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

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

Python

>>> from sage.all import *
>>> x,y,z = var('x y z')
>>> plot_vector_field3d((x*cos(z), -y*cos(z), sin(z)),
...                     (x,Integer(0),pi), (y,Integer(0),pi), (z,Integer(0),pi))
Graphics3d Object

same example with only a list of colors:

Sage

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

Python

>>> from sage.all import *
>>> plot_vector_field3d((x*cos(z), -y*cos(z), sin(z)),
...                     (x,Integer(0),pi), (y,Integer(0),pi), (z,Integer(0),pi),
...                     colors=['red','green','blue'])
Graphics3d Object

same example with only one color:

Sage

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

Python

>>> from sage.all import *
>>> plot_vector_field3d((x*cos(z), -y*cos(z), sin(z)),
...                     (x,Integer(0),pi), (y,Integer(0),pi), (z,Integer(0),pi), colors='red')
Graphics3d Object

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

Sage

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

Python

>>> from sage.all import *
>>> plot_vector_field3d((x*cos(z), -y*cos(z), sin(z)),
...                     (x,Integer(0),pi), (y,Integer(0),pi), (z,Integer(0),pi), plot_points=Integer(4))
Graphics3d Object

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

Sage

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

Python

>>> from sage.all import *
>>> plot_vector_field3d((x*cos(z), -y*cos(z), sin(z)),
...                     (x,Integer(0),pi), (y,Integer(0),pi), (z,Integer(0),pi), plot_points=[Integer(3),Integer(5),Integer(7)])
Graphics3d Object

same example with the arrows centered on the points:

Sage

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

Python

>>> from sage.all import *
>>> plot_vector_field3d((x*cos(z), -y*cos(z), sin(z)),
...                     (x,Integer(0),pi), (y,Integer(0),pi), (z,Integer(0),pi), center_arrows=True)
Graphics3d Object