BUILT-IN MATHEMATICA SYMBOL

ListPlot3D

ListPlot3D[array]
generates a three-dimensional plot of a surface representing an array of height values.

ListPlot3D

generates a plot of the surface with heights

at positions

.

ListPlot3D

plots the surfaces corresponding to each of the

.

MORE INFORMATION

ListPlot3D 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	{1,1,0.4}	bounding 3D box ratios
ClippingStyle	Automatic	how to draw clipped parts of the surface
ColorFunction	Automatic	how to determine the color of surfaces
ColorFunctionScaling	True	whether to scale arguments to ColorFunction
DataRange	Automatic	the range of and values to assume for data
Filling	None	filling under the surface
FillingStyle	Opacity[0.5]	style to use for filling
InterpolationOrder	None	the polynomial degree in each variable of surfaces used in joining data points
MaxPlotPoints	Automatic	the maximum number of points to include
Mesh	Automatic	how many mesh lines in each direction to draw
MeshFunctions	{#1&,#2&}	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
NormalsFunction	Automatic	how to determine effective surface normals
PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize
PlotRange	{Full,Full,Automatic}	the range of or other values to include
PlotRangePadding	Automatic	how much to pad the range of values
PlotStyle	Automatic	graphics directives to specify the style for the surface
RegionFunction	(True&)	how to determine whether a point should be included
TextureCoordinateFunction	Automatic	how to determine texture coordinates
TextureCoordinateScaling	True	whether to scale arguments to TextureCoordinateFunction
VertexColors	Automatic	colors to assume at each point
VertexNormals	Automatic	effective normals to assume at each point

In ListPlot3D[array], array must be a rectangular array. Each element can be either a single real number representing a value, or an triple.

There will be holes in the surface corresponding to array elements that do not represent explicit height values.

ListPlot3D[array] by default takes the and coordinate values for each data point to be successive integers starting at 1.

The elements of array can also be triples , specifying heights at explicit positions . The connectivity of the surface in this case is still taken to follow the 2D array.

In the default case with no explicit and given, the setting DataRange specifies the ranges of coordinate values to use.

With the default setting DataRange->Automatic, ListPlot3D will assume that the data being given is , rather than an n×3 array of height values.

ListPlot3D[list, DataRange->All] always takes list to represent an array of height values.

For ListPlot3D[array], Mesh->Full draws a mesh that crosses at the position of each data point.

array can be a SparseArray object.

The arguments supplied to functions in MeshFunctions and RegionFunction are , , and . Functions in ColorFunction and TextureCoordinateFunction are by default supplied with scaled versions of these arguments.

The setting for VertexColors must be an array or list with the same structure as the coordinate data.

An explicit setting for VertexColors overrides colors determined from ColorFunction.

ListPlot3D returns Graphics3D[data].

EXAMPLES

CLOSE ALL

Basic Examples (3)

Use an array of values to define heights for a surface:

Give explicit

coordinates for points on a surface:

Use different interpolations of data:

Use an array of values to define heights for a surface:

In[1]:=

Out[1]=

Give explicit

coordinates for points on a surface:

In[1]:=

Out[1]=

Use different interpolations of data:

In[1]:=

In[2]:=

Out[2]=

In[3]:=

Out[3]=

Scope (17)

For regular data consisting of

values, the

and

data ranges are taken to be integer values:

Provide explicit

and

data ranges by using DataRange:

Plot multiple sets of regular data:

For irregular data consisting of

triples the

and

data ranges are inferred from data:

Plot multiple sets of irregular data:

Areas around where the data is nonreal are excluded:

Use MaxPlotPoints to limit the number of points used:

PlotRange is selected automatically:

Use PlotRange to focus in on areas of interest:

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

Provide an explicit PlotStyle for the surface:

Provide separate styles for different surfaces:

Add labels:

Color the surface by height:

Provide overlay meshes:

Style the areas between mesh lines:

Provide an interactive Tooltip for a surface:

Fill below a surface:

Options (87)

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:

Do not use any boundary:

BoundaryStyle applies to holes cut by RegionFunction:

BoundaryStyle applies where there are jumps in the surface:

By default clipped regions have no color:

Do not draw clipped regions:

Make clipped regions partially transparent:

Color clipped regions red at the bottom and blue at the top:

Color by scaled

,

, and

values:

Color by scaled

and

coordinates:

Use ColorData for predefined color gradients:

Named color gradients color in the

direction:

ColorFunction has higher priority than PlotStyle:

ColorFunction has lower priority than MeshShading:

Use unscaled coordinates:

Unscaled coordinates are dependent on DataRange:

Arrays of height values are displayed against the number of elements in each direction:

Rescale to the sampling space:

Each dataset is scaled to the same domain:

Triples are interpreted as

coordinates:

Force interpretation as arrays of height values:

The dataset is normally interpreted as a list of

triples:

Fill to the bottom:

Filling occurs along the region cut by the RegionFunction:

Fill to both top and bottom:

Fill surface 1 to the bottom with blue and surface 2 to the top with red:

Fill below discrete regions:

Fill to the bottom with a variety of styles:

Fill to the plane

with red below and blue above:

Fill to the plane

from above only:

Points are normally joined with flat polygons:

Use zero-order or piecewise-constant interpolation:

Use third-order spline interpolation to fit the data:

Interpolation order 0 to 5:

For irregular data, zero-order interpolation gives Voronoi regions for each point:

ListPlot3D normally uses all of the points in the dataset:

Limit the number of points used in each direction:

MaxPlotPoints imposes a regular grid on irregular data:

The grid does not extend beyond the convex hull of the original data:

Use no mesh:

Show the initial and final sampling mesh:

The entire mesh for irregular data is a Delaunay triangulation:

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:

Use different styles for different mesh lines:

Use the

value as the mesh function:

Use mesh lines in the

and

directions:

Use mesh lines corresponding to fixed distances from the origin:

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:

Use red mesh lines:

Use red mesh lines in the

direction and thick mesh lines in the

direction:

Normals are automatically calculated:

Use None to get flat shading for all the polygons:

Vary the effective normals used on the surface:

VertexNormals has a higher priority than NormalsFunction:

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

Automatically compute the

range:

Use all points to compute the range:

Use an explicit

range to emphasize features:

Plot two surfaces with different styles:

Color a surface with diffuse purple:

Use Specularity to get highlights:

Use Opacity to get transparent surfaces:

Use separate styles for each of the surfaces:

Produce a wire mesh:

Plot over a region in

:

The region depends on DataRange:

Filling will fill from the region boundary:

Regions do not have to be connected:

Use any logical combination of conditions:

Textures use scaled

and

coordinates by default:

Use the

and

parameters:

Use unscaled coordinates:

Use textures to highlight how parameters map onto a surface:

Use scaled or unscaled coordinates for textures:

ListPlot3D normally uses an uncolored surface:

Specify random colors for each vertex:

Specify colors for multiple datasets:

ListPlot3D automatically computes surface normals from the geometry:

Specify random normals for each vertex:

Specify normals for multiple datasets:

Applications (5)

Plot an indexed family for functions:

Show iterates of the logistic map, emphasizing values at similar steps:

Show iterates of the logistic map, emphasizing values for particular initial values:

Plot Clebsch-Gordan coefficients as a function of

and

:

A square pulse and its discrete Fourier transform:

Show a color elevation map of the state of Colorado by using elevation data from cities:

Properties & Relations (14)

ListPlot3D produces an interpolating function surface:

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:

ListPlot3D associates values, normals, and colors with the vertices of polygons:

Raster, ArrayPlot, MatrixPlot, and ReliefPlot associate values with the whole polygon:

Use Plot3D for functions:

Use ListPointPlot3D to show three-dimensional points:

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:

Possible Issues (2)

The appearance of a plot may depend on the source of the data:

An

×3 matrix is by default interpreted as a list of triples:

Use DataRange->All to force interpretation as a matrix of

values:

Or provide an explicit list of data ranges to force interpretation as a matrix of

values:

Neat Examples (2)

Voronoi region interpolation:

Use an image from ExampleData:

Plot the dataset with vertex colors, simulating the texture: