z_cylindrical,title=z_cylindrical,orientation=132,71,axes=boxed

The command to create the plot from the Plotting Guide is

plot3drcosθ,r=0..10,θ=0..2π,coords=cylindrical,orientation=100,71

See Also

addcoords, coords, plot3d, plot3d/option, plots[changecoords], plots[coordplot]


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