This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# MeshFunctions

 MeshFunctionsis an option for plotting functions that specifies functions to use to determine the placement of mesh divisions.
• In Plot3D, the default setting MeshFunctions specifies that meshes corresponding to x and y coordinates should be constructed.
• With the setting MeshFunctions, each function defines a family of mesh divisions.
• By default, the mesh divisions are taken to lie at positions giving equally spaced values of .
• The arguments supplied to the and the default MeshFunctions settings are as follows:
 Plot and ListLinePlot x, y {#1&} ParametricPlot x, y, u or x, y, u, v {#3&} or {#3&,#4&} PolarPlot and ListPolarPlot x, y, , r (#3&) RegionPlot x, y {#1&,#2&} ContourPlot and ListContourPlot x, y, f {} DensityPlot and ListDensityPlot x, y, f {#1&,#2&} ContourPlot3D and ListContourPlot3D x, y, z, f {#1&,#2&,#3&} Plot3D and ListPlot3D x, y, z {#1&,#2&} ListSurfacePlot3D x, y, z {#1&,#2&,#3&} ParametricPlot3D x, y, z, u or x, y, z, u, v {#4&} or {#4&,#5&} RegionPlot3D x, y, z {#1&,#2&,#3&}
• Each effectively defines a foliation.
• The should normally be chosen to be continuous monotonic functions.
Put 5 mesh lines in the direction:
Show curves of constant real and imaginary parts of a function:
Show intersection points:
Put 5 mesh lines in the direction:
 Out[1]=

Show curves of constant real and imaginary parts of a function:
 Out[1]=

Show intersection points:
 Out[1]=
 Applications   (1)
Define two polynomials:
Use MeshFunctions to find the intercepts:
Use MeshFunctions to find the intersections between two functions:
A case where Fubini's theorem does not hold
Real and imaginary parts as mesh functions:
New in 6