# 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:

## Neat Examples(2)

Real and imaginary parts as mesh functions:

Wolfram Research (2007), MeshFunctions, Wolfram Language function, https://reference.wolfram.com/language/ref/MeshFunctions.html.

#### Text

Wolfram Research (2007), MeshFunctions, Wolfram Language function, https://reference.wolfram.com/language/ref/MeshFunctions.html.

#### CMS

Wolfram Language. 2007. "MeshFunctions." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MeshFunctions.html.

#### APA

Wolfram Language. (2007). MeshFunctions. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MeshFunctions.html

#### BibTeX

@misc{reference.wolfram_2022_meshfunctions, author="Wolfram Research", title="{MeshFunctions}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/MeshFunctions.html}", note=[Accessed: 29-June-2022 ]}

#### BibLaTeX

@online{reference.wolfram_2022_meshfunctions, organization={Wolfram Research}, title={MeshFunctions}, year={2007}, url={https://reference.wolfram.com/language/ref/MeshFunctions.html}, note=[Accessed: 29-June-2022 ]}