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PlotRange

PlotRange
is an option for graphics functions that specifies what range of coordinates to include in a plot.
  • PlotRange can be used for both two- and three-dimensional graphics.
  • The following settings can be used:
Allall points are included
Automaticoutlying points are dropped
Fullinclude full range of original data
maxexplicit limit for each function (see below)
{min,max}explicit limits for y (2D), z (3D) or array values
{{xmin,xmax},{ymin,ymax}}explicit limits for x and y
{{xmin,xmax},{ymin,ymax},{zmin,zmax}}explicit limits for x, y and z (3D)
  • When no explicit limits are given for a particular coordinate, a setting of Automatic is assumed.
  • With the Automatic setting, the distribution of coordinate values is found, and any points sufficiently far out in the distribution are dropped. Such points are often produced as a result of singularities in functions being plotted.
  • Any explicit limit or pair {min, max} can be replaced by a specification such as All or Automatic.
  • A setting such as {min, Automatic} gives a particular minimum value for a coordinate, with a maximum value to be determined automatically.
  • If a particular minimum or maximum is specified as {Automatic, Alpha} this means that the range should in effect be cut off beyond a fraction Alpha of points in the plot. When smooth curves or surfaces are plotted, the measure of points is based on projected length or area.
  • The setting Full can be used in Plot and related functions to specify that a range determined by the original input to the plotting function should be used.  »
  • Plot[f, {x, xmin, xmax}, PlotRange->Full] specifies that the full range {xmin, xmax} should be used, even if no actual values of f are plotted in part of that range.
  • With the setting PlotRange->s the following ranges are used:  »
Graphics{{-s,s},{-s,s}}
Graphics3D{{-s,s},{-s,s},{-s,s}}
Plot{Full,{-s,s}}
ListPlot and ListLinePlot {Full,{0,s}}
ParametricPlot and RegionPlot {{-s,s},{-s,s}}
ContourPlot and ListContourPlot{Full,Full,{-s,s}}
DensityPlot and ListDensityPlot{Full,Full,{-s,s}}
ArrayPlot{Full,Full,{0,s}}
Plot3D and ListPlot3D{Full,Full,{-s,s}}
ListSurfacePlot3D{{-s,s},{-s,s},{-s,s}}
ParametricPlot3D and RegionPlot3D{{-s,s},{-s,s},{-s,s}}
ContourPlot3D and ListContourPlot3D{Full,Full,Full,{-s,s}}
EXAMPLESCLOSE ALL
Basic Examples   (3)
Automatically drops outlying points:
Explicitly choose x and y ranges:
Explicitly choose a z range:
Choose the range to show all the existing points:
Use the full x,y range:
Automatically drops outlying points:
In[1]:=
Click for copyable input
Out[1]=
 
Explicitly choose x and y ranges:
In[1]:=
Click for copyable input
Out[1]=
Explicitly choose a z range:
In[2]:=
Click for copyable input
Out[2]=
 
Choose the range to show all the existing points:
In[1]:=
Click for copyable input
Out[1]=
Use the full x,y range:
In[2]:=
Click for copyable input
Out[2]=
Scope   (8)
Normally, plot functions drop outlying points, which is equivalent to PlotRange->Automatic:
PlotRange->All shows all of the points:
PlotRange for Graphics and Graphics3D is All, by default:
Drop outlying points, by setting PlotRange->Automatic:
Use PlotRange->All to include all points:
Use PlotRange->Full to include all the points and the original domain:
An explicit range can be given in each direction by {min, max}:
One value of the explicit range can be a symbol such as All or Automatic:
The interpretation of PlotRange->max depends on the function:
Any valid range specification can be given to each direction:
Generalizations & Extensions   (2)
Specify the fraction of points below and above the plot range limits:
Include 80% of points according to their x values:
Applications   (1)
Plot the CDF of the normal distribution with mu=0, sigma=1:
Exclude the y values above and below 20%:
Show the y values above 40%:
Properties & Relations   (7)
Use ClippingStyle to style the region clipped by PlotRange:
In ordinary graphics, objects can extend beyond the plot range:
Use PlotRangeClipping->True to clip objects to the range:
Normally, plot functions clip objects to the range:
By default, 2% of padding is added to the plot range in each direction:
Prevent padding by setting PlotRangePadding to None:
Include 1 coordinate unit of padding on all sides:
No padding is added if the plot range is explicit:
Scaled coordinates are given by fractions of the plot range:
Neat Examples   (3)
An elementary function with pole singularities:
A function with a curve singularity:
A function with random poles:
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