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# Plotting 3D fields

`sage.plot.plot3d.plot_field3d.``plot_vector_field3d`(functions, xrange, yrange, zrange, plot_points=5, colors='jet', center_arrows=False, **kwds)

  Plot a 3d vector field

  INPUT:

  - `functions` - a list of three functions, representing the x-, y-, and z-coordinates of a vector
  - `xrange`, `yrange`, and `zrange` - three tuples of the form (var, start, stop), giving the variables and ranges for each axis
  - `plot_points` (default 5) - either a number or list of three numbers, specifying how many points to plot for each axis
  - `colors` (default ‘jet’) - a color, list of colors (which are interpolated between), or matplotlib colormap name, giving the coloring of the arrows. If a list of colors or a colormap is given, coloring is done as a function of length of the vector
  - `center_arrows` (default False) - If True, draw the arrows centered on the points; otherwise, draw the arrows with the tail at the point
  - any other keywords are passed on to the plot command for each arrow

  EXAMPLES:

      sage: x,y,z=var('x y z')
      sage: plot_vector_field3d((x*cos(z),-y*cos(z),sin(z)), (x,0,pi), (y,0,pi), (z,0,pi))
      Graphics3d Object
      sage: plot_vector_field3d((x*cos(z),-y*cos(z),sin(z)), (x,0,pi), (y,0,pi), (z,0,pi),colors=['red','green','blue'])
      Graphics3d Object
      sage: plot_vector_field3d((x*cos(z),-y*cos(z),sin(z)), (x,0,pi), (y,0,pi), (z,0,pi),colors='red')
      Graphics3d Object
      sage: plot_vector_field3d((x*cos(z),-y*cos(z),sin(z)), (x,0,pi), (y,0,pi), (z,0,pi),plot_points=4)
      Graphics3d Object
      sage: plot_vector_field3d((x*cos(z),-y*cos(z),sin(z)), (x,0,pi), (y,0,pi), (z,0,pi),plot_points=[3,5,7])
      Graphics3d Object
      sage: plot_vector_field3d((x*cos(z),-y*cos(z),sin(z)), (x,0,pi), (y,0,pi), (z,0,pi),center_arrows=True)
      Graphics3d Object

  TESTS:

  This tests that trac ticket #2100 is fixed in a way compatible with this command:

      sage: plot_vector_field3d((x*cos(z),-y*cos(z),sin(z)), (x,0,pi), (y,0,pi), (z,0,pi),center_arrows=True,aspect_ratio=(1,2,1))
      Graphics3d Object

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