
Functions and linearity (1) 
Defined the function
decomposing each variable with a linear combination :
where is the coefficient for the combination,
we get
and finally

Functions and linearity (2) 
Once defined the linear combination
with
applying an affine transformation
we get

Perspective correct mapping 
In the system of coordinates where the observer O is in the point
and the projection screen has equation Y=d:

Given the real points
we have their perspective projections
; taking a linear combinations of them
we can locate the corresponding projected real point
on the real line joining
.
Using the notation for each coordinates of the new real point
and for the original real points ,
we have the Perspective correct mapping :
Wich is very different from the simple Affine texture mapping :
