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

• SliceDensityPlot3D evaluates f at values of x, y and z on a surface surf and uses a color function to map each value f[x,y,z] to a color.
• The plot visualizes the set , where is a color function.
• The following basic slice surfaces surfi can be given:
•  Automatic automatically determine slice surfaces "CenterPlanes" coordinate planes through the center "BackPlanes" coordinate planes at the back of the plot "XStackedPlanes" coordinate planes stacked along axis "YStackedPlanes" coordinate planes stacked along axis "ZStackedPlanes" coordinate planes stacked along axis "DiagonalStackedPlanes" planes stacked diagonally "CenterSphere" a sphere in the center "CenterCutSphere" a sphere with a cutout wedge "CenterCutBox" a box with a cutout octant
• SliceDensityPlot3D[f,{x,xmin,xmax},] is equivalent to SliceDensityPlot3D[f,Automatic,{x,xmin,xmax},] etc.
• The following parametrizations can be used for basic slice surfaces:
•  {"XStackedPlanes",n}, generate n equally spaced planes {"XStackedPlanes",{x1,x2,…}} generate planes for x=xi {"CenterCutSphere",ϕopen} cut angle ϕopen facing the view point {"CenterCutSphere",ϕopen,ϕcenter} cut angle ϕopen with center angle ϕcenter in plane
• "YStackedPlanes", "ZStackedPlanes" follow the specifications for "XStackedPlanes", with additional features shown in the scope examples.
• The following general slice surfaces surfi can be used:
•  expr0 implicit equation in x, y, and z, e.g. x y z-10 surfaceregion a two-dimensional region in 3D, e.g. Hyperplane volumeregion a three-dimensional region in 3D where surfi is taken as the boundary surface, e.g. Cuboid
• The following wrappers can be used for slice surfaces surfi:
•  Annotation[surf,label] provide an annotation Button[surf,action] define an action to execute when the surface is clicked EventHandler[surf,…] define a general event handler for the surface Hyperlink[surf,uri] make the surface act as a hyperlink PopupWindow[surf,cont] attach a popup window to the surface StatusArea[surf,label] display in status area when the surface is moused over Tooltip[surf,label] attach an arbitrary tooltip to the surface
• SliceDensityPlot3D has the same options as Graphics3D, with the following additions and changes: [List of all options]
•  Axes True whether to draw axes BoundaryStyle Automatic how to style surface boundaries BoxRatios {1,1,1} bounding 3D box ratios ClippingStyle None how to draw values clipped by PlotRange ColorFunction Automatic how to color the plot ColorFunctionScaling True whether to scale the arguments to ColorFunction PerformanceGoal \$PerformanceGoal aspects of performance to optimize PlotLegends None legends for color gradients PlotPoints Automatic initial number of samples for the function f and slice surfaces surfi in each direction PlotRange {Full,Full,Full,Automatic} range of f or other values to include PlotTheme \$PlotTheme overall theme for the plot RegionFunction (True&) how to determine whether a point should be included ScalingFunctions None how to scale individual coordinates TargetUnits Automatic desired units to use WorkingPrecision MachinePrecision the precision used in internal computations
• ColorFunction is by default supplied with the scaled value of f.
• RegionFunction is by default supplied with x, y, z and f.
• Possible settings for ScalingFunctions include:
•  sf scale the f density values {sx,sy,sz} scale x, y and z axes {sx,sy,sz,sf} scale x, y and z axes and f density values
• Common built-in scaling functions s include:
•  "Log" log scale with automatic tick labeling "Log10" base-10 log scale with powers of 10 for ticks "SignedLog" log-like scale that includes 0 and negative numbers "Reverse" reverse the coordinate direction "Infinite" infinite scale
• List of all options

•  AlignmentPoint Center the default point in the graphic to align with AspectRatio Automatic ratio of height to width Axes True whether to draw axes AxesEdge Automatic on which edges to put axes AxesLabel None axes labels AxesOrigin Automatic where axes should cross AxesStyle {} graphics directives to specify the style for axes Background None background color for the plot BaselinePosition Automatic how to align with a surrounding text baseline BaseStyle {} base style specifications for the graphic BoundaryStyle Automatic how to style surface boundaries Boxed True whether to draw the bounding box BoxRatios {1,1,1} bounding 3D box ratios BoxStyle {} style specifications for the box ClippingStyle None how to draw values clipped by PlotRange ClipPlanes None clipping planes ClipPlanesStyle Automatic style specifications for clipping planes ColorFunction Automatic how to color the plot ColorFunctionScaling True whether to scale the arguments to ColorFunction ContentSelectable Automatic whether to allow contents to be selected ControllerLinking False when to link to external rotation controllers ControllerPath Automatic what external controllers to try to use Epilog {} 2D graphics primitives to be rendered after the main plot FaceGrids None grid lines to draw on the bounding box FaceGridsStyle {} style specifications for face grids FormatType TraditionalForm default format type for text ImageMargins 0. the margins to leave around the graphic ImagePadding All what extra padding to allow for labels, etc. ImageSize Automatic absolute size at which to render the graphic LabelStyle {} style specifications for labels Lighting Automatic simulated light sources to use Method Automatic details of 3D graphics methods to use PerformanceGoal \$PerformanceGoal aspects of performance to optimize PlotLabel None a label for the plot PlotLegends None legends for color gradients PlotPoints Automatic initial number of samples for the function f and slice surfaces surfi in each direction PlotRange {Full,Full,Full,Automatic} range of f or other values to include PlotRangePadding Automatic how much to pad the range of values PlotRegion Automatic final display region to be filled PlotTheme \$PlotTheme overall theme for the plot PreserveImageOptions Automatic whether to preserve image options when displaying new versions of the same graphic Prolog {} 2D graphics primitives to be rendered before the main plot RegionFunction (True&) how to determine whether a point should be included RotationAction "Fit" how to render after interactive rotation ScalingFunctions None how to scale individual coordinates SphericalRegion Automatic whether to make the circumscribing sphere fit in the final display area TargetUnits Automatic desired units to use Ticks Automatic specification for ticks TicksStyle {} style specification for ticks TouchscreenAutoZoom False whether to zoom to fullscreen when activated on a touchscreen ViewAngle Automatic angle of the field of view ViewCenter Automatic point to display at the center ViewMatrix Automatic explicit transformation matrix ViewPoint {1.3,-2.4,2.} viewing position ViewProjection Automatic projection method for rendering objects distant from the viewer ViewRange All range of viewing distances to include ViewVector Automatic position and direction of a simulated camera ViewVertical {0,0,1} direction to make vertical WorkingPrecision MachinePrecision the precision used in internal computations

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 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:

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 :

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 on several planes:

Plot spherical waves 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_2024_slicedensityplot3d, author="Wolfram Research", title="{SliceDensityPlot3D}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/SliceDensityPlot3D.html}", note=[Accessed: 13-August-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_slicedensityplot3d, organization={Wolfram Research}, title={SliceDensityPlot3D}, year={2022}, url={https://reference.wolfram.com/language/ref/SliceDensityPlot3D.html}, note=[Accessed: 13-August-2024 ]}