The Structure of Graphics
"Graphics and Sound" discusses how to use functions like
Plot and
ListPlot to plot graphs of functions and data. Here, we discuss how
Mathematica represents such graphics, and how you can program
Mathematica to create more complicated images.
The basic idea is that
Mathematica represents all graphics in terms of a collection of
graphics primitives. The primitives are objects like
Point,
Line and
Polygon, that represent elements of a graphical image, as well as directives such as
RGBColor and
Thickness.
This generates a plot of a list of points.
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InputForm shows how Mathematica represents the graphics. Each point is represented as a coordinate in a Point graphics primitive. All the various graphics options used in this case are also given.
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Each complete piece of graphics in
Mathematica is represented as a
graphics object. There are several different kinds of graphics object, corresponding to different types of graphics. Each kind of graphics object has a definite head which identifies its type.
| Graphics[list] | general two-dimensional graphics |
| Graphics3D[list] | general three-dimensional graphics |
Graphics objects in Mathematica.
The functions like
Plot and
ListPlot discussed in
"The Structure of Graphics and Sound" all work by building up
Mathematica graphics objects, and then displaying them.
You can create other kinds of graphical images in
Mathematica by building up your own graphics objects. Since graphics objects in
Mathematica are just symbolic expressions, you can use all the standard
Mathematica functions to manipulate them.
Graphics objects are automatically formatted by the
Mathematica front end as graphics upon output. Graphics may also be printed as a side effect using the
Print command.
The Graphics object is computed by Mathematica, but its output is suppressed by the semicolon.
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A side effect output can be generated using the Print command. It has no Out[] label because it is a side effect.
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| Show[g, opts] | display a graphics object with new options specified by opts |
| Show[g1,g2,...] | display several graphics objects combined using the options from g1 |
| Show[g1,g2,...,opts] | display several graphics objects with new options specified by opts |
Displaying graphics objects.
Show can be used to change the options of an existing graphic or to combine multiple graphics.
This uses Show to adjust the Background option of an existing graphic.
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This uses Show to combine two graphics. The values used for PlotRange and other options are based upon those which were set for the first graphic.
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Here, new options are specified for the entire graphic.
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Local and global ways to modify graphics.
Given a particular list of graphics primitives,
Mathematica provides two basic mechanisms for modifying the final form of graphics you get. First, you can insert into the list of graphics primitives certain
graphics directives, such as
RGBColor, which modify the subsequent graphical elements in the list. In this way, you can specify how a particular set of graphical elements should be rendered.
This creates a two-dimensional graphics object that contains the Polygon graphics primitive.
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InputForm shows the complete graphics object.
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This takes the graphics primitive created above, and adds the graphics directives RGBColor and EdgeForm.
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By inserting graphics directives, you can specify how particular graphical elements should be rendered. Often, however, you want to make global modifications to the way a whole graphics object is rendered. You can do this using
graphics options.
By adding the graphics option Frame you can modify the overall appearance of the graphics.
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You can specify graphics options in
Show. As a result, it is straightforward to take a single graphics object, and show it with many different choices of graphics options.
Notice however that
Show always returns the graphics objects it has displayed. If you specify graphics options in
Show, then these options are automatically inserted into the graphics objects that
Show returns. As a result, if you call
Show again on the same objects, the same graphics options will be used, unless you explicitly specify other ones. Note that in all cases new options you specify will overwrite ones already there.
| Options[g] | give a list of all graphics options for a graphics object |
| Options[g,opt] | give the setting for a particular option |
Finding the options for a graphics object.
Some graphics options can be used as options to visualization functions which generate graphics. Options which can take the right-hand side of
Automatic are sometimes resolved into specific values by the visualization functions.
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Mathematica uses an internal algorithm to compute an explicit value for PlotRange in the resulting graphic.
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| FullGraphics[g] | translate objects specified by graphics options into lists of explicit graphics primitives |
Finding the complete form of a piece of graphics.
When you use a graphics option such as
Axes, the
Mathematica front end automatically draws objects such as axes that you have requested. The objects are represented merely by the option values rather than by a specific list of graphics primitives. Sometimes, however, you may find it useful to represent these objects as the equivalent list of graphics primitives. The function
FullGraphics gives the complete list of graphics primitives needed to generate a particular plot, without any options being used.
This plots a list of values.
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FullGraphics yields a graphics object that includes graphics primitives representing axes and so on.
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