116 
By multiplying the theoretical screen pixel height p with 
the increase factor - e.g., with a 1600% zoom in the factor 
is 16 - the height in millimeters of the “increased” screen 
pixel is acquired for a particular resolution (see: Table 6). 
The same procedure is applied for the calculation of the 
width of an “increased “ screen pixel in millimeters at a 
selected resolution. In this case the theoretical width a of 
the screen pixel must be multiplied by the increase factor 
(see: Table 6). 
Measured values on a 17" screen with shadow mask 
Resolution 
640x480 
1024x768 
1280x1024 
Increase 
“zoom in” 
n 
s 
n 
s 
n 
s 
1600% 
49-50 
33 
29-30 
20 
20-21 
15 
1200% 
36 
24 
21 
14-15 
15 
11 
800% 
24 
16 
13-15 
9-10 
10 
7 
300% 
8 
5-6 
3 
3 
2 
2 
200% 
5-6 
3 
2 
2 
1-2 
1 
100% 
3-4 
2 
1 P 
1 P 
n = number of rows; s = number of columns; P = screen pixel 
Table 5: Effects of the zoom function on a 17” screen with 
shadow mask. 
17" screen with shadow mask 
Resolution 
screen height 
/ number of 
rows 
theoretical 
height of 
the screen 
pixel 
[3 (mm) 
screen width 
/ number of 
columns 
theoretical 
width of 
the screen 
pixel 
a (mm) 
640x480 
800x600 
1024x768 
1152x864 
1280x1024 
233,172/480 
233,172/600 
233,172/768 
233,172/864 
233,172/1024 
0,485775 
0,38862 
0,303609 
0,269875 
0,227707 
310,896/640 
310,896/800 
310,896/1024 
310,896/1152 
310,896/1280 
0,485775 
0,38862 
0,303609 
0,269875 
0,2428875 
Table 6: Theoretical sizes of screen pixels on 17” screen 
with shadow mask. 
To determine the effective number of rows n and the 
number of columns s which in fact appear on the 17” 
screen with shadow mask, the value of n must be 
calculated with the equations (1) and the value s must be 
calculated with equations (2). Better understanding 
requires the comparison with figure 1. 
0.30 + (n-1) * 0,15 = Height 
n = (Height-0.30)/0,15 + 1 (1) 
n = number of rows 
0.30 + (s-1) * 0,22 = Width 
s = (Width - 030) / 0,22 + 1 (2) 
s= number of columns 
3.2 Generalization of the Transfer of Scan Pixels into 
Screen Pixels 
After the in the previous chapter carried out analysis of 
translating scan pixels into screen pixels at an integer 
number increase, it is now necessary to generalize the 
results of the analysis. In this chapter, we shall describe 
the transfer of scan pixels into screen pixels, i.e., the 
transfer of the pixmap coordinate system into the screen 
coordinate system. 
The screen coordinate system has its starting point in the 
lower left corner of the screen, its unit is a screen pixel, 
the positive direction of the x-axe spreads to the right and 
that of the y-axe spreads upwards in relation to the 
starting point. As we have already seen, the form and the 
size of the screen pixel change depending on the type 
and the size of the screen and of the selected resolution. 
Pixmap coordinate system also has its starting point in the 
lower left corner of the screen, its unit is scan pixel, the 
positive direction of the x-axe spreads to the right, and the 
positive direction of the y-axe spreads upwards in relation 
to the starting point. 
In general, the transfer between two coordinate systems 
is defined through linear transformation, which, in the 
matrix recording, looks as follows: P’ (x\ y’, 1) = M x P T , 
where M is transformation matrix and P T is the 
transponded vector (Malic 1998). Transformation matrix M 
can be divided into transformation matrix Mj with the 
requested coefficients t x and t y , into scaling matrix Ms with 
the requested coefficients s x and s y , and into rotation 
matrix Mr with the requested coefficients sin f; and cos f;. 
We are going to consider only the determination of the 
scaling matrix coefficients (Ms; s x and s y ) because they 
are responsible for the translation of scan pixels into 
screen pixels when the image is increased (zoom in) or 
decreased (zoom out) by means of pure hardware zoom, 
the so-called “pixel replication zoom”. 
Figure 7 shows the translation of a pixmap into the 
coordinate system of the screen with tension mask, 
whereby the scan pixel Py in the pixmap is defined by 
means of diagonally lying points A (i - 1, j - 1) and B (i,j), 
and the corresponding screen pixel P’y is also defined by 
means of diagonally lying points A’ (ua, v a ) and B’ (ub, vb). 
¡-1 I X 1*1 Ub 
a) to) 
Figure 7: Translation of scan pixels from pixmap a) into 
the coordinate system of the screen with tension mask b). 
Scan pixel is increased or decreased by the given scale 
factor N and then it is recalculated into the screen 
coordinate system. While this is being done, the relations 
between the sides (b/a) must be taken into account, 
because scan pixels are square in form, whereas screen 
pixels take up various rectangular shapes. The 
coefficients s x and s y of the scaling matrix Ms are used for 
mathematical description of that procedure (equations 
(3)): 
s x = N * b/a and s y = N (3) 
Through translation functions f( X ) and g( y ) the concrete 
scan pixel Py, defined by means of the points A and B, is 
translated into the corresponding screen pixel P’y defined 
by the points A’ and B’. Here the acquired coordinates