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 allBasic Examples (3)
Applications (1)
Use MeshFunctions to find the 
intercepts:
Use MeshFunctions to find the intersections between two functions:
Neat Examples (2)
A case where Fubini's theorem does not hold [more info]:
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