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 coordplot
 plotting of 2-D coordinate systems

 Calling Sequence coordplot(coord, rangelist, eqns)

Parameters

 coord - name of the coordinate system to plot rangelist - coordinate ranges eqns - optional equations

Description

 • The plots[coordplot] function plots "graph paper" of the two dimensional coordinate systems currently supported in Maple.  The 2-D plane is divided into a grid of lines of constant value, which are then mapped into the Cartesian plane by way of the coordinate transformation for the specified system coord.  See coords for details of each of the coordinate systems available.
 • Certain default values are associated with each coordinate system, in order to present better quality 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 available coordinate systems are:  bipolar, cardioid, cartesian, cassinian, elliptic, hyperbolic, invcassinian, invelliptic, logarithmic, logcosh, maxwell, parabolic, polar, rose, and tangent.
 • See addcoords for information on adding further coordinate systems and associated coordplot information (defaults).
 • rangelist is a list of two real ranges, one each for the two coordinate variables.  It must be specified for coordinate systems that do not have previously stored default information.
 • The optional equations eqns consist of the following, in addition to or in place of the standard plot options:

 'color' = color_list 'grid' = grid_list 'labeling' = label_type 'linestyle' = style_list 'view' = view_range

 • colour, color = color_list
 color_list should be a list of two names, each name indicating one of the colors currently supported in plot[color].  The default is [red, blue].
 • grid = [integer1, integer2]
 grid is a two element list of integers.  The first integer value indicates the number of grid lines in the x-direction, the second indicates the number used in the y-direction.  Hence, the original plane will be divided into a grid of integer1 x integer2 lines, and mapped by the coordinate transform into the Cartesian plane.  The default value depends on the coordinate system.
 • labeling or labelling = label_type
 label_type may be true, false, front, middle, or rear.  Labeling will result in the constant value associated with each line to be printed at one of three positions along the line.  The default is for labeling to be off (false).
 • linestyle = [value1, value2]
 linestyle is a list of two values. Each of value1 and value2 can be one of the line style names describe in the plot/option help page.
 • view = [a1..a2, b1..b2]
 view is a list of two real ranges.  It is used to specify the size of the view window used to display the coordinate plot.  Each coordinate system has an associated list of view values which may be changed by this option.
 • The command with(plots,coordplot) allows the use of the abbreviated form of this command.

Examples

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

 > $\mathrm{with}\left(\mathrm{plots}\right):$
 > $\mathrm{coordplot}\left(\mathrm{maxwell}\right)$
 > $\mathrm{coordplot}\left(\mathrm{maxwell},\mathrm{view}=\left[-0.5..0.5,0.5..1.5\right],\mathrm{labeling}=\mathrm{false}\right)$
 > $\mathrm{coordplot}\left(\mathrm{invcassinian}\right)$
 > $\mathrm{coordplot}\left(\mathrm{cassinian},\mathrm{linestyle}=\left[\mathrm{solid},\mathrm{dot}\right],\mathrm{labeling}=\mathrm{front},\mathrm{font}=\left[\mathrm{TIMES},8\right]\right)$
 > $\mathrm{coordplot}\left(\mathrm{logcosh},\left[-1..1,\frac{\mathrm{\pi }}{10}..\frac{2\mathrm{\pi }}{5}\right],\mathrm{scaling}=\mathrm{constrained}\right)$
 > $a≔\mathrm{plot}\left({\mathrm{sin}\left(x\right)}^{2}-{\mathrm{cos}\left(x\right)}^{2},x=0..2\mathrm{\pi },\mathrm{coords}=\mathrm{polar},\mathrm{thickness}=0\right):$
 > $b≔\mathrm{coordplot}\left(\mathrm{polar},\left[0..\frac{3}{2},0..2\mathrm{\pi }\right],\mathrm{labeling}=\mathrm{true}\right):$
 > $\mathrm{display}\left(\left[a,b\right]\right)$
 > $\mathrm{r1}≔\mathrm{plot}\left(\mathrm{sin}\left(\mathrm{cos}\left(x\right)\right),x=-2\mathrm{\pi }..2\mathrm{\pi },\mathrm{coords}=\mathrm{bipolar},\mathrm{thickness}=3\right):$
 > $\mathrm{r2}≔\mathrm{coordplot}\left(\mathrm{bipolar}\right):$
 > $\mathrm{display}\left(\left[\mathrm{r1},\mathrm{r2}\right]\right)$
 > $\mathrm{infolevel}\left[\mathrm{coordplot}\right]≔2:$
 > $\mathrm{coordplot}\left(\mathrm{rose}\right)$
 plots/coordplot:   u range:    -2 .. 2 plots/coordplot:   v range:    0 .. 2 plots/coordplot:   grid: [   13   13   ] plots/coordplot:   view:   [0 .. 3, 0 .. 3] plots/coordplot:   labelling:    false

The command to create the plot from the Plotting Guide is

 > $\mathrm{coordplot}\left(\mathrm{polar},\left[0..\frac{3}{2},0..2\mathrm{\pi }\right],\mathrm{labeling}=\mathrm{false}\right)$
 plots/coordplot:   u range:    0 .. 3/2 plots/coordplot:   v range:    0 .. 2*Pi plots/coordplot:   grid: [   7   13   ] plots/coordplot:   view:   [DEFAULT, DEFAULT] plots/coordplot:   labelling:    false