NEC µPD72257 Preliminary User's Manual page 243

Drawing Engine
In O' the mapping is like this:
0 u 0
  ~   
 
' 0
p =     ⇒ p =     =  
0 0
0 v 0
    
0
dx u
   ~   

1 1
d =     ⇒ p =     =  
1 1
dy v
    
1 1
dx u
   ~  

2 2
d =     ⇒ p =     =
2 2
dy v
   
2 2
This is a linear mapping the can be described by a 2x2 matrix.
m m
~  
  
p M p = '   11 12 ⋅   p
= ⋅
m m
 
21 22
w 0
    
⇒     = M ⋅ d ∧     = M
1
0 h
   
If you expand this and sort the equations you get 2 equation systems each with 2
unkowns. These can be described more easily with a new matrix.
dx dy

  1
A =
Let
dx dy

2
w m w
     
11
    = A ⋅     ∧     = A
0 m 0
     
12
This can be easily solved with determinants
1 1
Let c = =
det A dx ⋅ dy −
1 2
Then the resulting constants are:
du
m = c ⋅ w ⋅ dy =
11 2
dx
du
m c w dx
= − ⋅ ⋅ =
12 2
dy
dv
m = c ⋅ h ⋅ dx =
21 1
dx
dv
m c h dx
= − ⋅ ⋅ =
22 2
dy
To calculate the start values for u and v at the top of the bounding box the
transformation into O from O' has to be reversed. Let u
then:
u − w
  

( )
s
    M p c  
= ⋅ − = ⋅
0
v + h
  
s
Preliminary User's Manual S19203EE1V3UM00

 

w

 
0

0
 
   
h
 
'

⋅ d
2

1  
then the equation system can be rewritten as:

2
m
 
11
⋅    
m
 
12
dx ⋅ dy
2 1
( )
⋅ x ⋅ dy − y ⋅ dx

0 2 0 2
 
( )
⋅ x ⋅ dy − y ⋅ dx

0 1 0 1
Chapter 8
and v be the start values
s s
243