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ListVectorDisplacementPlot3D—Wolfram Documentation

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ListVectorDisplacementPlot3D[{{{vx₁₁,vy₁₁,vz₁₁},…,{vx_1n,vy_1n,vz_1n}},…,{{vx_m1,vy_m1,vz_m1},…,{vx_mn,vy_mn,vz_mn}}}]

generates a displacement plot from an array of vector displacements {vx_ij,vy_ij,vz_ij}.

ListVectorDisplacementPlot3D[{{{x₁,y₁,z₁},{vx₁,vy₁,vz₁}},…,{{x_n,y_n,z_n},{vx_n,vy_n,vz_n}}}]

generates a displacement plot from displacements {vx_i,vy_i,vz_i} at point {x_i,y_i,z_i}.

ListVectorDisplacementPlot3D[{{{{vx₁₁,vy₁₁,vz₁₁},s₁₁},…,{{vx_1n,vy_1n,vz_1n},s_1n}},…,{{{vx_m1,vy_m1,vz_m1},s_m1},…,{{vx_mn,vy_mn,vz_mn},s_mn}}}]

uses the scalar values s_ij to color the displaced region.

ListVectorDisplacementPlot3D[{{{x₁,y₁,z₁},{{vx₁,vy₁,vz₁},s₁}},…,{{x_n,y_n,z_n},{{vx_n,vy_n,vz_n},s_n}}}]

uses the scalar values s_i at point {x_i,y_i,z_i} to color the displaced region.

• ListVectorDisplacementPlot3D generates a displacement plot using the vector field data over a region. By default, the size of the displacement is automatically scaled so that both small and large displacements remain visible. The displaced region is by default colored according to the magnitude of the displacement.
• If no scalar field values are given, they are taken to be the norm of the vector field.
• ListVectorDisplacementPlot3D by default interpolates the data given and plots vectors for the vector field at a regular grid of positions.
• ListVectorDisplacementPlot3D has the same options as Graphics3D, with the following additions and changes: [List of all options]
• The arguments supplied to functions in MeshFunctions, RegionFunction, ColorFunction and VectorColorFunction are x, y, z, v_x, v_y, v_z, s.
• The default setting MeshFunctions{#7&} draws mesh lines for the scalar field s.
• By default, the displacement plot shows a representation of the original region and the displaced region.
• RegionBoundaryStyle and RegionFillingStyle can be used to change the style of the original region.
• Additional settings for VectorPoints to show displacement arrows include:
• Automatic automatically chosen points All use the original data points "Boundary" points along the boundary of reg
• By default, displacement arrows connect locations in the original region with the corresponding displaced locations.
• VectorSizesFull shows the full displacement rather than a scaled representation.

Plot a displacement field colored by its norm interpolated from a specified set of vectors:

Plot the vector field from data specifying coordinates and vectors. The reference region is the convex hull of the coordinates:

Specify a scalar field to color the deformed region:

Specify the reference region:

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

Specify the coordinates and the vector field:

Specify the coordinates, the vector field and a scalar field:

Generate random points in a vector field:

By default, the reference region is the convex hull of the coordinates:

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

Restrict vectors to points on the boundary:

Specify other vectors:

Displacements can be drawn to scale:

Specify the region:

Specify the region with a RegionFunction:

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:

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:

By default, the aspect ratio is Automatic:

Set the box ratios:

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:

Use the natural range of norm values:

Control the scaling of the individual arguments of the ColorFunction:

By default, the reference region is taken to be the index range of the data array:

Specify the data range for the reference region:

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:

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

Use circular mesh lines in the reference region:

Style the mesh lines:

Style the mesh lines differently in different directions:

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:

Use more points to get smoother regions:

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:

Specify the boundary style of the reference region:

Remove the boundary of the reference region:

Specify the filling of the reference region:

Remove the filling for the reference region:

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

Specify the relative width of a vector marker:

Use the natural range of norm values for vector colors:

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:

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:

Specify the range of vector norms:

Style the clipped vectors:

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:

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:

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 VectorSizesFull 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 a 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 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:

The face of the displayed region is fixed (no displacement) and a uniform load of 10 kPa is applied to the face in the positive direction:

Obtain data from a numerical solver of the form {location vector, displacement vector} assuming that the region is linearly elastic:

Visualize the deformed region. Since the displacements are exaggerated in the plot, use a legend to indicate the actual sizes of the displacements:

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