# 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:

A 3d vector field:

```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
```

same example with only a list of colors:

```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
```

same example with only one color:

```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
```

same example with the same plot points for the three axes:

```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
```

same example with different number of plot points for each axis:

```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
```

same example with the arrows centered on the points:

```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
```