ListVectorPlot3D [varr]
generates a 3D vector plot from a 3D array of vector field values.
ListVectorPlot3D [{data1,data2,…}]
plots data for several vector fields.
ListVectorPlot3D
ListVectorPlot3D [varr]
generates a 3D vector plot from a 3D array of vector field values.
ListVectorPlot3D [{data1,data2,…}]
plots data for several vector fields.
Details and Options
- ListVectorPlot3D is also known as 3D field plot and 3D direction plot.
- ListVectorPlot3D displays a vector field by drawing arrows normalized to a fixed length. The arrows are colored by default according to the magnitude of the vector field.
- The vector field has value varr〚i,j,k〛 at .
- ListVectorPlot3D by default interpolates the data given and plots vectors for the vector field at a regular 3D grid of positions.
- ListVectorPlot3D has the same options as Graphics3D , with the following additions and changes: [List of all options]
-
- With the setting VectorPoints All , ListVectorPlot3D instead shows vectors associated with the particular vector field data points given.
- The individual arrows are scaled to fit inside bounding balls around each point.
- VectorScaling scales the magnitudes of the vectors into the range of arrow sizes smin to smax given by VectorSizes .
- VectorScaling Automatic will scale the arrow lengths depending on the vector magnitudes:
- Common markers include:
-
"Arrow3D" 3D arrow-shaped marker"Arrow" 2D arrow-shaped marker"Tube" tube segment aligned in the field direction"Segment" line segment aligned in the field direction
- VectorColorFunction None will draw the arrows with the style specified by VectorStyle .
- The arguments supplied to functions in RegionFunction and VectorColorFunction are x, y, z, vx, vy, vz, Norm [{vx,vy,vz}].
- Possible settings for ScalingFunctions are:
-
{sx,sy,sz} scale x, y and z axes
- Common built-in scaling functions s include:
-
"Log" log scale with automatic tick labeling"Log10" base-10 log scale with powers of 10 for ticks"SignedLog" log-like scale that includes 0 and negative numbers"Reverse" reverse the coordinate direction"Infinite" infinite scale
-
ImageMargins 0. the margins to leave around the graphicPreserveImageOptions Automatic whether to preserve image options when displaying new versions of the same graphicRotationAction "Fit" how to render after interactive rotation
List of all options
Examples
open all close allBasic Examples (4)
Plot the vector field interpolated from a specified set of vectors:
Plot the vector field from data specifying coordinates and vectors:
Include a legend showing the vector magnitudes:
Use tube segments as markers to represent the vectors:
Scope (15)
Sampling (6)
Plot vectors for a regular collection of vectors and give a data range for the domain:
Explicitly set the number of vectors in each direction:
Plot two vector fields:
Plot vectors over a specified region:
Plot a vector field with vectors placed with specified densities:
Plot a field with arrows placed at random locations:
Plot the vectors that go through a set of seed points:
Presentation (9)
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 arrowhead size:
Use legends for multiple datasets:
Use a highly stylized theme:
Use a log scale in the z direction:
Options (98)
Axes (3)
AxesLabel (3)
No axes labels are drawn by default:
Place a label on the axis:
Specify axes labels:
AxesOrigin (2)
The position of the axes is determined automatically:
Specify an explicit origin for the axes:
AxesStyle (4)
Change the style for the axes:
Specify the style of each axis:
Use different styles for the ticks and the axes:
Use different styles for the labels and the axes:
BoxRatios (2)
DataRange (1)
By default, the data range is taken to be the index range of the data array:
Specify the data range for the domain:
EvaluationMonitor (1)
Count how many times the vector field interpolating function is evaluated:
ImageSize (7)
Use named sizes such as Tiny , Small , Medium and Large :
Specify the width of the plot:
Specify the height of the plot:
Allow the width and height to be up to a certain size:
Specify the width and height for a graphic, padding with space if necessary:
Setting AspectRatio Full will fill the available space:
Use maximum sizes for the width and height:
Use ImageSize Full to fill the available space in an object:
Specify the image size as a fraction of the available space:
PerformanceGoal (2)
Generate a higher-quality plot:
Emphasize performance, possibly at the cost of quality:
PlotLegends (4)
Use legends for color gradients:
Use legends for multiple datasets:
Use SwatchLegend to change the legend's appearance:
Use Placed to put legends above the plot:
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:
Change the color scheme:
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:
ScalingFunctions (2)
By default, linear scales are used:
Reverse the direction of the z direction:
Ticks (6)
Ticks are placed automatically in each plot:
Use Ticks None to not draw any tick marks:
Place tick marks at specific positions:
Draw tick marks at the specified positions with the specified labels:
Specify tick marks with scaled lengths:
Customize each tick with position, length, labeling and styling:
TicksStyle (3)
By default, the ticks and tick labels use the same styles as the axis:
Specify overall ticks style, including the tick labels:
Specify tick style for each of the axes:
VectorAspectRatio (2)
Change arrowhead sizes:
Use scaled sizes:
VectorColorFunction (4)
VectorColorFunctionScaling (4)
By default, scaled values are used:
Use VectorColorFunctionScalingFalse 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 (8)
Use automatically determined vector points:
Use named VectorPoints settings:
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:
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:
VectorScaling (2)
Use an automatically determined vector scale:
With the vector scaling function set to None , all vectors have the same size:
VectorSizes (2)
The sizes of the displayed vector is determined automatically:
Specify the range of arrow lengths:
VectorStyle (2)
VectorColorFunction has precedence over colors in VectorStyle :
Use VectorColorFunction None to specify colors with VectorStyle :
Applications (2)
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:
Add an inner sphere:
Properties & Relations (12)
Use VectorPlot3D to visualize functions:
Use StreamPlot3D to visualize functions with streamlines instead of vectors:
Plot vectors along surfaces with ListSliceVectorPlot3D :
Use ListStreamPlot3D to plot a 3D field as streamlines:
Use ListVectorPlot for plotting 2D vectors:
Use ListStreamPlot to plot with streamlines instead of vectors:
Use ListVectorDensityPlot to add a density plot of the scalar field:
Use ListStreamDensityPlot to plot streams instead of vectors:
Use VectorDisplacementPlot to visualize the effect of a displacement vector field on a specified region:
Use ListVectorDisplacementPlot to visualize the effect of displacement field data on a region:
Use ListLineIntegralConvolutionPlot to plot the line integral convolution of a vector field:
Use VectorDisplacementPlot3D to visualize the effect of a displacement vector field on a specified 3D region:
Use ListVectorDisplacementPlot3D to visualize the effect of a 3D displacement vector field based on data:
Use GeoVectorPlot to plot vectors on a map:
Use GeoStreamPlot to use streams instead of vectors:
Related Guides
History
Introduced in 2008 (7.0) | Updated in 2014 (10.0) ▪ 2020 (12.1) ▪ 2022 (13.1)
Text
Wolfram Research (2008), ListVectorPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/ListVectorPlot3D.html (updated 2022).
CMS
Wolfram Language. 2008. "ListVectorPlot3D." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/ListVectorPlot3D.html.
APA
Wolfram Language. (2008). ListVectorPlot3D. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ListVectorPlot3D.html
BibTeX
@misc{reference.wolfram_2025_listvectorplot3d, author="Wolfram Research", title="{ListVectorPlot3D}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/ListVectorPlot3D.html}", note=[Accessed: 24-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_listvectorplot3d, organization={Wolfram Research}, title={ListVectorPlot3D}, year={2022}, url={https://reference.wolfram.com/language/ref/ListVectorPlot3D.html}, note=[Accessed: 24-November-2025]}