VectorDensityPlot

VectorDensityPlot[{{vx,vy},s},{x,xmin,xmax},{y,ymin,ymax}]

generates a vector plot of the vector field {vx,vy} as a function of x and y, superimposed on a density plot of the scalar field s.

VectorDensityPlot[{vx,vy},{x,xmin,xmax},{y,ymin,ymax}]

takes the scalar field to be the norm of the vector field.

VectorDensityPlot[{{vx,vy},{wx,wy},,s},{x,xmin,xmax},{y,ymin,ymax}]

plots several vector fields.

VectorDensityPlot[,{x,y}reg]

takes the variables {x,y} to be in the geometric region reg.

Details and Options

Examples

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Basic Examples  (4)

Plot the vector field {y,-x} with background color based on the field magnitude:

Plot a vector field with the background color based on a different scalar field:

Add a legend for the scalar field:

Change the color schemes for the vector and scalar fields:

Scope  (19)

Sampling  (9)

Visualize a vector field with the background based on :

Use Evaluate to evaluate the vector field symbolically before numeric assignment:

Plot a vector field with vectors placed with specified densities:

Plot the vectors that go through a set of seed points:

Create a hexagonal grid of field vectors with a different number of arrows for and :

Specify a list of points for showing field vectors:

Plot vectors over a specified region:

The domain may be specified by a region:

The domain may be specified by a MeshRegion:

Presentation  (10)

Plot a vector field with arrows scaled according to their magnitudes:

Use a single color for the arrows:

Specify the sizes of the arrows:

Plot a vector field with the background and vectors colored according to the field magnitude:

Use a named appearance to draw the vectors:

VectorColorFunction takes precedence over colors in VectorStyle:

Set VectorColorFunctionNone to specify colors with VectorStyle:

Set the marker style for multiple vector fields:

Apply vector style:

Include a legend for the scalar field:

Options  (86)

AspectRatio  (2)

By default, the aspect ratio is 1:

Set the aspect ratio:

Background  (1)

Use colored backgrounds:

BoundaryStyle  (2)

By default, region boundaries have no style:

Change the style of the boundary:

ColorFunction  (5)

Color the scalar field magnitude with a named color gradient from ColorData:

Specify a different scalar field:

Use ColorData for predefined color gradients:

Specify a color function that blends two colors by the coordinate:

Use ColorFunctionScaling->False to get unscaled values:

ColorFunctionScaling  (4)

By default, scaled values are used:

Use ColorFunctionScaling->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:

EvaluationMonitor  (2)

Show where the vector field function is sampled:

Count the number of times the vector field function is evaluated:

FrameLabel  (1)

Label the axes:

MaxRecursion  (1)

Refine the plot where it changes quickly:

Mesh  (5)

By default, no mesh lines are displayed:

Show the initial and final sampling meshes:

Use a specific number of mesh lines:

Specify mesh lines:

Use different styles for different mesh lines:

MeshFunctions  (3)

By default, mesh lines correspond to the magnitude of the field:

Use the value as the mesh function:

Use mesh lines corresponding to fixed distances from the origin:

MeshShading  (3)

Use None to remove regions:

Styles are used cyclically:

Use indexed colors from ColorData cyclically:

MeshStyle  (1)

Apply a variety of styles to the mesh lines:

PerformanceGoal  (2)

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

PlotLegends  (2)

No legends are included by default:

Include a legend for the scalar field:

PlotRange  (3)

The full plot range is used by default:

Specify an explicit limit for both and ranges:

Specify different and ranges:

PlotTheme  (2)

Use a theme with a high contrast color scheme:

Change the color scheme:

RegionBoundaryStyle  (6)

Show the region being plotted:

Show the region defined by a region function:

The boundaries of full rectangular regions are not shown:

Use None to not show the boundary:

Specify a style for the boundary:

Specify a style for full rectangular regions:

RegionFunction  (3)

Plot vectors only over a specified region:

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

Use any logical combination of conditions:

VectorAspectRatio  (2)

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

Increase the relative width of a vector marker:

VectorColorFunction  (4)

Color the vectors according to their norm:

Use any named color gradient from ColorData:

Color the vectors according to their values:

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  (4)

Vectors are drawn as arrows by default:

Use a named appearance to draw the vectors:

Use different markers for different vector fields:

By default, markers are centered on vector points:

Start the vectors at the points:

End the vectors at the points:

VectorPoints  (9)

Use automatically determined vector points:

Use symbolic names to specify the set of field vectors:

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

Create a hexagonal 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 hexagonal grid:

The location for vectors is given in the middle of the drawn vector:

Use a rectangular mesh instead of a hexagonal mesh:

Use a mesh generated from a triangularization of the region:

VectorScaling  (2)

Use automatically determined vector scaling:

By default, arrows are all the same length:

VectorRange  (4)

The clipping of vectors with very small or very large magnitudes is done automatically:

Specify the range of vector norms:

Suppress the clipped vectors:

Show all the vectors:

VectorSizes  (3)

Specify the relative size of vectors as a fraction of the largest vector:

Specify min and max of the vector sizes with automatic scaling:

Use symbolic names to control the size of vectors:

VectorStyle  (6)

VectorColorFunction takes precedence over colors in VectorStyle:

Set VectorColorFunctionNone to specify colors with VectorStyle:

Set the style for multiple vector fields:

Plot the vector fields without arrowheads:

Use Arrowheads to specify an explicit style of the arrowheads:

Specify both arrow tail and head:

Graphics primitives without Arrowheads are scaled:

Applications  (3)

Visualize a vector field with the background based on the field's divergence:

Visualize a vector field with the background based on the magnitude of the field's curl:

Explore various streamline styles and scales with several examples:

Generate icons to graphically represent field choices:

Click on the field icons to switch field plots:

Properties & Relations  (10)

Use ListVectorDensityPlot to plot data with a density plot of the scalar field:

Use VectorPlot to plot functions without a density plot:

Use ListStreamDensityPlot to plot data with streamlines instead of vectors:

Use ListVectorPlot for plotting data without a density plot:

Use VectorPlot3D to visualize 3D vector fields:

Use SliceVectorPlot3D to visualize 3D vector fields along a surface:

Scalar fields can be plotted by themselves with DensityPlot:

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

Plot vectors on surfaces with SliceVectorPlot3D:

Plot complex numbers as a vector field:

Neat Examples  (1)

Constrain the vector plot to a variety of regions:

Wolfram Research (2008), VectorDensityPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/VectorDensityPlot.html (updated 2020).

Text

Wolfram Research (2008), VectorDensityPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/VectorDensityPlot.html (updated 2020).

BibTeX

@misc{reference.wolfram_2020_vectordensityplot, author="Wolfram Research", title="{VectorDensityPlot}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/VectorDensityPlot.html}", note=[Accessed: 10-May-2021 ]}

BibLaTeX

@online{reference.wolfram_2020_vectordensityplot, organization={Wolfram Research}, title={VectorDensityPlot}, year={2020}, url={https://reference.wolfram.com/language/ref/VectorDensityPlot.html}, note=[Accessed: 10-May-2021 ]}

CMS

Wolfram Language. 2008. "VectorDensityPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/VectorDensityPlot.html.

APA

Wolfram Language. (2008). VectorDensityPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VectorDensityPlot.html