Graphics Reference
In-Depth Information
he Cartesian product of two sets A and B is the set consisting of all possible or-
dered pairs
,wherea is a member of set A and b is a member of set B.Manyof
our innovative graphs are formed as a rectangular set of panels, or subgraphs, where
eachpanelisbasedononepairfromaCartesianproduct.hesetsdefiningtheCarte-
sian productdiffer for each graph type. For example, a set can be a collection of vari-
ables,functionsofasinglevariable,levelsofasinglefactor,functionsofafittedmodel,
different models, etc.
WhenconstructingagraphthatcanbeenvisionedasaCartesianproduct,itisnec-
essary that the code writer be aware of the Cartesian product relationship. he code
for such a graph includes a command that explicitly states the Cartesian product.
(
a, b
)
Trellis Paradigm
6.2.1
Manyofthegraphsinthisarticleareconstructedusingthetrellisparadigmpioneered
by S-Plus. he trellis system of graphics is based on the paradigm of repeating the
same graphical specifications foreach element in a Cartesian productof levels of one
or more factors.
he majority of the methods supplied in the S-Plus
trellis
library are based
on a typical formula having the structure
(
.
)
y~x|a*b
where
y
is either continuous or a factor
x
is continuous
a
is a factor
b
is a factor
and each panel is a plot of
y~x
for the subset of the data defined by the Cartesian
product of the levels of
a
and
b
.
Implementation of Trellis Graphics
6.2.2
heconceptoftrellisplotscanbeimplementedinanygraphicssystem.IntheSfamily
of languages (S-Plus and R), selection of the set of panels, assignment of individual
observations to one panel in the set, and coordinated scaling across all panels is au-
tomated in response to a formula specification at the user level. In other languages
that are capable of displaying multiple panels on the same physical page, the user (at
this writing) is responsible for those tasks.
heterm“trellis”comesfromgardening,whereitdescribesanopenstructureused
as a support for vines. In graphics, a trellis provides a framework in which related
graphs can be placed.
