Built-in Mathematica Symbol

ListPlot3D

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

ListPlot3D[{{x₁, y₁, z₁}, {x₂, y₂, z₂}, ...}]
generates a plot of the surface with heights z_i at positions {x_i, y_i}.

ListPlot3D[{data₁, data₂, ...}]
plots the surfaces corresponding to each of the data_i.

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 x and y 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 z 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
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 z 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 x and y coordinate values for each data point to be successive integers starting at 1.

The elements of array can also be triples {x₁₁, y₁₁, z₁₁}, specifying heights z_ij at explicit positions {x_ij, y_ij}. The connectivity of the surface in this case is still taken to follow the 2D array.

In the default case with no explicit x and y given, the setting DataRange->{{x_min, x_max}, {y_min, y_max}} specifies the ranges of coordinate values to use.

With the default setting DataRange->Automatic, ListPlot3D[{{a₁₁, a₁₂, a₁₃}, ..., {a_n1, a_n2, a_n3}}] will assume that the data being given is {{x₁, y₁, z₁}, ...}, 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.

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