# MeshFunctions

is an option for plotting functions that specifies functions to use to determine the placement of mesh divisions.

# Details • In Plot3D, the default setting MeshFunctions->{#1&,#2&} specifies that meshes corresponding to x and y coordinates should be constructed.
• With the setting MeshFunctions->{m1,m2,}, each function mi defines a family of mesh divisions.
• By default, the mesh divisions are taken to lie at positions giving equally spaced values of mi[].
• The arguments supplied to the mi 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, θ, 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 mi effectively defines a foliation.
• The mi should normally be chosen to be continuous monotonic functions.

# Examples

open allclose all

## Basic Examples(3)

Put 5 mesh lines in the direction:

Show curves of constant real and imaginary parts of a function:

Show intersection points:

## Applications(1)

Define two polynomials:

Use MeshFunctions to find the intercepts:

Use MeshFunctions to find the intersections between two functions: