This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# VectorPlot3D

 VectorPlot3D generates a 3D vector plot of the vector field as a function of x, y, and z. VectorPlot3Dplots several vector fields.
• VectorPlot3D by default shows vectors from the vector field at a regular grid of 3D positions.
• VectorPlot3D omits any vectors for which the etc. do not evaluate to real numbers.
• VectorPlot3D has attribute HoldAll, and evaluates the only after assigning specific numerical values to x, y, and z.
• In some cases it may be more efficient to use Evaluate to evaluate the symbolically before specific numerical values are assigned to x, y, and z.
 BoxRatios {1,1,1} ratio of height to width EvaluationMonitor None expression to evaluate at every function evaluation Method Automatic methods to use for the plot PerformanceGoal \$PerformanceGoal aspects of performance to try to optimize PlotRange {Full,Full,Full} range of x, y, z values to include PlotRangePadding Automatic how much to pad the range of values RegionFunction True& determine what region to include VectorColorFunction None how to color vectors VectorColorFunctionScaling True whether to scale the argument to VectorColorFunction VectorPoints Automatic the number or placement of vectors to plot VectorScale Automatic the scale and size of vectors to plot VectorStyle Automatic how to draw vectors WorkingPrecision MachinePrecision precision to use in internal computations
Plot a vector field:
Plot a vector field:
 Out[1]=
 Scope   (11)
Plot multiple vector fields:
Use Evaluate to evaluate the vector field symbolically before numeric assignment:
Plot vectors over specified regions:
Plot a vector field with vectors placed with specified densities:
Plot a field with arrows placed at random locations:
Plot a vector field with arrows colored by the Norm of the field:
Plot with 3D arrows:
Plot a field with arbitrary three-dimensional shapes:
Color and scale the vectors based on the norm of the field:
Plot a vector field with arrows of specified size:
Vary the arrow length and arrowhead size:
 Options   (52)
By default BoxRatios is set to Automatic:
Make the height appear twice the width and length:
Show where the function is sampled:
Count how many times the vector field function is evaluated:
Generate a higher-quality plot:
Emphasize performance, possibly at the cost of quality:
The full plot range is used by default:
Use all points to compute the range:
Specify an explicit limit for , , and ranges:
Specify an explicit range that applies to all , , and ranges:
Specify an explicit range:
Specify an explicit minimum range:
Specify an explicit range:
Specify an explicit maximum range:
Specify an explicit range:
Specify different , , and ranges:
Padding is computed automatically by default:
Specify no padding for all , , and ranges:
Specify an explicit padding for all , , and ranges:
Specify different padding for , , and ranges:
Use different padding forms for each dimension:
Plot vectors only over certain quadrants:
Plot vectors only over regions where the field magnitude is above a given threshold:
Use any logical combination of conditions:
Color the vectors according to their norm:
Use any named color gradient from ColorData:
Color the vectors according to their value:
Use VectorColorFunctionScaling->False to get unscaled values:
By default, scaled values are used:
Use VectorColorFunctionScaling->False to get unscaled values:
Use unscaled coordinates in the direction and scaled coordinates in the direction:
Explicitly specify the scaling for each color function argument:
Use automatically determined vector points:
Use symbolic names to specify the set of field vectors:
Create a regular grid of field vectors with the same number of arrows for , , and :
Create a regular grid of field vectors with a different number of arrows for , , and :
Specify a list of points for showing field vectors:
Use a different number of field vectors on a regular grid:
The location for vectors is given in the middle of the drawn vector:
Use automatically determined vector scale:
Specify the relative size of vectors as a fraction of the diagonal of the plot range:
Use symbolic names to control the size of vectors:
With the vector scaling function set to None, then all vectors have the same size:
Specify an absolute size for the arrowheads:
Specify arrowhead size relative to the length of the arrow:
Scale the vector length by the absolute value of the coordinate:
Plot a vector field using 3D arrows:
Use Graphics3D as a style for the 3D arrows:
3D graphics primitives without Arrowheads are scaled based on the vector scale:
 Applications   (3)
Use a contour plot to visualize the region of a vector plot:
Plot a vector field over a particular region:
Create a contour plot of the vector plot's region:
Combine the vector and contour plots:
Plot the vector field in a spherical region.