VectorPlot3D

VectorPlot3D[{vx,vy,vz},{x,xmin,xmax},{y,ymin,ymax},{z,zmin,zmax}]

generates a 3D vector plot of the vector field {vx,vy,vz} as a function of x, y, and z.

VectorPlot3D[{field1,field2,},{x,xmin,xmax},{y,ymin,ymax},{z,zmin,zmax}]

plots several vector fields.

VectorPlot3D[,{x,y,z}reg]

takes the variables {x,y,z} to be in the geometric region reg.

Details and Options

Examples

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Basic Examples  (4)

Plot a vector field:

Include a legend for the vector magnitudes:

Use tube segments as markers to represent the vectors:

Plot a vector field inside the unit ball:

Scope  (13)

Sampling  (5)

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 multiple vector fields with different colors for each field:

Presentation  (8)

Plot a vector field with arrows scaled according to their magnitudes:

Use a single color for the arrows:

Plot with 3D arrows:

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:

Include a legend:

Use a highly stylized theme:

Options  (64)

BoxRatios  (2)

By default, BoxRatios is set to Automatic:

Make the height appear twice the width and length:

EvaluationMonitor  (2)

Show where the function is sampled:

Count how many times the vector field function is evaluated:

PerformanceGoal  (2)

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

PlotLegends  (5)

No legends are included by default:

Add a legend that indicates vector norms:

Include a legend for two fields:

Include the vector fields in the legend:

Control the placement of the legend:

PlotRange  (9)

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:

Specify an explicit minimum range:

Specify an explicit range:

Specify an explicit maximum range:

Specify an explicit range:

Specify different , , and ranges:

PlotRangePadding  (8)

Padding is computed automatically by default:

Specify no padding for all , , and ranges:

Specify an explicit padding for all , , and ranges:

Add 10% padding to all , , and ranges:

Specify padding for and ranges:

Specify different padding for , , and ranges:

Specify padding for the range:

Use different padding forms for each dimension:

PlotTheme  (2)

Use a theme with dense vector points and legends:

Reduce the number of vector points:

RegionBoundaryStyle  (5)

Show the region defined by a region function:

Use None to not show the boundary:

Specify a style for the boundary:

The boundaries of full rectangular regions are not shown:

Specify a style for full rectangular regions:

RegionFunction  (3)

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:

VectorAspectRatio  (2)

The default aspect ratio for a vector marker is 1/4:

Increase the relative width of a vector marker:

VectorColorFunction  (4)

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:

VectorColorFunctionScaling  (4)

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:

VectorMarkers  (3)

By default, 3D arrows are used:

Use other named markers:

Use Placed to control the arrow placement relative to the vector points:

VectorPoints  (7)

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 packed grid:

The location for vectors is given in the middle of the drawn vector:

Start the vectors at the points:

VectorRange  (4)

The clipping of vectors with very small or very large magnitudes is done automatically:

Specify the range of vector norms:

Suppress the clipped vectors:

Show all the vectors:

VectorStyle  (2)

VectorColorFunction takes precedence over colors in VectorStyle:

Use VectorColorFunctionNone to specify colors with VectorStyle:

Applications  (1)

An electrostatic potential built from a collection of point charges at positions :

An electric field between two charges and :

The electrostatic potential between two charges and :

The electric field between two charges and :

Combine both visualizations:

Properties & Relations  (8)

Use ListVectorPlot3D to visualize data:

Plot vectors along surfaces with SliceVectorPlot3D:

Use StreamPlot3D to plot streamlines for a 3D vector field:

Use VectorPlot for plotting 2D vectors:

Use StreamPlot to plot with streamlines instead of vectors:

Use VectorDensityPlot to add a density plot of the scalar field:

Use LineIntegralConvolutionPlot to plot the line integral convolution of a vector field:

Plot a complex function as a vector field:

Wolfram Research (2008), VectorPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/VectorPlot3D.html (updated 2020).

Text

Wolfram Research (2008), VectorPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/VectorPlot3D.html (updated 2020).

BibTeX

@misc{reference.wolfram_2021_vectorplot3d, author="Wolfram Research", title="{VectorPlot3D}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/VectorPlot3D.html}", note=[Accessed: 30-July-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_vectorplot3d, organization={Wolfram Research}, title={VectorPlot3D}, year={2020}, url={https://reference.wolfram.com/language/ref/VectorPlot3D.html}, note=[Accessed: 30-July-2021 ]}

CMS

Wolfram Language. 2008. "VectorPlot3D." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/VectorPlot3D.html.

APA

Wolfram Language. (2008). VectorPlot3D. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VectorPlot3D.html