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 plot a 3-D gradient vector field

 Calling Sequence gradplot3d(f, r1, r2, r3) gradplot3d(f, r1, r2, r3,...)

Parameters

 f - function or set of function to be plotted r1 - range r2 - range r3 - range

Description

 • A typical call to the gradplot3d function is gradplot3d(f, x=a..b, y=c..d, z=p..q), where f is a Maple expressions in x, y, and z, and $a..b$, $c..d$, and $p..q$ specifies the axes ranges of the field. The result is a three dimensional vectorfield with the gradient vector evaluated at (x, y, z) located at this point.
 • A call to gradplot3d produces a PLOT3D data structure, which is then printed.  For information on these data structures, see plot3d/structure.
 • Remaining arguments are interpreted as options which are specified as equations of the form option = value.  In particular, the arrows option allows one to specify the style of arrow used to represent a vector. The possibilities  are LINE, THIN, SLIM and THICK with THIN being the default.  The grid option allows one to set the initial size of the two or three dimensional grid. The defaults is [8,8,8]. The remaining options are the same as those available for the plot3d command. For more information, see plot3d/option.
 • gradplot3d may be defined by with(plots) or with(plots,gradplot3d). It can also be used by the name plots[gradplot3d].

Examples

 > $\mathrm{with}\left(\mathrm{plots}\right):$
 > $\mathrm{gradplot3d}\left({\left({x}^{2}+{y}^{2}+{z}^{2}+1\right)}^{\frac{1}{2}},x=-2..2,y=-2..2,z=-2..2\right)$
 > $\mathrm{gradplot3d}\left({x}^{2}+2{y}^{2}+z+1,x=-1..1,y=-1..1,z=-1..1,\mathrm{grid}=\left[5,5,5\right]\right)$

The command to create the plot from the Plotting Guide is

 > $\mathrm{gradplot3d}\left(\mathrm{sin}\left(xyz\right),x=-\mathrm{π}..\mathrm{π},y=-\mathrm{π}..\mathrm{π},z=-\mathrm{π}..\mathrm{π},\mathrm{grid}=\left[4,4,4\right],\mathrm{color}=\mathrm{black},\mathrm{arrows}=\mathrm{THICK}\right)$