ListSliceVectorPlot3D

ListSliceVectorPlot3D[array,surf]

generates a vector plot from a 3D array of vector field values over the slice surface surf.

ListSliceVectorPlot3D[,{surf1,surf2,}]

generates a slice vector plot over several surfaces surf1, surf2, .

Details and Options

  • ListSliceVectorPlot3D plots a vector field defined over a 3D region by using surfaces to slice the region, and placing arrows on those surfaces. By default, the direction of the vector is indicated by the direction of the arrow, and the magnitude is indicated by its color.
  • The array represents values in a volume, where by default the point {k,j,i} is taken to have value arrayi,j,k with 1ir, 1js, and 1kt for an array of dimension {r,s,t,3}.
  • The following basic slice surfaces surfi can be given:
  • Automaticautomatically determine slice surfaces
    "CenterPlanes"coordinate planes through the center
    "BackPlanes"coordinate planes at the back of the plot
    "XStackedPlanes"coordinate planes stacked along axis
    "YStackedPlanes"coordinate planes stacked along axis
    "ZStackedPlanes"coordinate planes stacked along axis
    "DiagonalStackedPlanes"planes stacked diagonally
    "CenterSphere"a sphere in the center
    "CenterCutSphere"a sphere with a cutout wedge
    "CenterCutBox"a box with a cutout octant
  • ListSliceVectorPlot3D[data] is equivalent to ListSliceVectorPlot3D[data,Automatic].
  • The following parametrizations can be used for basic slice surfaces:
  • {"XStackedPlanes",n},generate n equally spaced planes
    {"XStackedPlanes",{x1,x2,}}generate planes for x=xi
    {"CenterCutSphere",ϕopen}cut angle ϕopen facing the view point
    {"CenterCutSphere",ϕopen,ϕcenter}cut angle ϕopen with center angle ϕcenter in -plane
  • "YStackedPlanes", "ZStackedPlanes" follow the specifications for "XStackedPlanes", with additional features shown in the scope examples.
  • The following general slice surfaces surfi can be used:
  • surfaceregiona two-dimensional region in 3D, e.g. Hyperplane
    volumeregiona three-dimensional region in 3D where surfi is taken as the boundary surface, e.g. Cuboid
  • The following wrappers can be used for slice surfaces surfi:
  • Annotation[surf,label]provide an annotation
    Style[surf,style]style the surface
    Button[surf,action]define an action to execute when the surface is clicked
    EventHandler[surf,]define a general event handler for the surface
    Hyperlink[surf,uri]make the surface act as a hyperlink
    PopupWindow[surf,cont]attach a popup window to the surface
    StatusArea[surf,label]display in status area when the surface is moused over
    Tooltip[surf,label]attach an arbitrary tooltip to the surface
  • ListSliceVectorPlot3D has the same options as Graphics3D, with the following additions and changes:
  • AxesTruewhether to draw axes
    BoundaryStyleAutomatichow to style surface boundaries
    BoxRatios{1,1,1}ratio of height to width
    ClippingStyleAutomatichow to display arrows outside the vector range
    DataRangeAutomaticthe range of x, y, and z values to assume for data
    MethodAutomaticmethods to use for the plot
    PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
    PlotPointsAutomaticapproximate number of samples for the slice surfaces surfi in each direction
    PlotRange{Full,Full,Full}range of x, y, z values to include
    PlotRangePaddingAutomatichow much to pad the range of values
    PlotStyleAutomaticstyle directives for each slice surface
    PlotTheme$PlotThemeoverall theme for the plot
    RegionBoundaryStyleNonehow to style plot region boundaries
    RegionFunctionTrue&determine what region to include
    TargetUnitsAutomaticdesired units to use
    VectorAspectRatioAutomaticwidth-to-length ratio for arrows
    VectorColorFunctionAutomatichow to color vectors
    VectorColorFunctionScalingTruewhether to scale the argument to VectorColorFunction
    VectorMarkersAutomaticthe shape of the arrows
    VectorPointsAutomaticthe number or placement of vectors to plot
    VectorScaleAutomaticthe scale and size of vectors to plot
    VectorRangeAutomaticrange of vector lengths to show
    VectorScalingNonehow to scale the sizes of arrows
    VectorSizesAutomaticsizes of displayed arrows
    VectorStyleAutomatichow to draw vectors
  • 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:
  • RegionFunction is supplied with x, y, z, vx, vy, vz, Norm[{vx,vy,vz}].
  • VectorColorFunction is by default supplied with scaled x, y, z, vx, vy, vz, Norm[{vx,vy,vz}].
  • For an array of dimension {r,s,t,3}, the setting DataRangeAutomatic is equivalent to DataRange{{1,r},{1,s},{1,t}}.
  • Slice surfaces can be styled using a Style wrapper and PlotStyle option with the Style wrapper taking precedence over PlotStyle. None can be used to indicate that no slice surface should be shown.

Examples

open allclose all

Basic Examples  (2)

Plot a vector field over a surface:

Use a general slice surface:

Scope  (21)

Surfaces  (9)

Generate a plot over standard slice surfaces:

Standard axis-aligned stacked slice surfaces:

Standard boundary surfaces:

Plot over any surface region:

A volume slice region is equivalent to plotting over RegionBoundary[reg]:

Plot over the surface :

Plot over multiple slice surfaces:

Specify the number of stacked planes:

Specify the cutting angle for a center-cut sphere slice:

Data  (4)

For regular data consisting of vectors, the , , and data reflects its positions in the array:

Provide explicit , , and data ranges by using DataRange:

Use VectorPoints to specify the number of arrows:

Plot a vector field given by QuantityArray:

Use RegionFunction to expose obscured slices:

Presentation  (8)

Use PlotTheme to immediately get overall styling:

Control the display of axes with Axes:

Label axes using AxesLabel and the whole plot using PlotLabel:

Color the vectors by their magnitude with VectorColorFunction:

Use VectorStyle to control the shape of the vectors:

Scale to reflect vector magnitudes:

Style the slice surface boundaries with BoundaryStyle:

TargetUnits specifies which units to use in the visualization:

Options  (51)

Axes  (3)

Axes are drawn by default:

Use Axes->False to remove the axes:

Draw only some axes:

BoundaryStyle  (1)

Style the surface boundaries:

BoxRatios  (3)

By default, the edges of the bounding box have the same length:

Use BoxRatios-> Automatic to show the natural scale of the 3D coordinate values:

Use custom length ratios for each side of the bounding box:

ClippingStyle  (4)

By default, clipped vectors are given a constant color that is consistent with the minimum or maximum vector lengths given by VectorRange:

Suppress the clipped vectors:

Style the clipped vectors:

Style the short and long clipped vectors differently:

DataRange  (2)

By default, the data range is taken to be the dimension of the array:

Explicitly specify the data range:

PerformanceGoal  (2)

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

PlotLegends  (1)

Use a legend to indicate vector magnitudes:

PlotRange  (2)

Show All vectors by default:

Show a select range:

PlotRangePadding  (5)

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:

PlotTheme  (3)

Use a theme:

Regular options override PlotTheme settings, in this case turning off FaceGrids:

Compare different plot themes:

RegionFunction  (2)

Use RegionFunction to specify what regions of the slice surfaces to include:

Plot vectors only over regions where the field magnitude is above a given threshold:

VectorColorFunction  (5)

By default, vectors are colored according to their norm:

Change the color function:

Use any named color gradient from ColorData:

Color the vectors according to their value:

Use VectorColorFunctionScalingFalse to get unscaled values:

VectorColorFunctionScaling  (3)

By default, scaled values are used:

Use VectorColorFunctionScaling->False to get unscaled values:

Explicitly specify the scaling for each color function argument:

VectorMarkers  (2)

The default vector marker is "Arrow3D":

Use other named markers:

VectorPoints  (3)

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 :

VectorRange  (3)

Specify the range of vector norms that are displayed with varying color:

Combine with ClippingStyle to remove the clipped vectors:

Or specify a different style for clipped vectors:

VectorScaling  (3)

By default, arrows are displayed with a constant length:

Use Automatic to scale arrows proportionally to the corresponding vector norm:

Use VectorSizes to specify the range of relative lengths of the arrows:

VectorSizes  (2)

Make the vectors half of the default size:

With VectorScaling, VectorSizes controls the range of the lengths of the arrows relative to the default size:

VectorStyle  (1)

VectorColorFunction has precedence over VectorStyle:

TargetUnits  (1)

Specify which units to use in the visualization:

Applications  (7)

Basic Vector Fields  (3)

Constant vector fields from data:

A circulating flow from data:

Divergent flow:

Convergent flow:

Image Processing  (1)

Visualize the gradient vectors of a 3D image:

Compute the vector orientations:

Convert to vector data:

Show the vectors with the image:

Fluid Dynamics  (2)

Visualize Hill's spherical vortex, with vortex radius and velocity :

Compute velocity vectors:

Visualize the vortex by coloring based on the flow speed:

Visualize the divergence-free field of a scalar function :

Visualize the vortices formed by these fields:

Gradient Fields  (1)

Observe the gradient field superimposed on a density plot of a function:

Properties & Relations  (5)

Use ListVectorPlot3D for a full volume visualization of the vector field:

Use SliceVectorPlot3D for functions:

Use ListVectorPlot for vector plots in 2D:

Use ListStreamPlot or ListLineIntegralConvolutionPlot for vector fields in 2D:

Use GeoVectorPlot to plot vectors on a map:

Wolfram Research (2015), ListSliceVectorPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/ListSliceVectorPlot3D.html (updated 2020).

Text

Wolfram Research (2015), ListSliceVectorPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/ListSliceVectorPlot3D.html (updated 2020).

BibTeX

@misc{reference.wolfram_2020_listslicevectorplot3d, author="Wolfram Research", title="{ListSliceVectorPlot3D}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/ListSliceVectorPlot3D.html}", note=[Accessed: 14-April-2021 ]}

BibLaTeX

@online{reference.wolfram_2020_listslicevectorplot3d, organization={Wolfram Research}, title={ListSliceVectorPlot3D}, year={2020}, url={https://reference.wolfram.com/language/ref/ListSliceVectorPlot3D.html}, note=[Accessed: 14-April-2021 ]}

CMS

Wolfram Language. 2015. "ListSliceVectorPlot3D." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/ListSliceVectorPlot3D.html.

APA

Wolfram Language. (2015). ListSliceVectorPlot3D. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ListSliceVectorPlot3D.html