ListVectorPlot3D

ListVectorPlot3D[array]
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. By default, the direction of the vector is indicated by the direction of the arrow, and the magnitude is indicated by its color.
- 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:
-
BoxRatios Automatic ratio of height to width ClippingStyle Automatic how to display arrows outside the vector range DataRange Automatic the range of x, y, and z values to assume for data Method Automatic methods to use for the plot PerformanceGoal $PerformanceGoal aspects of performance to try to optimize PlotLegends None legends to include PlotRange {Full,Full,Full} range of x, y, z values to include PlotRangePadding Automatic how much to pad the range of values PlotTheme $PlotTheme overall theme for the plot RegionBoundaryStyle Automatic how to style plot region boundaries RegionFunction (True&) determine what region to include ScalingFunctions None how to scale individual coordinates VectorAspectRatio Automatic width-to-length ratio for arrows VectorColorFunction Automatic how to color vectors VectorColorFunctionScaling True whether to scale the argument to VectorColorFunction VectorPoints Automatic the number or placement of arrows VectorRange Automatic range of vector lengths to show VectorScaling None how to scale the sizes of arrows VectorSizes Automatic sizes of displayed arrows VectorStyle Automatic how to draw arrows - 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



Examples
open allclose allBasic Examples (4)
Scope (15)
Sampling (6)
Options (70)
BoxRatios (2)
DataRange (1)
PerformanceGoal (2)
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)
PlotRangePadding (8)
RegionBoundaryStyle (5)
Show the region defined by a region function:
Use None to not show the boundary:
Specify a style for the boundary:
RegionFunction (3)
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 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)
VectorScaling (2)
Use an automatically determined vector scale:
With the vector scaling function set to None, all vectors have the same size:
VectorSizes (2)
VectorStyle (2)
VectorColorFunction has precedence over colors in VectorStyle:
Use VectorColorFunctionNone to specify colors with VectorStyle:
Applications (2)
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:
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