CRITERIA FOR THE DESIGN OP OPTIMAL PROCESS CONTROL GRAPHIC DISPLAYS
2. To select a minimum number of fonts all of them belonging to only one graphical entity and with a minimum number of
2.3.21 can always be applicable depending on the considera
tions stated.
Finally, we know that the sophisticated graphical displays use generally random-scanning to produce the pictures on the screen. This scanning method permits the successive use of the different types of generators /used for the generation
45
-of vectors, characters, circles, etc,/ one after each other, depending only on the program prepared.
Returning to Exp. 2.3.21, it is seen that in all cases we obtain positive and integral values for "z". This means that the only way to diminish the number of information bits
per picture is using either in the system:
- a small total number of graphical entities "k"
- a small total number of fonts "J" per graphical entity - a small total number of graphical elements "I" per font - a small number of graphical elements "b" requiring absolute
position information
- and a minimal number of addressable points "N" on the useful surface.
Obviously, no influence can be exerted over the value ”B"
because it depends on the specific picture displayed.
Y/e shall analize now some alternatives in order to minimize the Exp. 2.3.21. First of all, we shall analize the term
"blogzN " .
This term gives the total number of information bits
required to position absolutely all the graphical elements
"b" which require it, belonging to any font, on whichever of the possible addressable points "N" of the useful surface
"s" .
In the most general case, every graphical element composing a picture requires position information to be settled in place on the useful surface "S". However, it does not have any visual information itself, though it is necessary for the composition of the picture in a comprehensible form to the observer or operator. As its frequency of utilization
46
-increases with the complexity of the picture, some solu
tions have been found to diminish the total number of in
formation bits used for positioning operation. The most important one is the facility of relative positioning in almost all graphical display, thus saving position instruc
tions since the different graphical elements are settled like if they were "connected" or "joined" together with each other. Nevertheless, the use of absolute positioning is
indispensable to position physically independent parts of the whole picture, or at least, at the beginning of the picture’s tracing.
It is of great importance not only to minimize the number of times the position information must be used, but to see that the number of information bits required for positioning be a minimum. To give higher flexibility to present displays, the number of addressable points "N " on the screen has been commonly raised as high as possible, being limited mainly by the cost. This is the case of the costly sophisticated
graphical displays.
One on the main goals in this study is to meet the condi
tions for a graphical display of wide applicability, but with low cost. Por this reason, we analyze the possibilities of using a lesser number of addressable points for
positioning operation of graphical elements without considerable loss of flexibility.
Let
X = log2N N>1 ; X>0 (2.3.23)
be a function where "N" is the total number of addressable points on the useful surface "S" and "X" the minimum number of information bits required to define uniquely any of them /See Exp. 2.3.2/.
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-The general mathematical expression of the logarithmic func
tion is C 311D:
X = logfa ^ (2.3.24)
Exp. 2.3-24, with similar conditions to those of the Exp.
2.3.23, that is:
У
— >_ 1 ; x >_0 a
has a relative minimum for "x" in the value y=a /Pig. 2.2/.
Fig. 2.2
If Exp. 2.3.23 is written in a similar form, we have:
X = log2 I N>1 ; X>0
Hence, comparing this expression with Exp. 2.3.24, it is seen that it has a relative minimum in N=1 in the range specified. This is the case of the slide projecting display system analized above; a position information lesser than this is not possible.
If we write now the Exp. 2.3.23 in the form:
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-X = log2h U N>h>l ; X>0 (2.3.25)
it remains the same.
Exp. 2.3.25 can also be written as:
X = log2h + 1одг ^ (2.3.26)
N N
In this expression, the term log2^/ if ^ > 1 , has a minimum in N=h by similar considerations than formerly.
Exp. 2.3.26 can be interpreted as a solution for our purpose, if the useful surface "S" having a total number of
addressable points "N" is completely subdivided in "c"N
equal portions each one having "h" points. Thus, N 11is now the arbitrary number of addressable joints /from the total number "N"/ for each equal portion obtained as product of the subdivision. For this consideration, of course, we have considered an uniformly ordered arrangement of all the points on the surface.
Now if we consider the quantity of points "h" as the necessary and sufficient amount of points to represent a unity of visual information, then the term log2 ^ N can be
considered now as the number of information bits required to position each one of these unities of information on the useful surface "S".
The term
X = log2h N^h>l ; X>0
gives us the number of information bits saved with this artifice.
Then, we can conclude that the number of information bits
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-required for positioning has been reduced in a quantity equal to logzh, i.e.
X' = X - log2h = log2^
represents the number of bits required now to position each unity of information created.
The result of this analysis is no more than the solution given to the well-known alphanumerical display, where the unities of information consist in a specific and well-known limited number of alphabet letters, digits and punctuation marks from a given font.
In this study, based on the above, we propose a similar solution for an interactive graphical display oriented to process control application.
As a result of this, we can consider now as the only one type of graphical entity, those portions in which the useful surface have been subdivided. Thus, in our analysis we have now:
к = 1
which is the minimal possible value for this variable.
In order to minimize the other parts of this term, that is the value "b", three solutions can be proposed:
- to make a great use of relative positioning in creating the pictures,
- to make a great use of the repetition facility to represent the graphical elements,
- to make a great use of graphical subroutines, i.e. to use macroinstructions to represent those part in the picture which have the same topology.
We shall consider these three alternatives as new criteria
51 -2.4.2 Hypothesis
In order to get practical results, the following hypothesis is stated for further analysis:
- All the cells must have the same area.
Then: s=s~=...=s = s
1 2 n
Therefore, from Exp. 2.4.1:
ns = S (2.4.2)
where : S n s
is the total area of the useful surface
is the total number of cells within the surface is the area of a single cell.