SliceContourPlot3D

SliceContourPlot3D[f,surf,{x,xmin,xmax},{y,ymin,ymax},{z,zmin,zmax}]

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

SliceContourPlot3D[f,surf,{x,y,z}reg]

restricts the surface to be within region reg.

SliceContourPlot3D[f,{surf1,surf2,},]

generates contour plots over several slices.

Details and Options

Examples

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Basic Examples  (2)

Plot the contours of the function over slice planes through the center:

Plot the contours over the surface :

Scope  (24)

Surfaces  (9)

Generate a contour plot over standard slice surfaces:

Standard axis-aligned stacked slice surfaces:

Standard boundary surfaces:

Plot the contours over any surface region:

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

Plot the contours over the surface :

Plot the contours over multiple surfaces:

Specify the number of stacked planes:

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

Sampling  (4)

Use Contours to specify the number of contours:

Or the list of function values to put contours:

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  (11)

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 regions between contours with ContourShading:

Use ContourStyle to style the contour lines:

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  (43)

BoundaryStyle  (1)

Style the slice surface boundaries with BoundaryStyle:

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 contours according to the values:

Use a named color gradient:

Use red when :

ColorFunctionScaling  (2)

By default, scaled values are used:

Use ColorFunctionScalingFalse to get unscaled values:

Contours  (4)

Use 5 equally spaced contours:

Use automatic contour selection:

Specify an explicit set of contours:

Use specific contours with specific styles:

ContourStyle  (1)

Specify a style for all contours:

ContourShading  (4)

ContourShadingAutomatic computes contour region shading from the ColorFunction:

Cyclically repeat shading styles:

Leave every third contour region empty, starting from the second:

Leave the regions between contours blank:

PerformanceGoal  (2)

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

PlotLegends  (4)

Add a color bar for the different values:

PlotLegends automatically picks up Contours and ContourShading values:

With the setting ContourShadingAutomatic, the colors are derived from ColorFunction:

Control placement of the legend with Placed:

PlotPoints  (1)

Use more plot points to get a smoother contour:

PlotRange  (3)

Show All contours by default:

Show a select range:

Show only function values between 0 and 2:

This is equivalent to the fully qualified form:

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  (17)

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:

Distribution Functions  (6)

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:

Correlation between y and z only:

Correlation between y and z only, but larger variance in the z component:

Visualize the PDF of a ProductDistribution:

A product of three different distributions:

A product of bivariate and univariate distributions:

Plot the pdf of a CopulaDistribution:

Visualize the PDF of a kernel density estimate of some trivariate data:

Potential and Wave Functions  (4)

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

Alternatively, show the 17<=TemplateBox[{f}, Abs]<=21 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 :

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 z axis:

The solution evolves in time along the z axis:

Visualize Wolfram's nonlinear wave equation in two spatial dimensions with time represented along the z 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 SliceDensityPlot3D for continuous densities on surfaces:

Use ContourPlot3D for constant value surfaces:

Use DensityPlot3D for full volume visualization of the function values:

Use ListSliceContourPlot3D for data:

Use ContourPlot for contour 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), SliceContourPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/SliceContourPlot3D.html (updated 2022).

Text

Wolfram Research (2015), SliceContourPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/SliceContourPlot3D.html (updated 2022).

CMS

Wolfram Language. 2015. "SliceContourPlot3D." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/SliceContourPlot3D.html.

APA

Wolfram Language. (2015). SliceContourPlot3D. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SliceContourPlot3D.html

BibTeX

@misc{reference.wolfram_2024_slicecontourplot3d, author="Wolfram Research", title="{SliceContourPlot3D}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/SliceContourPlot3D.html}", note=[Accessed: 21-July-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_slicecontourplot3d, organization={Wolfram Research}, title={SliceContourPlot3D}, year={2022}, url={https://reference.wolfram.com/language/ref/SliceContourPlot3D.html}, note=[Accessed: 21-July-2024 ]}