ListSurfacePlot3D

ListSurfacePlot3D[{{x₁,y₁,z₁},{x₂,y₂,z₂},…}]

plots a three-dimensional surface constructed to fit the specified points.

Details and Options

ListSurfacePlot3D attempts to reconstruct smooth surfaces defined by sets of points.
Surfaces generated by ListSurfacePlot3D can "fold over", and do not need to have a single value for given and values.
The order in which , , points are supplied to ListSurfacePlot3D does not affect the results.
ListSurfacePlot3D has the same options as Graphics3D, with the following additions and changes:

	Axes	True	whether to draw axes
	BoundaryStyle	Automatic	how to draw boundary lines for surfaces
	BoxRatios	Automatic	bounding 3D box ratios
	ColorFunction	Automatic	how to determine the color of the surface
	ColorFunctionScaling	True	whether to scale arguments to ColorFunction
	MaxPlotPoints	Automatic	the maximum number of points to include
	Mesh	Automatic	how many mesh lines in each direction to draw
	MeshFunctions	{#1&,#2&,#3&}	how to determine the placement of mesh lines
	MeshShading	None	how to shade regions between mesh lines
	MeshStyle	Automatic	the style for mesh lines
	Method	Automatic	the method to use for interpolation and data reduction
	PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize
	PlotLegends	None	legends for surfaces
	PlotRange	All	the range of values to include
	PlotRangePadding	Automatic	how much to pad the range of values
	PlotStyle	Automatic	graphics directives to specify the style for the surface
	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
	TextureCoordinateFunction	Automatic	how to determine texture coordinates
	TextureCoordinateScaling	True	whether to scale arguments to TextureCoordinateFunction

ListSurfacePlot3D yields a surface that fits the data provided, but may not necessarily contain the specific points defined by the data.
The arguments supplied to functions in MeshFunctions and RegionFunction are x, y, and z. Functions in ColorFunction and TextureCoordinateFunction are by default supplied with scaled versions of these arguments.
ListSurfacePlot3D returns Graphics3D[GraphicsComplex[data]].
Possible settings for ScalingFunctions include:
s_y scale the y axis

{s_x,s_y} scale x and y axes
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 (1)

Reconstruct a surface from 3D data:

Process and style the resulting surface:

Scope (12)

Data (4)

Nonreal data is excluded:

Use MaxPlotPoints to limit the number of points used:

Use PlotRange to focus in on areas of interest:

Use RegionFunction to restrict the surface to a region given by inequalities:

Presentation (8)

Provide an explicit PlotStyle for the surface:

Add labels:

Color the surface by height:

Provide overlay meshes:

Style the areas between mesh lines:

Use a theme with a dark background and grid lines:

Use a theme with minimum styling:

Use ScalingFunctions to flip the x axis:

Options (41)

BoundaryStyle (4)

Use a black boundary around the edges of the surface:

Use a thick boundary around the edges of the surface:

Use a thick red boundary around the edges of the surface:

BoundaryStyle applies to holes cut by RegionFunction:

ColorFunction (4)

Color by scaled , , and values:

Named color gradients color in the direction:

ColorFunction has higher priority than PlotStyle:

ColorFunction has lower priority than MeshShading:

ColorFunctionScaling (1)

Use unscaled coordinates when calculating the color:

Mesh (5)

Use no mesh:

Show the sampling mesh:

Use 5 mesh lines in each direction:

Use 3 mesh lines in the direction and 6 mesh lines in the direction:

Use mesh lines at specific values:

MeshFunctions (2)

Use a mesh evenly spaced in the , , and directions:

Use an arbitrary mesh function:

MeshShading (4)

Use None to remove regions:

Lay a checkerboard pattern over a surface:

MeshShading has a higher priority than PlotStyle:

MeshShading has a higher priority than ColorFunction:

MeshStyle (2)

Use red mesh lines:

Use red mesh lines in the direction, blue in the direction, and thick in the direction:

PlotStyle (6)

Color a surface with diffuse cyan:

Use Specularity to get highlights:

Use Opacity to get transparent surfaces:

Produce a wire mesh:

ColorFunction has higher priority than PlotStyle:

MeshShading has a higher priority than PlotStyle:

PlotTheme (1)

Use a theme with a bold color scheme and simple ticks:

Change the color function:

RegionFunction (3)

Select a region in , , and :

Select the region where :

ScalingFunctions (4)

By default, plots have linear scales in all directions:

Log-scaled plots will only plot regions in which Log is defined: XXXX Broken

Use a shifted log scale to show a function with negative values:

Use ScalingFunctions to reverse the coordinate direction in the direction:

TextureCoordinateFunction (4)

Textures use scaled and coordinates by default:

Use the and coordinates:

Use unscaled coordinates:

Use textures to highlight how parameters map onto a surface:

TextureCoordinateScaling (1)

Use scaled or unscaled coordinates for textures:

Applications (1)

Reconstruct a sphere:

Add "noise" to the data:

Properties & Relations (13)

ListPlot3D always assumes a function surface with one sheet:

ListSurfacePlot3D can fill in any number of sheets:

ListSurfacePlot3D produces an approximating general surface:

ListPlot3D constructs a function surface that oscillates rapidly in the direction:

When using multiple values for each , value, the duplicates are discarded by ListPlot3D:

ListSurfacePlot3D still reconstructs the general surface:

Use ListPointPlot3D to show three-dimensional points:

Use ListContourPlot3D to find contours through values associated with , , data:

Use ListContourPlot to create contours from continuous data:

Use ListDensityPlot to create densities from continuous data:

Use ArrayPlot for arrays of discrete data:

Use MatrixPlot for structural plots of matrices:

Use ReliefPlot for matrices corresponding to medical and geographic values:

Use ListLogPlot, ListLogLogPlot, and ListLogLinearPlot for logarithmic plots:

Use ListPolarPlot for polar plots:

Use DateListPlot to show data over time:

Use ParametricPlot3D for three-dimensional parametric curves and surfaces:

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