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MeshFunctions

MeshFunctions
is an option for plotting functions that specifies functions to use to determine the placement of mesh divisions.
  • 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 ListLinePlotx, y {#1&}
ParametricPlotx, y, u or x, y, u, v {#3&} or {#3&,#4&}
PolarPlot and ListPolarPlot
x, y, Theta, r(#3&)
RegionPlotx, 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 ListPlot3Dx, y, z {#1&,#2&}
ListSurfacePlot3Dx, y, z {#1&,#2&,#3&}
ParametricPlot3Dx, y, z, u or x, y, z, u, v {#4&} or {#4&,#5&}
RegionPlot3Dx, y, z {#1&,#2&,#3&}
  • Each mi effectively defines a foliation.
  • The mi should normally be chosen to be continuous monotonic functions.
EXAMPLESCLOSE ALL
Basic Examples   (3)
Put 5 mesh lines in the z direction:
Show curves of constant real and imaginary parts of a function:
Show intersection points:
Put 5 mesh lines in the z direction:
In[1]:=
Click for copyable input
Out[1]=
 
Show curves of constant real and imaginary parts of a function:
In[1]:=
Click for copyable input
Out[1]=
 
Show intersection points:
In[1]:=
Click for copyable input
Out[1]=
Applications   (1)
Define two polynomials:
Use MeshFunctions to find the x 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:
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