SliceDensityPlot3D

SliceDensityPlot3D[f,surf,{x,x_min,x_max},{y,y_min,y_max},{z,z_min,z_max}]

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 surf_i 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,x_min,x_max},…] is equivalent to SliceDensityPlot3D[f,Automatic,{x,x_min,x_max},…] 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=x_i
	{"CenterCutSphere",ϕ_open}	cut angle ϕ_open facing the view point
	{"CenterCutSphere",ϕ_open,ϕ_center}	cut angle ϕ_open with center angle ϕ_center in plane

"YStackedPlanes", "ZStackedPlanes" follow the specifications for "XStackedPlanes", with additional features shown in the scope examples.
The following general slice surfaces surf_i 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 surf_i is taken as the boundary surface, e.g. Cuboid

The following wrappers can be used for slice surfaces surf_i:

	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:

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 surf_i 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:
s_f scale the f density values

{s_x,s_y,s_z} scale x, y and z axes

{s_x,s_y,s_z,s_f} 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

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 , 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 ρ_ab 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 $cos(omega TemplateBox[{{p, -, {p, _, i}}}, Norm])$ 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:

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SliceDensityPlot3D

Details and Options

Examples

Basic Examples (2)