This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# ListVectorDensityPlot

 ListVectorDensityPlot[array] generates a vector plot from a 2D array of vector and scalar field values . ListVectorDensityPlotgenerates a vector plot from vector and scalar field values given at specified points . ListVectorDensityPlotplots data for several vector and scalar fields.
• ListVectorDensityPlot generates a vector plot of the vector field, superimposed on a background density plot of the scalar field.
• If no scalar field values are given, they are taken to be the norm of the vector field.
• ListVectorDensityPlot[array] arranges successive rows of array up the page, and successive columns across.
• ListVectorDensityPlot by default interpolates the data given and plots vectors for the vector field at a regular grid of positions.
 AspectRatio 1 ratio of height to width BoundaryStyle None how to draw RegionFunction boundaries BoxRatios Automatic effective 3D box ratios for simulated lighting ColorFunction Automatic how to color background densities ColorFunctionScaling True whether to scale arguments to ColorFunction DataRange Automatic the range of x and y values to assume for data EvaluationMonitor None expression to evaluate at every function evaluation Frame True whether to draw a frame around the plot FrameTicks Automatic frame tick marks LightingAngle None effective angle for simulated lighting MaxRecursion Automatic the maximum number of recursive subdivisions allowed for the scalar field Mesh None how many mesh lines to draw in the background MeshFunctions {#5&} how to determine the placement of mesh lines MeshShading None how to shade regions between mesh lines MeshStyle Automatic the style of mesh lines Method Automatic methods to use for the plot PerformanceGoal \$PerformanceGoal aspects of performance to try to optimize PlotRange {Full,Full} range of x, y values to include PlotRangePadding Automatic how much to pad the range of values RegionFunction True& determine what region to include VectorColorFunction None how to color vectors VectorColorFunctionScaling True whether to scale the arguments to VectorColorFunction VectorPoints Automatic the number or placement of vectors to plot VectorScale Automatic the scale and size of vectors to plot VectorStyle Automatic how to draw vectors WorkingPrecision MachinePrecision precision to use in internal computations
• The default setting MeshFunctions draws mesh lines for the scalar field s.
Plot the vector field with its norm as a background interpolated from a specified set of vectors:
Plot the vector field from data specifying coordinates and vectors:
Plot the vector field with its norm as a background interpolated from a specified set of vectors:
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Plot the vector field from data specifying coordinates and vectors:
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 Scope   (16)
Plot streamlines for a regular collection of vectors, and give a data range for the domain:
Plot an irregular collection of vectors:
Show all of the specified field vectors:
Explicitly set the number of vectors in each direction:
Use an explicit scalar field:
Use an explicit scalar field on an irregular collection of vectors:
Plot two vector fields with background based on the norm of the first:
Specify a list of points for showing field vectors:
Plot a vector field with streamlines placed with specified densities:
Plot the vectors that go through a set of seed points:
Plot vectors over a specified region:
Plot a vector field with constant size arrows:
Plot a vector field with arrows of specified size:
Vary the arrow length and arrowhead size:
Plot a vector field with the background and vectors colored according to the field magnitude:
Set the style for multiple vector fields:
Apply a variety of vector styles:
Plot vectors and streamlines together:
 Options   (117)
By default, the aspect ratio is 1:
Set the aspect ratio:
Use colored backgrounds:
By default, region boundaries have no style:
Apply a variety of styles to region boundaries:
Color the field magnitude using Hue:
Color using Hue based on :
Use any named color gradient from ColorData:
Use ColorData for predefined color gradients:
Specify a color function that blends two colors by the coordinate:
Use ColorFunctionScaling->False to get unscaled values:
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:
By default, the data range is taken to be the index range of the data array:
Specify the data range for the domain:
Count the number of times the vector field function is evaluated:
Label the axes:
Vary the lighting angle from (right of the plot) to (top of the plot):
Fix the lighting angle at (right of the plot), and vary the altitude from to :
Refine the plot where it changes quickly:
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:
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:
Use None to remove regions:
Styles are used cyclically:
Use indexed colors from ColorData cyclically:
Apply a variety of styles to the mesh lines:
Do not use normals in shading:
Randomly vary the effective normals:
Generate a higher-quality plot:
Emphasize performance, possibly at the cost of quality:
The full plot range is used by default:
Specify an explicit limit for both and ranges:
Specify an explicit range that applies to both and ranges:
Specify an explicit range:
Specify an explicit minimum range:
Specify an explicit range:
Specify an explicit maximum range:
Specify different and ranges:
Plot vectors only over certain quadrants:
Plot vectors only over regions where the field magnitude is above a given threshold:
Use any logical combination of conditions:
Color streamlines according to the norm of the vector field:
Use any named color gradient from ColorData:
Use ColorData for predefined color gradients:
Specify a color function that blends two colors by the coordinate:
Use StreamColorFunctionScaling->False to get unscaled values:
By default, scaled values are used:
Use StreamColorFunctionScaling->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:
Specify a specific maximum number of streamlines:
Use symbolic names to specify the number of streamlines:
Use both automatic and explicit seeding with styles for explicitly seeded streamlines:
Specify the minimum distance between streamlines:
Specify the minimum distance between streamlines at the start and end of a streamline:
Control the maximum length that each streamline can have:
Create full streamlines without segmentation:
Use curves for streamlines:
Use symbolic names to control the lengths of streamlines:
Specify segment lengths:
Specify an explicit dashing pattern for streamlines:
Specify the number of points rendered on each streamline segment:
Specify absolute aspect ratios relative to the longest line segment:
Specify relative aspect ratios relative to each line segment:
Scale the length of the arrows by the coordinate:
Apply a variety of styles to the streamlines:
Set the style for multiple vector fields:
Use named styles:
Named arrow styles:
Named dot styles:
Named pointer styles:
Named dart styles:
Color the vectors according to their norms:
Use any named color gradient from ColorData:
Color the vectors according to their values:
Use VectorColorFunctionScaling->False to get unscaled values:
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:
Use automatically determined vector points:
Show all of the specified field vectors:
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 :
Create a regular 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 regular grid:
The location for vectors is given in the middle of the drawn vector:
Use an automatically determined vector scale:
Specify the relative size of vectors as a fraction of the diagonal of the plot range:
Use symbolic names to control the size of vectors:
With the vector scaling function set to None, all vectors have the same size:
Specify an absolute size for the arrowheads:
Specify arrowhead size relative to the length of the arrow:
Scale the vector length by the absolute value of the coordinate:
By default, the vector length is scaled by the norm of the vector field:
Set the style for the displayed vectors:
Set the style for multiple vector fields:
Plot the vector fields without arrowheads:
Plot the vector field with a named vector style:
Arrow vector styles:
Circular vector styles:
Dart vector styles:
Vector styles with dots:
Pointer vector styles:
Specify both arrow tail and head:
Graphics primitives without Arrowheads are scaled based on the vector scale:
Change the scaling using the VectorScale option:
 Applications   (3)
Visualize a sampled vector field with the background based on the field's divergence:
Visualize the first horizontal and vertical Gaussian derivatives of an image:
Combine the vertical and horizontal Gaussian derivatives:
Compute wind velocity from given coordinates:
Filter unavailable data:
Outline of Africa:
Wind velocity and temperatures over Africa:
Use VectorDensityPlot to plot functions with a density plot of the scalar field:
Use ListVectorPlot for plotting data without a density plot:
Use ListStreamDensityPlot to plot with streamlines instead of vectors:
Use VectorPlot to plot functions without a density plot:
Use ListVectorPlot3D to visualize 3D vector field data:
Scalar fields can be plotted by themselves with ListDensityPlot:
Use ListLineIntegralConvolutionPlot to plot the line integral convolution of vector field data:
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