1.9.5 Contour and Density Plots
ContourPlot[f, {x,  ,  }, {y,  ,  }]
| | make a contour plot of f as a function of x and y |
DensityPlot[f, {x,  ,  }, {y,  ,  }]
| | make a density plot of f |
Contour and density plots. This gives a contour plot of the function  . | |
In[1]:=
ContourPlot[Sin[x] Sin[y], {x, -2, 2}, {y, -2, 2}]
|
Out[1]=
|
|
A contour plot gives you essentially a "topographic map" of a function. The contours join points on the surface that have the same height. The default is to have contours corresponding to a sequence of equally spaced z values. Contour plots produced by Mathematica are by default shaded, in such a way that regions with higher z values are lighter.
| option name | default value | | | ColorFunction | Automatic | what colors to use for shading; Hue uses a sequence of hues | | Contours | 10 | the total number of contours, or the list of z values for contours | | PlotRange | Automatic | the range of values to be included; you can specify { ,  }, All or Automatic | | ContourShading | True | whether to use shading | | PlotPoints | 25 | number of evaluation points in each direction | | Compiled | True | whether to compile the function being plotted |
Some options for ContourPlot. The first set can also be used in Show. | Particularly if you use a display or printer that does not handle gray levels well, you may find it better to switch off shading in contour plots. | |
In[2]:=
Show[%, ContourShading -> False]
|
Out[2]=
|
|
You should realize that if you do not evaluate your function on a fine enough grid, there may be inaccuracies in your contour plot. One point to notice is that whereas a curve generated by Plot may be inaccurate if your function varies too quickly in a particular region, the shape of contours can be inaccurate if your function varies too slowly. A rapidly varying function gives a regular pattern of contours, but a function that is almost flat can give irregular contours. You can typically overcome such problems by increasing the value of PlotPoints. | Density plots show the values of your function at a regular array of points. Lighter regions are higher. | |
In[3]:=
DensityPlot[Sin[x] Sin[y], {x, -2, 2}, {y, -2, 2}]
|
Out[3]=
|
|
| You can get rid of the mesh like this. But unless you have a very large number of regions, plots usually look better when you include the mesh. | |
In[4]:=
Show[%, Mesh -> False]
|
Out[4]=
|
|
| option name | default value | | | ColorFunction | Automatic | what colors to use for shading; Hue uses a sequence of hues | | Mesh | True | whether to draw a mesh | | PlotPoints | 25 | number of evaluation points in each direction | | Compiled | True | whether to compile the function being plotted |
Some options for DensityPlot. The first set can also be used in Show.
|
