VectorDisplacementPlot3D

VectorDisplacementPlot3D[{vx,vy,vz},{x,xmin,xmax},{y,ymin,ymax},{z,zmin,zmax}]

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

VectorDisplacementPlot3D[{vx,vy,vz},{x,y,z}reg]

plots the displacement over the geometric region reg.

VectorDisplacementPlot3D[{{vx,vy,vz},s},]

uses the scalar field s to style the displacement.

Details

Examples

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Basic Examples  (5)

Plot a reference region and the corresponding (scaled) deformed region for a specified displacement field:

Include a legend for the norms of the displacements:

Show a sampling of displacement vectors that extend from points in the reference region to corresponding points in the deformed region:

Use a scalar field other than the norm of the displacement field to color the deformed region:

Show a twisted elastic bar:

Scope  (18)

Sampling  (11)

Visualize a scaled displacement field by comparing a reference and a deformed region:

Vectors are drawn from points in the reference region to corresponding points in the (scaled) deformed region:

Specify other vector locations:

Displacements can be drawn to scale:

Use the displacement field over a specified region:

The domain may be specified by a region:

The domain may be a curve:

The domain may be an ImplicitRegion:

The domain may be a ParametricRegion:

The domain may be a MeshRegion:

The domain may be a BoundaryMeshRegion:

Presentation  (7)

Specify the ColorFunction for the deformed region:

Specify the VectorColorFunction independently of the ColorFunction:

Use a single color for the arrows:

Include a legend for the norms of the displacements:

Include a legend for the optional scalar field:

Include a Mesh:

Draw displacements to scale:

Options  (63)

BoxRatios  (2)

By default, the aspect ratio is Automatic:

Set the box ratios:

BoundaryStyle  (3)

By default, the boundary style matches the interior colors in the deformed region:

Specify the BoundaryStyle:

BoundaryStyle applies to regions cut by RegionFunction:

ColorFunction  (4)

By default, the deformed region is colored by the norm of the field:

Specify a scalar field for the colors:

Use a named color gradient:

Specify a custom ColorFunction:

ColorFunctionScaling  (2)

Use the natural range of norm values:

Control the scaling of the individual arguments of the ColorFunction:

Mesh  (6)

Specify a Mesh to visualize the displacements:

Show the initial and final sampling mesh:

Specify 10 mesh lines in the direction, 5 in the direction and 3 in the direction:

Use mesh lines at specific values:

Highlight specific mesh lines:

Mesh lines are suppressed in the reference region if the boundary and filling of the reference region are removed:

MeshFunctions  (2)

By default, the mesh lines are parallel to the , and planes in the reference region:

Use circular mesh lines in the reference region:

MeshStyle  (2)

Style the mesh lines:

Style the mesh lines differently in different directions:

PlotLegends  (3)

Include a legend to show the color range of vector norms:

Include a legend to show the color range of an optional scalar field:

Control the placement of the legend:

PlotPoints  (1)

Use more points to get smoother regions:

PlotRange  (3)

The full PlotRange is used by default:

Specify an explicit limit that is shared by the , and directions:

Specify different plot ranges in the , and directions:

PlotStyle  (3)

Remove the filling for the deformed region:

Apply a Texture to the deformed region:

ColorFunction has precedence over PlotStyle:

RegionBoundaryStyle  (2)

Specify the boundary style of the reference region:

Remove the boundary of the reference region:

RegionFillingStyle  (2)

Specify the filling of the reference region:

Remove the filling for the reference region:

RegionFunction  (1)

Use a RegionFunction to specify the reference region:

VectorAspectRatio  (2)

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

Specify the relative width of a vector marker:

VectorColorFunction  (3)

By default, if VectorColorFunction is Automatic, then the VectorColorFunction matches the ColorFunction:

Specify a VectorColorFunction that is different from the ColorFunction:

Use no VectorColorFunction:

VectorColorFunctionScaling  (1)

Use the natural range of norm values for vector colors:

VectorMarkers  (3)

By default, vectors are drawn from points in the reference region to corresponding points in the deformed region:

Use a named appearance to draw the vectors:

Center the markers at the sampled points:

VectorPoints  (9)

No vectors are shown by default:

Show vectors sampled from the entire original region:

Sample vectors from the boundary of the region:

Use symbolic names to specify the density of vectors:

Use symbolic names to specify the arrangement of vectors:

Specify the number of vectors in the , and directions:

Specify a different number of vectors in the , and directions:

Give specific locations for vectors:

Along a curve, vectors are equally spaced by default:

VectorRange  (2)

Specify the range of vector norms:

Style the clipped vectors:

VectorScaling  (2)

By default, vectors extend from points in the reference region to corresponding points in the deformed region:

Set all vectors to have the same size:

VectorSizes  (4)

By default, vectors extend from points in the reference region to corresponding points in the deformed region:

Suppress scaling of the displacement vectors so that a rotation of 45° looks appropriate:

Specify the displacement size relative to the default scaled displacement:

Suppress scaling of the displacement vectors even if no vectors are displayed:

VectorStyle  (1)

VectorColorFunction has precedence over VectorStyle:

Applications  (19)

Basic Applications  (16)

A constant displacement field moves each point in the reference region by the same amount:

Note that the displacements are automatically scaled so that very small and very large displacements are both visible:

Use VectorSizesFull to display the actual sizes of displacements:

Color is used to indicate the magnitude of the displacements:

Color the region by a different scalar function:

Use arrows to indicate initial and final locations for sample points:

Visualize a dilation in the direction:

Visualize a contraction in the direction:

Visualize dilations in the and directions and a contraction in the direction:

Visualize extension and contraction of a spring in the direction:

Visualize a shear in the direction applied to the faces :

Visualize a shear in the direction applied to the faces :

Visualize a combined shear:

Visualize a rotation about the axis:

Visualize a combined dilation and rotation:

Visualize a deformation that is localized near the origin:

Solid Mechanics  (3)

Consider a homogeneous, isotropic, linearly elastic material. Specify Young's modulus and Poisson's ratio:

Applying a uniform tensile load of magnitude in the direction:

If , then the resulting deformation involves extension in the direction and contraction in the and directions:

If , then the load is compressive and the resulting deformation involves compression in the direction and expansion in the and directions:

Replace the region with a cylinder:

Consider an elliptic cylinder centered on the axis:

Apply constant torque to the ends of the bar:

Specify the magnitude of the applied torque:

If the material is linearly elastic with shear modulus , then the resulting displacement field is:

Use a mesh to illustrate the twisting of the bar:

Compute the nontrivial shear stresses:

Use the shear stresses to color the region:

Compute the deflection of a spoon held fixed at the end and with a force applied at the top.

Set up variables and parameters:

Set up the PDE and the geometry:

Visualize the displacement:

Properties & Relations  (9)

Use ListVectorDisplacementPlot3D to visualize a deformation based on displacement field data:

Use VectorDisplacementPlot to visualize the deformation of a region associated with a displacement vector field:

Use ListVectorDisplacementPlot to visualize the same deformation based on data:

Use VectorPlot to directly plot a vector field:

Use StreamPlot to plot with streamlines instead of vectors:

Use ListVectorPlot or ListStreamPlot for plotting data:

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

Use StreamDensityPlot to plot streamlines instead of vectors:

Use ListVectorDensityPlot or ListStreamDensityPlot for plotting data:

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

Use VectorPlot3D and StreamPlot3D to visualize 3D vector fields:

Use ListVectorPlot3D or ListStreamPlot3D to plot with data:

Plot vectors on surfaces with SliceVectorPlot3D:

Use ListSliceVectorPlot3D to plot with data:

Use ComplexVectorPlot or ComplexStreamPlot to visualize a complex function of a complex variable as a vector field or with streamlines:

Use GeoVectorPlot to plot vectors on a map:

Use GeoStreamPlot to plot streamlines instead of vectors:

Wolfram Research (2021), VectorDisplacementPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/VectorDisplacementPlot3D.html.

Text

Wolfram Research (2021), VectorDisplacementPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/VectorDisplacementPlot3D.html.

CMS

Wolfram Language. 2021. "VectorDisplacementPlot3D." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/VectorDisplacementPlot3D.html.

APA

Wolfram Language. (2021). VectorDisplacementPlot3D. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VectorDisplacementPlot3D.html

BibTeX

@misc{reference.wolfram_2022_vectordisplacementplot3d, author="Wolfram Research", title="{VectorDisplacementPlot3D}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/VectorDisplacementPlot3D.html}", note=[Accessed: 27-November-2022 ]}

BibLaTeX

@online{reference.wolfram_2022_vectordisplacementplot3d, organization={Wolfram Research}, title={VectorDisplacementPlot3D}, year={2021}, url={https://reference.wolfram.com/language/ref/VectorDisplacementPlot3D.html}, note=[Accessed: 27-November-2022 ]}