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 coordplot3d
 representation of 3-D coordinate systems

 Calling Sequence coordplot3d(coord, rangelist, constlist, eqns)

Parameters

 coord - name of the coordinate system to plot rangelist - (optional) list of coordinate ranges; [range1, range2, range3] constlist - (optional) list of lists of coordinate constant values eqns - optional equations

Description

 • The plots[coordplot3d] function plots a graphical representation of most of the three dimensional coordinate systems currently supported in Maple. Each of the coordinates is held constant at a certain value (see below), while the other two vary.  This gives rise to intersecting surfaces, one for each constant value.  See coords for details of each of the coordinate systems available.
 • Certain default values are associated with each coordinate system, in order to present visually understandable results.  To see these default values, set infolevel[coordplot] to 2.  All of these default values may be overridden by the optional equations (see below).
 • The coordinate systems that can be plotted are:  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, tangentcylindrical, tangentsphere, and toroidal.
 • For information on adding further coordinate systems and associated coordplot3d information (defaults), see addcoords.
 • rangelist is a list of three real ranges, each corresponding to a range of values to be used for a coordinate variable.  rangelist must be specified for coordinate systems that do not have previously stored default information.
 • constlist is a list of lists, each "sub-list" corresponding to a particular coordinate, and the values it is to have when being held constant.  Note this must be input as a list of lists, as each coordinate variable may take multiple constant values.
 • The optional equations eqns consist of the following, in addition to or in place of the standard plot3d options:

 'color' = color_info 'grid' = grid_list 'labeling' = label_info 'style' = style_n 'view' = view_range

 • colour, color = color_name
 color_info should be a name, or a list of names, each name indicating one of the colors currently supported in plot[color].  In the instance of a list, the number of colors specified must match the total number of constant values used.  The default is for u-constant surfaces to be red, v-constant surfaces to be green, and w-constant surfaces to be blue.
 • grid = [integer1,integer2]
 grid_list is a two element list of integers.  These integers indicate the number of divisions to be applied (respectively) to each of the two coordinate values that varies, as the other is held constant. The default is [22, 22].
 • labeling or labelling = label_info
 label_info may be true, false, or a three element list, specifying a label name for each of the coordinates variables (in this instance, labeling is automatically turned on).  The default is for labeling to be off (false).  Note that labels are printed for each sheet, at a $\frac{3}{4},\frac{3}{4}$ position relative to the size of the sheet.  Hence, they may be difficult to find, due to characteristics (e.g. obstructions) of the coordinate system.  Rotating the plot will generally bring them into view.
 • style = style_n
 style_n is a PLOT3D structure STYLE name. The default is 'HIDDEN'.
 • view = [$\mathrm{a1}..\mathrm{a2},\mathrm{b1}..\mathrm{b2},\mathrm{c1}..\mathrm{c2}$]
 view_range is a list of three real ranges.  It is used to specify the size of the view box used to display the coordinate plot.  Each coordinate system has an associated list of view values which may be changed by this option.  For coordinate systems that do not have stored default information, the default is to use an arbitrary view (that is, one large enough to display the entire plot).

Examples

If infolevel is set to a greater integer (possible settings are 1 through 5), more detailed information about the computation methods is displayed.

 > $\mathrm{with}\left(\mathrm{plots}\right):$
 > $\mathrm{Digits}≔10:$
 > $\mathrm{coordplot3d}\left(\mathrm{maxwellcylindrical}\right)$
 > $\mathrm{coordplot3d}\left(\mathrm{maxwellcylindrical},\mathrm{view}=\left[-0.75..0.75,0.15..1.5,-0.5..0.5\right],\mathrm{grid}=\left[30,30\right],\mathrm{labeling}=\left[\mathrm{\eta },\mathrm{\psi },z\right]\right)$
 > $\mathrm{coordplot3d}\left(\mathrm{rectangular}\right)$
 > $\mathrm{infolevel}\left[\mathrm{coordplot3d}\right]≔2:$
 > $\mathrm{coordplot3d}\left(\mathrm{rosecylindrical}\right)$
 plots/coordplot3d:   u const values:   [1] plots/coordplot3d:   v const values:   [1] plots/coordplot3d:   w const values:   [0] plots/coordplot3d:   u range:   -2 .. 2 plots/coordplot3d:   v range:   0 .. 2 plots/coordplot3d:   w range:   -1 .. 1 plots/coordplot3d:   view:   [0 .. 3, 0 .. 3, -1 .. 1]
 > $\mathrm{coordplot3d}\left(\mathrm{sixsphere}\right)$
 plots/coordplot3d:   u const values:   [.6, -.6] plots/coordplot3d:   v const values:   [.55, -.55] plots/coordplot3d:   w const values:   [.5, -.5] plots/coordplot3d:   u range:   -1 .. 1 plots/coordplot3d:   v range:   -1 .. 1 plots/coordplot3d:   w range:   -1 .. 1 plots/coordplot3d:   view:   [-2 .. 2, -2 .. 2, -2 .. 2]
 > $\mathrm{coordplot3d}\left(\mathrm{sixsphere},\left[\left[0.7\right],\left[0.45\right],\left[0.3\right]\right],\left[-2..2,-2..2,-2..2\right],\mathrm{grid}=\left[29,29\right],\mathrm{view}=\left[-2..2.4,-2..2.4,-1.2..3.2\right],\mathrm{style}='\mathrm{WIREFRAME}'\right)$
 plots/coordplot3d:   u const values:   [.7] plots/coordplot3d:   v const values:   [.45] plots/coordplot3d:   w const values:   [.3] plots/coordplot3d:   u range:   -2 .. 2 plots/coordplot3d:   v range:   -2 .. 2 plots/coordplot3d:   w range:   -2 .. 2 plots/coordplot3d:   view:   [-2 .. 2.4, -2 .. 2.4, -1.2 .. 3.2]

The command to create the plot from the Plotting Guide is

 > $\mathrm{coordplot3d}\left(\mathrm{paraboloidal},\mathrm{labeling}=\mathrm{false}\right)$
 plots/coordplot3d:   u const values:   [.5] plots/coordplot3d:   v const values:   [.5] plots/coordplot3d:   w const values:   [1/3*Pi] plots/coordplot3d:   u range:   0 .. 1 plots/coordplot3d:   v range:   0 .. 1 plots/coordplot3d:   w range:   0 .. 2*Pi plots/coordplot3d:   view:   [-1 .. 1, -1 .. 1, -.6 .. .6]