SliceDensityPlot3D

SliceDensityPlot3D[f,surf,{x,xmin,xmax},{y,ymin,ymax},{z,zmin,zmax}]

generates a density plot of f over the slice surface surf as a function of x, y, and z.

SliceDensityPlot3D[f,surf,{x,y,z}∈reg]

restricts the surface to be within region reg.

SliceDensityPlot3D[f,{surf1,surf2,…},…]

generates density plots over several slices.

Details and Options

Examples

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Basic Examples  (2)

Plot the density of on coordinate planes through the center of the plot range:

Plot the density on the surface :

Scope  (21)

Surfaces  (9)

Generate a density plot over standard slice surfaces:

Standard axis-aligned stacked slice surfaces:

Standard boundary surfaces:

Plot the densities over any surface region:

Plotting over a volume primitive is equivalent to plotting over RegionBoundary[reg]:

Plot the densities over the surface :

Plot the densities over multiple surfaces:

Specify the number of stack planes:

Specify the cutting angle for a center-cut sphere slice:

Sampling  (3)

Areas where the function becomes nonreal are excluded:

Use RegionFunction to expose obscured slices:

The domain may be specified by a region including Cone:

A formula region including ImplicitRegion:

A mesh-based region including BoundaryMeshRegion:

Presentation  (9)

Use PlotTheme to immediately get overall styling:

Use PlotLegends to get a color bar for the different values:

Control the display of axes with Axes:

Label axes using AxesLabel and the whole plot using PlotLabel:

Color the plot by the function values with ColorFunction:

Style the slice surface boundaries with BoundaryStyle:

TargetUnits specifies which units to use in the visualization:

Create a plot with a log-scaled axis:

Reverse the coordinate direction in the direction:

Options  (33)

BoundaryStyle  (1)

Style the slice surface boundaries:

BoxRatios  (3)

By default, the edges of the bounding box have the same length:

Use BoxRatios->Automatic to show the natural scale of the 3D coordinate values:

Use custom length ratios for each side of the bounding box:

ClippingStyle  (2)

Color clipped regions:

Remove clipped regions with None:

ColorFunction  (3)

Color the slice surfaces according to the density values :

Use a named color gradient available in ColorData:

Use red when :

ColorFunctionScaling  (2)

By default, scaled values are used:

Use ColorFunctionScaling->False to get access to unscaled f values:

PerformanceGoal  (2)

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

PlotLegends  (3)

Show a legend for the densities:

PlotLegends automatically matches the color function:

Control placement of the legend with Placed:

PlotPoints  (1)

Use PlotPoints to determine sampling of slice surfaces:

PlotRange  (3)

Show All contours by default:

Show a select range:

Show only function values between 0 and 2:

Or with the fully qualified specification:

PlotTheme  (3)

Use a theme with detailed grid lines, ticks, and legends:

Any option setting overrides PlotTheme settings, in this case removing face grids:

Compare different plot themes:

RegionFunction  (2)

Include only the contours where or :

Include only the contours where :

ScalingFunctions  (5)

By default, plots have linear scales in all directions:

Create a plot with a log-scaled axis:

Use ScalingFunctions to scale to reverse the coordinate direction in the direction:

Use a scale defined by a function and its inverse:

Slice surfaces that are defined relative to the bounding box are unaffected by scaling functions:

TargetUnits  (2)

Axes and legends are labeled with the units specified by TargetUnits:

Units specified by Quantity are converted to those specified by TargetUnits:

WorkingPrecision  (1)

Evaluate functions using machine-precision arithmetic:

Applications  (16)

Elementary Functions  (4)

Plot the function :

Plot the functions and :

Plot the functions and :

Plot the functions and :

Plot the functions and :

Plot the functions and :

Plot , a product of univariate functions:

Plot and , univariate and bivariate functions:

Plot , a trivariate function:

Plot a sum of exponentials sum_ialpha_i exp(-TemplateBox[{{p, -, {p, _, i}}}, Norm]^2):

Pick the points randomly in a box:

Compare with other ways of visualizing:

Show them together:

Distribution Functions  (5)

Plot the PDF of a distribution:

Simulate the distribution and show point distribution:

Plot the CDF of a distribution:

The SurvivalFunction:

The HazardFunction:

Explore Correlation parameters for a MultinormalDistribution, where ρab is the correlation between a and b:

Correlation between x and y only:

Use planes given by the covariance matrix:

Visualize the PDF of a ProductDistribution:

A product of three different distributions:

Visualize the PDF of a kernel density estimate of some trivariate data, where density > 0.01:

Potential and Wave Functions  (4)

Plot the phase using color on the isosurface of a quadrupole potential:

Alternatively, show the 17<=TemplateBox[{f}, Abs]<=140 on several planes:

Plot spherical waves cos(omega TemplateBox[{{p, -, {p, _, i}}}, Norm]) from three sources in space:

Plot hydrogen orbital densities for quantum numbers , , :

Plot on a surface:

Plot :

An electrostatic potential built from a collection of point charges at positions :

Two charges and :

Plot iso charge surfaces:

Show them together:

Partial Differential Equations  (3)

Visualize a nonlinear sine-Gordon equation in two spatial dimensions with periodic boundary conditions, with time represented along the axis:

The solution evolves in time along the axis:

Visualize Wolfram's nonlinear wave equation in two spatial dimensions, with time represented along the axis:

Visualize solutions to 3D partial differential equations. In this case, a Poisson equation over a Ball and Dirichlet boundary conditions:

Properties & Relations  (5)

Use SliceContourPlot3D for contours on surfaces:

Use ContourPlot3D for constant value surfaces:

Use DensityPlot3D for full volume visualization of the function values:

Use ListSliceDensityPlot3D for data:

Use DensityPlot for density plots in 2D:

Possible Issues  (1)

Slice surfaces with a constant value may appear noisy:

The function is constant on the chosen slice surface:

Choosing a different slice surface gives a reasonable picture of the function:

Wolfram Research (2015), SliceDensityPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/SliceDensityPlot3D.html (updated 2022).

Text

Wolfram Research (2015), SliceDensityPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/SliceDensityPlot3D.html (updated 2022).

CMS

Wolfram Language. 2015. "SliceDensityPlot3D." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/SliceDensityPlot3D.html.

APA

Wolfram Language. (2015). SliceDensityPlot3D. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SliceDensityPlot3D.html

BibTeX

@misc{reference.wolfram_2025_slicedensityplot3d, author="Wolfram Research", title="{SliceDensityPlot3D}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/SliceDensityPlot3D.html}", note=[Accessed: 25-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_slicedensityplot3d, organization={Wolfram Research}, title={SliceDensityPlot3D}, year={2022}, url={https://reference.wolfram.com/language/ref/SliceDensityPlot3D.html}, note=[Accessed: 25-May-2025 ]}