is an option for plotting functions that specifies functions to use to determine the placement of mesh divisions.
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:
-
x, y, θ, r (#3&)x, y, f {}x, y, f {#1&,#2&}x, y, z, f {#1&,#2&,#3&}
- Each mi effectively defines a foliation.
- The mi should normally be chosen to be continuous monotonic functions.
Examples
open all close allBasic 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)
A case where Fubini's theorem does not hold [more info]:
Real and imaginary parts as mesh functions:
Related Guides
History
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_2025_meshfunctions, author="Wolfram Research", title="{MeshFunctions}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/MeshFunctions.html}", note=[Accessed: 18-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_meshfunctions, organization={Wolfram Research}, title={MeshFunctions}, year={2007}, url={https://reference.wolfram.com/language/ref/MeshFunctions.html}, note=[Accessed: 18-November-2025]}