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SliceVectorPlot3D
✖
SliceVectorPlot3D
generates a vector plot of the field {vx,vy,vz} over the slice surface surf.
restricts the surface surf to be within the region reg.
generates vector plots over several slice surfaces surfi.
Details and Options




- SliceVectorPlot3D evaluates the field function {vx,vy,vz} at values of x, y and z on a surface surf and displays the results as arrows colored by magnitude.
- The plot visualizes the set
.
- SliceVectorPlot3D[f,{x,xmin,xmax},…] is equivalent to SliceVectorPlot3D[f,Automatic,{x,xmin,xmax},…] etc.
- The following basic slice surfaces surfi can be given:
-
Automatic automatically 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 - 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 the 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:
-
expr0 implicit equation in x, y, and z, e.g. x y z-10 surfaceregion a two-dimensional region in 3D, e.g. Hyperplane volumeregion a 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 - SliceVectorPlot3D has the same options as Graphics3D, with the following additions and changes: [List of all options]
-
Axes True whether to draw axes BoundaryStyle Automatic how to style surface boundaries BoxRatios {1,1,1} ratio of height to width ClippingStyle Automatic how to display arrows outside the vector range Method Automatic methods to use for the plot PerformanceGoal $PerformanceGoal aspects of performance to try to optimize PlotLegends None legends to include PlotPoints Automatic approximate number of samples for the slice surfaces surfi in each direction PlotRange {Full,Full,Full} range of x, y, z values to include PlotRangePadding Automatic how much to pad the range of values PlotStyle Automatic style directives for each slice surface PlotTheme $PlotTheme overall theme for the plot RegionBoundaryStyle None how to style plot region boundaries RegionFunction (True&) determine what region to include ScalingFunctions None how to scale axes TargetUnits Automatic desired units to use VectorAspectRatio Automatic width-to-length ratio for arrows VectorColorFunction Automatic how to color vectors VectorColorFunctionScaling True whether to scale the argument to VectorColorFunction VectorMarkers Automatic the shape of the arrows VectorPoints Automatic the number or placement of vectors to plot 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 vectors WorkingPrecision MachinePrecision precision to use in internal computations - 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}].
- 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.
- Possible settings for ScalingFunctions include:
-
{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 -
AlignmentPoint Center the default point in the graphic to align with AspectRatio Automatic ratio of height to width Axes True whether to draw axes AxesEdge Automatic on which edges to put axes AxesLabel None axes labels AxesOrigin Automatic where axes should cross AxesStyle {} graphics directives to specify the style for axes Background None background color for the plot BaselinePosition Automatic how to align with a surrounding text baseline BaseStyle {} base style specifications for the graphic BoundaryStyle Automatic how to style surface boundaries Boxed True whether to draw the bounding box BoxRatios {1,1,1} ratio of height to width BoxStyle {} style specifications for the box ClippingStyle Automatic how to display arrows outside the vector range ClipPlanes None clipping planes ClipPlanesStyle Automatic style specifications for clipping planes ContentSelectable Automatic whether to allow contents to be selected ControllerLinking False when to link to external rotation controllers ControllerPath Automatic what external controllers to try to use Epilog {} 2D graphics primitives to be rendered after the main plot FaceGrids None grid lines to draw on the bounding box FaceGridsStyle {} style specifications for face grids FormatType TraditionalForm default format type for text ImageMargins 0. the margins to leave around the graphic ImagePadding All what extra padding to allow for labels, etc. ImageSize Automatic absolute size at which to render the graphic LabelStyle {} style specifications for labels Lighting Automatic simulated light sources to use Method Automatic methods to use for the plot PerformanceGoal $PerformanceGoal aspects of performance to try to optimize PlotLabel None a label for the plot PlotLegends None legends to include PlotPoints Automatic approximate number of samples for the slice surfaces surfi in each direction PlotRange {Full,Full,Full} range of x, y, z values to include PlotRangePadding Automatic how much to pad the range of values PlotRegion Automatic final display region to be filled PlotStyle Automatic style directives for each slice surface PlotTheme $PlotTheme overall theme for the plot PreserveImageOptions Automatic whether to preserve image options when displaying new versions of the same graphic Prolog {} 2D graphics primitives to be rendered before the main plot RegionBoundaryStyle None how to style plot region boundaries RegionFunction (True&) determine what region to include RotationAction "Fit" how to render after interactive rotation ScalingFunctions None how to scale axes SphericalRegion Automatic whether to make the circumscribing sphere fit in the final display area TargetUnits Automatic desired units to use Ticks Automatic specification for ticks TicksStyle {} style specification for ticks TouchscreenAutoZoom False whether to zoom to fullscreen when activated on a touchscreen VectorAspectRatio Automatic width-to-length ratio for arrows VectorColorFunction Automatic how to color vectors VectorColorFunctionScaling True whether to scale the argument to VectorColorFunction VectorMarkers Automatic the shape of the arrows VectorPoints Automatic the number or placement of vectors to plot 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 vectors ViewAngle Automatic angle of the field of view ViewCenter Automatic point to display at the center ViewMatrix Automatic explicit transformation matrix ViewPoint {1.3,-2.4,2.} viewing position ViewProjection Automatic projection method for rendering objects distant from the viewer ViewRange All range of viewing distances to include ViewVector Automatic position and direction of a simulated camera ViewVertical {0,0,1} direction to make vertical WorkingPrecision MachinePrecision precision to use in internal computations


List of all options




Examples
open allclose allBasic Examples (2)Summary of the most common use cases
Scope (28)Survey of the scope of standard use cases
Surfaces (9)
Generate a plot over standard slice surfaces:

https://wolfram.com/xid/0jz5vd8rwvd50o-y8d13b

Standard axis-aligned stacked slice surfaces:

https://wolfram.com/xid/0jz5vd8rwvd50o-dz1bje


https://wolfram.com/xid/0jz5vd8rwvd50o-h3vd5f


https://wolfram.com/xid/0jz5vd8rwvd50o-4zw5yb

Plotting over a volume primitive is equivalent to plotting over RegionBoundary[reg]:

https://wolfram.com/xid/0jz5vd8rwvd50o-gi3uji


https://wolfram.com/xid/0jz5vd8rwvd50o-mdide3

Plot a vector field over multiple slice surfaces:

https://wolfram.com/xid/0jz5vd8rwvd50o-cnqk2o

Specify the number of stacked planes:

https://wolfram.com/xid/0jz5vd8rwvd50o-44kz5c

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

https://wolfram.com/xid/0jz5vd8rwvd50o-y2cv0v

Sampling (3)
Use VectorPoints to specify the number of arrows:

https://wolfram.com/xid/0jz5vd8rwvd50o-tmpgyf

Use RegionFunction to expose obscured slices:

https://wolfram.com/xid/0jz5vd8rwvd50o-dhqoa

The domain may be specified by a region including Cone:

https://wolfram.com/xid/0jz5vd8rwvd50o-pu0wit

A formula region including ImplicitRegion:

https://wolfram.com/xid/0jz5vd8rwvd50o-j02kuu

https://wolfram.com/xid/0jz5vd8rwvd50o-g3ao4p

A mesh-based region including BoundaryMeshRegion:

https://wolfram.com/xid/0jz5vd8rwvd50o-mn7ny


https://wolfram.com/xid/0jz5vd8rwvd50o-dxaox6

Presentation (16)
Use VectorScaling to show arrows scaled according to their magnitudes:

https://wolfram.com/xid/0jz5vd8rwvd50o-i2gp1

Use VectorSizes to prevent arrows from being too small:

https://wolfram.com/xid/0jz5vd8rwvd50o-ek76wv

Use VectorRange to control which vectors are plotted:

https://wolfram.com/xid/0jz5vd8rwvd50o-gise0n

Use ClippingStyle to control the appearance of the clipped vectors:

https://wolfram.com/xid/0jz5vd8rwvd50o-ee7bf5

Use PlotTheme to immediately get overall styling:

https://wolfram.com/xid/0jz5vd8rwvd50o-4bu8j7

Use PlotLegends to get a color bar for the different values:

https://wolfram.com/xid/0jz5vd8rwvd50o-4mxsp7

Control the display of axes with Axes:

https://wolfram.com/xid/0jz5vd8rwvd50o-28yjny

Label axes using AxesLabel and the whole plot using PlotLabel:

https://wolfram.com/xid/0jz5vd8rwvd50o-738fd2

Color the vectors by their magnitude with VectorColorFunction:

https://wolfram.com/xid/0jz5vd8rwvd50o-zerbye

Use VectorMarkers to control the shape of the vectors:

https://wolfram.com/xid/0jz5vd8rwvd50o-saa1a9

Use VectorAspectRatio to modify the width-to-length ratio of the arrows:

https://wolfram.com/xid/0jz5vd8rwvd50o-kgynoj

Style the slice surface boundaries with BoundaryStyle:

https://wolfram.com/xid/0jz5vd8rwvd50o-63ar8l

Highlight a RegionFunction with RegionBoundaryStyle:

https://wolfram.com/xid/0jz5vd8rwvd50o-uay3o

Style a RegionFunction with RegionBoundaryStyle:

https://wolfram.com/xid/0jz5vd8rwvd50o-crp409

TargetUnits specifies which units to use in the visualization:

https://wolfram.com/xid/0jz5vd8rwvd50o-t20rv


https://wolfram.com/xid/0jz5vd8rwvd50o-lcy9qy

Options (60)Common values & functionality for each option
BoundaryStyle (1)
BoxRatios (3)
By default, the edges of the bounding box have the same length:

https://wolfram.com/xid/0jz5vd8rwvd50o-tu0uqo

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

https://wolfram.com/xid/0jz5vd8rwvd50o-2k9uve

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

https://wolfram.com/xid/0jz5vd8rwvd50o-d474zo

ClippingStyle (4)
By default, clipped vectors are given a constant color that is consistent with the minimum or maximum vector lengths given by VectorRange:

https://wolfram.com/xid/0jz5vd8rwvd50o-7tivj


https://wolfram.com/xid/0jz5vd8rwvd50o-ijt8mp


https://wolfram.com/xid/0jz5vd8rwvd50o-24h0e

Style the short and long clipped vectors differently:

https://wolfram.com/xid/0jz5vd8rwvd50o-ciwfq4

PerformanceGoal (2)
PlotLegends (3)
No legends are included by default:

https://wolfram.com/xid/0jz5vd8rwvd50o-9pv422

Include a legend that indicates the vector norms by color:

https://wolfram.com/xid/0jz5vd8rwvd50o-pny74l

With multiple fields and VectorColorFunction set to None, use a legend to identify each field:

https://wolfram.com/xid/0jz5vd8rwvd50o-byqwxt

Or use the fields in the legend:

https://wolfram.com/xid/0jz5vd8rwvd50o-yhmfx

PlotRange (2)
Show All vectors by default:

https://wolfram.com/xid/0jz5vd8rwvd50o-8an6kh


https://wolfram.com/xid/0jz5vd8rwvd50o-9fjtuk

PlotRangePadding (7)
Padding is computed automatically by default:

https://wolfram.com/xid/0jz5vd8rwvd50o-d2h2aw

Specify no padding for all ,
, and
ranges:

https://wolfram.com/xid/0jz5vd8rwvd50o-oou6sl

Specify an explicit padding for all ,
, and
ranges:

https://wolfram.com/xid/0jz5vd8rwvd50o-dfhomi

Add 10% padding to all ,
, and
ranges:

https://wolfram.com/xid/0jz5vd8rwvd50o-4ms5i1

Specify different padding for ,
, and
ranges:

https://wolfram.com/xid/0jz5vd8rwvd50o-zbuldg

Specify padding for the range:

https://wolfram.com/xid/0jz5vd8rwvd50o-lvdx4r

Use different padding forms for each dimension:

https://wolfram.com/xid/0jz5vd8rwvd50o-65dzhn

PlotTheme (3)

https://wolfram.com/xid/0jz5vd8rwvd50o-8jdeuv

Override PlotTheme styles by explicitly setting options:

https://wolfram.com/xid/0jz5vd8rwvd50o-f9se6e

Compare different plot themes:

https://wolfram.com/xid/0jz5vd8rwvd50o-7w6re4

RegionBoundaryStyle (3)
By default, a region function is not explicitly shown:

https://wolfram.com/xid/0jz5vd8rwvd50o-c52nhb

A similar effect can be created by combining VectorRange and ClippingStyle:

https://wolfram.com/xid/0jz5vd8rwvd50o-ddicry

Show the boundary of a region defined by a region function:

https://wolfram.com/xid/0jz5vd8rwvd50o-cl5p7d

Style the boundary of the region:

https://wolfram.com/xid/0jz5vd8rwvd50o-hmfzhi

RegionFunction (3)
Plot vectors only over certain quadrants:

https://wolfram.com/xid/0jz5vd8rwvd50o-juf837

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

https://wolfram.com/xid/0jz5vd8rwvd50o-05j3p7

Use any logical combination of conditions:

https://wolfram.com/xid/0jz5vd8rwvd50o-5e2mos

ScalingFunctions (4)
By default, plots have linear scales in all directions:

https://wolfram.com/xid/0jz5vd8rwvd50o-jcblr5

Create a plot with a reversed axis:

https://wolfram.com/xid/0jz5vd8rwvd50o-164fd6

Scaling functions are applied to slices that are defined in terms of the variables:

https://wolfram.com/xid/0jz5vd8rwvd50o-7qcyha

Slice surfaces that are defined relative to the bounding box are unaffected by scaling functions:

https://wolfram.com/xid/0jz5vd8rwvd50o-r41lez

VectorAspectRatio (1)
VectorAspectRatio specifies the width of the arrow over its length:

https://wolfram.com/xid/0jz5vd8rwvd50o-d4fo4t

VectorColorFunction (5)
By default, vectors are colored according to their norm:

https://wolfram.com/xid/0jz5vd8rwvd50o-dhwjvp


https://wolfram.com/xid/0jz5vd8rwvd50o-l4o9lw

Use any named color gradient from ColorData:

https://wolfram.com/xid/0jz5vd8rwvd50o-jk16xa

Color the vectors according to their value:

https://wolfram.com/xid/0jz5vd8rwvd50o-f41zkj

Use VectorColorFunctionScaling->False to get unscaled values:

https://wolfram.com/xid/0jz5vd8rwvd50o-tn2l2r

VectorColorFunctionScaling (3)
By default, scaled values are used:

https://wolfram.com/xid/0jz5vd8rwvd50o-rrfrkq

Use VectorColorFunctionScaling->False to get unscaled values:

https://wolfram.com/xid/0jz5vd8rwvd50o-m2zw8g

Explicitly specify the scaling for each color function argument:

https://wolfram.com/xid/0jz5vd8rwvd50o-2ujx9a

VectorMarkers (3)
The default vector marker is "Arrow3D":

https://wolfram.com/xid/0jz5vd8rwvd50o-boaqv7


https://wolfram.com/xid/0jz5vd8rwvd50o-fjvwri

By default, arrows are centered at sampled points. Use Placed to start the arrow at the sampled point:

https://wolfram.com/xid/0jz5vd8rwvd50o-bxuabj

VectorPoints (4)
Use automatically determined vector points:

https://wolfram.com/xid/0jz5vd8rwvd50o-l3pq8l

Use symbolic names to specify the set of field vectors:

https://wolfram.com/xid/0jz5vd8rwvd50o-i2b0f2

Create a regular grid of field vectors with the same number of arrows for ,
, and
:

https://wolfram.com/xid/0jz5vd8rwvd50o-oedlna

Use a different number of vectors in each direction:

https://wolfram.com/xid/0jz5vd8rwvd50o-nprksi

VectorRange (3)
Specify the range of vector norms that are displayed with varying color:

https://wolfram.com/xid/0jz5vd8rwvd50o-et3f6g

Combine with ClippingStyle to remove the clipped vectors:

https://wolfram.com/xid/0jz5vd8rwvd50o-khfu4x

Or specify a different style for clipped vectors:

https://wolfram.com/xid/0jz5vd8rwvd50o-dh65i2

VectorScaling (3)
By default, arrows are displayed with a constant length:

https://wolfram.com/xid/0jz5vd8rwvd50o-tkjrrw

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

https://wolfram.com/xid/0jz5vd8rwvd50o-jn3oti

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

https://wolfram.com/xid/0jz5vd8rwvd50o-bzkgac

VectorSizes (2)
Make the vectors half of the default size:

https://wolfram.com/xid/0jz5vd8rwvd50o-gmfzju

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

https://wolfram.com/xid/0jz5vd8rwvd50o-qkzqs

VectorStyle (1)
VectorColorFunction has precedence over VectorStyle:

https://wolfram.com/xid/0jz5vd8rwvd50o-mwrofr


https://wolfram.com/xid/0jz5vd8rwvd50o-f21cei

Applications (23)Sample problems that can be solved with this function
Basic Vector Fields (3)

https://wolfram.com/xid/0jz5vd8rwvd50o-1jmh66


https://wolfram.com/xid/0jz5vd8rwvd50o-zuqhms

A circulating flow around the axis:

https://wolfram.com/xid/0jz5vd8rwvd50o-bngsn2


https://wolfram.com/xid/0jz5vd8rwvd50o-haam0d


https://wolfram.com/xid/0jz5vd8rwvd50o-c09gnd

Differential Equations (9)
Illustrate the behavior of a linear system of differential equations in the case when
is diagonal:

https://wolfram.com/xid/0jz5vd8rwvd50o-j7ehrt

https://wolfram.com/xid/0jz5vd8rwvd50o-itdcqw

Solve the corresponding differential equation starting on the slice surfaces:

https://wolfram.com/xid/0jz5vd8rwvd50o-hqpu2s

https://wolfram.com/xid/0jz5vd8rwvd50o-m90gh

https://wolfram.com/xid/0jz5vd8rwvd50o-c5vg6r

The differential equation solution follows the arrows in the plot all converging to the origin:

https://wolfram.com/xid/0jz5vd8rwvd50o-c0zxr

Automate the previous example and analyze all the possible sign combinations of the real eigenvalues for , where
is a diagonal matrix with eigenvalues
:

https://wolfram.com/xid/0jz5vd8rwvd50o-e29kqw
For , there is stability along the
,
, and
directions:

https://wolfram.com/xid/0jz5vd8rwvd50o-bhwmji

For , there is stability along
and
, but instability along
:

https://wolfram.com/xid/0jz5vd8rwvd50o-cwew0k

For , there is stability along
and instability along
and
:

https://wolfram.com/xid/0jz5vd8rwvd50o-fdjh33

For , there is instability along
,
, and
:

https://wolfram.com/xid/0jz5vd8rwvd50o-d4fbih

Define a matrix and compute its eigenvalues:

https://wolfram.com/xid/0jz5vd8rwvd50o-71qp2

Since is symmetric, its eigenspaces
,
and
are mutually orthogonal:

https://wolfram.com/xid/0jz5vd8rwvd50o-emtf9s

Generate the orthogonal complements of the eigenspaces:

https://wolfram.com/xid/0jz5vd8rwvd50o-ippykn

Plot the vector field and observe the effects of the eigenvalues:

https://wolfram.com/xid/0jz5vd8rwvd50o-djcdvn

The plane orthogonal to contains
and
, so the origin is attractive in
and repulsive in
:

https://wolfram.com/xid/0jz5vd8rwvd50o-9nbde

The plane orthogonal to contains
and
, so the field points directly toward
:

https://wolfram.com/xid/0jz5vd8rwvd50o-him13w

The plane orthogonal to contains
and
, so the field points directly away from
:

https://wolfram.com/xid/0jz5vd8rwvd50o-c5jm7

Define a matrix and compute its eigenvalues:

https://wolfram.com/xid/0jz5vd8rwvd50o-d2xbz6

The eigenvalues and eigenvectors of indicate a sink at the origin for the vector field
with spiral behavior around the
axis:

https://wolfram.com/xid/0jz5vd8rwvd50o-dg1xem

Examine the vector field in planes orthogonal to
:

https://wolfram.com/xid/0jz5vd8rwvd50o-d34tc0

Compute solutions of the linear system of differential equations for several initial conditions:

https://wolfram.com/xid/0jz5vd8rwvd50o-miriti
Add the solutions of to the vector field:

https://wolfram.com/xid/0jz5vd8rwvd50o-dserk1

Define a new matrix and compute its eigenvalues and eigenvectors:

https://wolfram.com/xid/0jz5vd8rwvd50o-caqt2

The eigenspace is a plane through the origin with normal
, so solutions of
are attracted to the origin while spiraling around
:

https://wolfram.com/xid/0jz5vd8rwvd50o-fls4bq

https://wolfram.com/xid/0jz5vd8rwvd50o-dsnnas

https://wolfram.com/xid/0jz5vd8rwvd50o-f9knd8

Illustrate the behavior of a linear system of differential equations in the case when
is block diagonal, with one real and two complex conjugate eigenvalues. The matrix
has eigenvalues
,
, and
:

https://wolfram.com/xid/0jz5vd8rwvd50o-bbcpk9

Construct a matrix with eigenvalues
,
, and
:

https://wolfram.com/xid/0jz5vd8rwvd50o-ccoop0

https://wolfram.com/xid/0jz5vd8rwvd50o-bs7eme

Find solutions to the corresponding differential equation:

https://wolfram.com/xid/0jz5vd8rwvd50o-h4hawg

https://wolfram.com/xid/0jz5vd8rwvd50o-c7ci2h

https://wolfram.com/xid/0jz5vd8rwvd50o-o5ytco

Show vector field and solutions together:

https://wolfram.com/xid/0jz5vd8rwvd50o-8no5k

Automate the previous example and analyze for different real and
:

https://wolfram.com/xid/0jz5vd8rwvd50o-cvgu98

https://wolfram.com/xid/0jz5vd8rwvd50o-di6wc


https://wolfram.com/xid/0jz5vd8rwvd50o-j308r5


https://wolfram.com/xid/0jz5vd8rwvd50o-r1nrv


https://wolfram.com/xid/0jz5vd8rwvd50o-cpcn89

Solve an initial value problem with a solution that is contained in a cylinder:

https://wolfram.com/xid/0jz5vd8rwvd50o-faw39x

Graph the surface, the vector field on the surface and the solution of the initial value problem:

https://wolfram.com/xid/0jz5vd8rwvd50o-cw7u2m

Solve an initial value problem with a solution contained in a sphere:

https://wolfram.com/xid/0jz5vd8rwvd50o-ibfxrs

Graph the surface, the vector field on the surface and the solution of the initial value problem:

https://wolfram.com/xid/0jz5vd8rwvd50o-nvdp0

Solve an initial value problem with a solution contained in a hyperbolic paraboloid:

https://wolfram.com/xid/0jz5vd8rwvd50o-d8g08m

Graph the surface, the vector field on the surface and the solution of the initial value problem:

https://wolfram.com/xid/0jz5vd8rwvd50o-bh2qkp

Fluid Dynamics (2)
Visualize Hill's spherical vortex, with vortex radius and velocity
:

https://wolfram.com/xid/0jz5vd8rwvd50o-qym5dp

https://wolfram.com/xid/0jz5vd8rwvd50o-mjc5g2

https://wolfram.com/xid/0jz5vd8rwvd50o-5pyio8
Visualize the vortex, with flow rotation highlighted in red:

https://wolfram.com/xid/0jz5vd8rwvd50o-fob0u

Visualize the divergence-free field of a scalar function :

https://wolfram.com/xid/0jz5vd8rwvd50o-zrzbl9

https://wolfram.com/xid/0jz5vd8rwvd50o-cg4me
Visualize the vortices formed by these fields:

https://wolfram.com/xid/0jz5vd8rwvd50o-znju1


https://wolfram.com/xid/0jz5vd8rwvd50o-1y7vkw

Solid Mechanics (2)
A solid cylinder with a tensile load:

https://wolfram.com/xid/0jz5vd8rwvd50o-rt66k

A solid cylinder with a compressive load:

https://wolfram.com/xid/0jz5vd8rwvd50o-f3cwsw

A hollow cylinder with internal and external pressures:

https://wolfram.com/xid/0jz5vd8rwvd50o-mmhsqk

An elastic bar in the shape of a circular cylinder with radius 1 has a net torque applied at both ends. The resulting displacement field is
, where
is the shear modulus, the nonzero stresses are
and
and the forces on the surfaces
are the tractions:

https://wolfram.com/xid/0jz5vd8rwvd50o-b53v4n

https://wolfram.com/xid/0jz5vd8rwvd50o-zhf82

https://wolfram.com/xid/0jz5vd8rwvd50o-j7f6qm

Display the displacement field that results from the applied forces:

https://wolfram.com/xid/0jz5vd8rwvd50o-ejghc2

https://wolfram.com/xid/0jz5vd8rwvd50o-bpby0b

Electromagnetism (1)
The vector field from an electrostatic potential:

https://wolfram.com/xid/0jz5vd8rwvd50o-r70ri8

https://wolfram.com/xid/0jz5vd8rwvd50o-nxb8fs
The resulting force vector field:

https://wolfram.com/xid/0jz5vd8rwvd50o-gikyvt

The force field on the center planes:

https://wolfram.com/xid/0jz5vd8rwvd50o-kmzsr

The force field on equipotential surfaces:

https://wolfram.com/xid/0jz5vd8rwvd50o-cw9851

Flux (3)
Visualize the outward pointing unit normal vectors to a surface:

https://wolfram.com/xid/0jz5vd8rwvd50o-zygdn

https://wolfram.com/xid/0jz5vd8rwvd50o-nvvzf9

Define vector field and compute the unit normals to the surface
:

https://wolfram.com/xid/0jz5vd8rwvd50o-el8bqo

https://wolfram.com/xid/0jz5vd8rwvd50o-c6zlh

Visualize the vector field and the unit normals to
:

https://wolfram.com/xid/0jz5vd8rwvd50o-d2txua

The flux density of through
is zero since
is orthogonal to the normals of
:

https://wolfram.com/xid/0jz5vd8rwvd50o-ermy7h

Define vector field and compute the unit normals to the surface
:

https://wolfram.com/xid/0jz5vd8rwvd50o-gw80b8

https://wolfram.com/xid/0jz5vd8rwvd50o-gw4u7s

Visualize the vector field and the unit normals to
:

https://wolfram.com/xid/0jz5vd8rwvd50o-j9v1ti

Compute the flux density of through
:

https://wolfram.com/xid/0jz5vd8rwvd50o-h0a6ak

The total flux is zero because the negative flux is canceled by the positive flux. Visualize this by coloring the surface by the flux density:

https://wolfram.com/xid/0jz5vd8rwvd50o-ux4b4

Other Applications (3)
Visualize the "hairy ball theorem" (https://mathworld.wolfram.com/HairyBallTheorem.html) that, loosely speaking, says that you cannot comb the hair on a sphere without leaving a whorl:

https://wolfram.com/xid/0jz5vd8rwvd50o-fcpai8

Show a vector field in a tangent plane:

https://wolfram.com/xid/0jz5vd8rwvd50o-d6a0bo

Choose 10 random points on the unit sphere:

https://wolfram.com/xid/0jz5vd8rwvd50o-dq173m
Compute the angles ϕ and θ for the points at :

https://wolfram.com/xid/0jz5vd8rwvd50o-l2m4y1
Plot geodesics from to the target points:

https://wolfram.com/xid/0jz5vd8rwvd50o-hflnhi
Show the sphere, geodesics, target points, and a vector field of tangents for the geodesics:

https://wolfram.com/xid/0jz5vd8rwvd50o-eopb9m

Properties & Relations (10)Properties of the function, and connections to other functions
Use VectorPlot3D for a full volume visualization of the vector field:

https://wolfram.com/xid/0jz5vd8rwvd50o-4kw5kb

Use ListSliceVectorPlot3D for data:

https://wolfram.com/xid/0jz5vd8rwvd50o-ywzg95

https://wolfram.com/xid/0jz5vd8rwvd50o-3v60u6

Use VectorPlot for vector plots in 2D:

https://wolfram.com/xid/0jz5vd8rwvd50o-z3puov

Use StreamPlot or LineIntegralConvolutionPlot for vector fields in 2D:

https://wolfram.com/xid/0jz5vd8rwvd50o-ieaf06

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

https://wolfram.com/xid/0jz5vd8rwvd50o-cibhhq

Use StreamDensityPlot to use streams instead of vectors:

https://wolfram.com/xid/0jz5vd8rwvd50o-kxyms1

Use VectorDisplacementPlot to visualize the effect of a displacement vector field on a specified region:

https://wolfram.com/xid/0jz5vd8rwvd50o-czkc2f

Use VectorDisplacementPlot3D to visualize the effect of a displacement vector field on a specified 3D region:

https://wolfram.com/xid/0jz5vd8rwvd50o-mhw7bs

Use StreamPlot3D to plot 3D fields as streamlines:

https://wolfram.com/xid/0jz5vd8rwvd50o-6tfyz8

Plot complex functions as a vector field with ComplexVectorPlot:

https://wolfram.com/xid/0jz5vd8rwvd50o-rjlzpk

Plot streams instead of vectors with ComplexStreamPlot:

https://wolfram.com/xid/0jz5vd8rwvd50o-h5phyg

Use GeoVectorPlot to plot vectors on a map:

https://wolfram.com/xid/0jz5vd8rwvd50o-d0ztmc

Use GeoStreamPlot to use streams instead of vectors:

https://wolfram.com/xid/0jz5vd8rwvd50o-k2t1cp

Wolfram Research (2015), SliceVectorPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/SliceVectorPlot3D.html (updated 2022).
Text
Wolfram Research (2015), SliceVectorPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/SliceVectorPlot3D.html (updated 2022).
Wolfram Research (2015), SliceVectorPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/SliceVectorPlot3D.html (updated 2022).
CMS
Wolfram Language. 2015. "SliceVectorPlot3D." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/SliceVectorPlot3D.html.
Wolfram Language. 2015. "SliceVectorPlot3D." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/SliceVectorPlot3D.html.
APA
Wolfram Language. (2015). SliceVectorPlot3D. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SliceVectorPlot3D.html
Wolfram Language. (2015). SliceVectorPlot3D. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SliceVectorPlot3D.html
BibTeX
@misc{reference.wolfram_2025_slicevectorplot3d, author="Wolfram Research", title="{SliceVectorPlot3D}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/SliceVectorPlot3D.html}", note=[Accessed: 15-March-2025
]}
BibLaTeX
@online{reference.wolfram_2025_slicevectorplot3d, organization={Wolfram Research}, title={SliceVectorPlot3D}, year={2022}, url={https://reference.wolfram.com/language/ref/SliceVectorPlot3D.html}, note=[Accessed: 15-March-2025
]}