BUILT-IN MATHEMATICA SYMBOL

# VectorDensityPlot

VectorDensityPlot[{{vx, vy}, s}, {x, xmin, xmax}, {y, ymin, ymax}]
generates a vector plot of the vector field 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.

## Details and OptionsDetails and Options

• VectorDensityPlot by default shows vectors from the vector field at a regular grid of positions.
• VectorDensityPlot omits any vectors for which the etc. do not evaluate to real numbers.
• VectorDensityPlot treats the variables x and y as local, effectively using Block.
• VectorDensityPlot has attribute HoldAll, and evaluates the , etc. only after assigning specific numerical values to x and y.
• In some cases it may be more efficient to use Evaluate to evaluate the , etc. symbolically before specific numerical values are assigned to x and y.
• VectorDensityPlot has the same options as Graphics, with the following additions and changes:
•  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 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 PlotLegends None legends to include 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 arguments supplied to functions in MeshFunctions, RegionFunction, ColorFunction, and VectorColorFunction are x, y, , , s.
• The default setting MeshFunctions->{#5&} draws mesh lines for the scalar field s.

## ExamplesExamplesopen allclose all

### Basic Examples (3)Basic Examples (3)

Plot the vector field with background color based on the field magnitude:

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Plot two vector fields with background color based on the first field's magnitude:

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Plot two vector fields with background color based on the function :

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