Dithering
Syntax: |
DENSITY\DITHERING { x y } z { p1 p2 }
|
Qualifiers: |
\LEGEND, \DITHERVECTOR, \CONTOURS, \LEVELS, \AREAS, \VOLUMES, \LINES, \EQUALLYSPACED,
\PARTIAL, \XPROFILE, \YPROFILE, \BORDER, \AXES, \RESET
|
Defaults: |
if
|
In this type of density plot, by default, the range of data values is divided into ten (10) equally spaced levels and a different dithering pattern is associated with each level. A value is interpolated at every pixel location within the bounds of the data region to determine the level for that point. The dithering pattern for that level then determines whether that pixel is to be lit up. Thus, the boundaries of the data are divided up into different dithering pattern regions.
Input variables
If z
is a vector, the parameters x
and y
are expected and must be vectors. x
and y
are assumed to represent a scattered set
of points, where z[i]
is the altitude corresponding to the location
(x[i],y[i])
. A matrix is interpolated on these scattered points by means of a Thiessen
triangulation of the plane. The three vectors must be the same length.
If z
is a matrix, the parameters x
and y
default to
[1;2;3;...]
, but if entered they must be vectors. Each matrix element,
z[i,j]
, is associated with the coordinates (x[j],y[i])
. The
length of x
must be equal to the number of columns of z
and the length of
y
must be equal to the number of rows. The vectors x
and
y
are used for scaling the axes.
Dithering pattern definition
The default dithering pattern vector is:
[ 1;1; 2;1; 2;2; 3;2; 3;3; 4;3; 4;4; 5;5; 6;6; 0;0 ]
A user defined dithering pattern can be entered by using the
\DITHERVECTOR
qualifier and entering the
dithering pattern vector, d
, as the first parameter.
The dithering pattern is determined by pairs of numbers from
d
, so the number of dithering patterns defined by d
is ½ the
length of d
.
For pattern number i
, every
d[2i-1]
th pixel is lit up horizontally, and every
d[2i]
th pixel is lit up vertically. For example, if
d[1]=1
and d[2]=1
, then for level 1
every pixel is lit up, while if
d[3]=2
and d[4]=3
, then for level 2
every
second pixel is lit up horizontally and every third pixel is lit up vertically.
Changing the range of values
The optional parameters p1
and p2
can be used to broaden or shrink
the range of data values. If zmax
is the maximum value of the data and zmin
} is the minimum value of the
data, the full colour range will be from a minimum of
min = p1*(zmax-zmin)+zmin
to a maximum of max = p2*(zmax-zmin)+zmin
.
If z
is a data value and if
z < p1*(zmax-zmin)+zmin
,
that data value is treated as zmin
.
If z > p1*(zmax-zmin)+zmin
,
that data value is treated as zmax
.
The default values are: p1=0
and p2=1
.
Legend
If the \LEGEND
qualifier is used, a legend is
drawn along the right side of the axes. The legend requires the right end of the
x-axis to be set to 75%
of the window, that is,
XUPPERAXIS
is set to 75%
.
When a y-profile is drawn, using the
\YPROFILE
qualifier, the right edge of the
axis box must allow space for the profile as well as a possible legend. If a
y-legend profile and a legend are present, then
XUPPERAXIS
is set to 65%
. If a
y-legend profile is present but not a legend, then
XUPPERAXIS
is set to 85%
.
By default, XUPPERAXIS
is reset to its former value after the
DENSITY
command. If the /-RESET
qualifier is used, the
axis location is not reset.
Contours
By default, a contour line is drawn around the boundary of each dithering
pattern region. If the \-LINES
qualifier is
used, then these contour lines will not be drawn.
If the qualifier \CONTOURS
is used, an
automatically created vector named
DENSITY$CONTOURS
will be made which will
contain the boundary values of each region. If there are N
regions, the
length of DENSITY$CONTOURS
will be
N+1
.
User specified contour levels
A specific set of contour levels can be entered by using
\LEVELS
and entering a vector of contour level
values, lvl
, as the first parameter,
unless the \DITHERVECTOR
qualifier is also used,
in which case the contour level vector should be the second parameter. If both are
used, and the length of the dithering vector is N
, the length of the
level vector must be N/2 - 1
. Suppose that
zmin
and zmax
are the minimum and
maximum of the data z
. The level vector must be
strictly monotonically increasing, with lvl[1] > zmin
and lvl[#] < zmax
.
The \EQUALLYSPACED
qualifier only applies
to the case of a dithering type density plot with legend, where the user supplies the
contour levels, for example:
DENSITY\DITHERING\LEVELS\LEGEND\EQUALLYSPACED lvl x y m
If the \EQUALLYSPACED
qualifier is used, the
legend boxes will all be the same size, irregardless of the values specified in the
levels vector, lvl
.
Areas and volumes
If the \AREAS
qualifier is used, an
automatically created vector named DENSITY$AREAS
will be made which will contain the percentage areas contained within each region. If
the \VOLUMES
qualifier is used, an automatically created vector named
DENSITY$VOLUMES
will be made which will
contain the percentage volumes contained within each region. If there are
N
regions, the length of
DENSITY$AREAS
and
DENSITY$VOLUMES
will both be N
.
Also, the sum of the elements of each of these vectors will always be
100
.
Examples
These examples use the following vectors.
X=[ 1; 0; 1; 0; .2; .3; .5; .8] Y=[ 5; 5; 0; 0; 1;1.5; 2.5; 4] Z=[ 10; 10; 10; 10; -100; 10; -100; 500] D=[ 1;1; 2;2; 4;4; 7;7; 11;11; 0;0 ]
DENSITY\DITHERING X Y Z
DENSITY\DITHERING\LEGEND X Y Z
DENSITY\DITHERING\DITHERVECTOR\LEGEND D X Y Z