                   ==========================================
                   The Scale2x, Scale3x and Scale4x algorithm
                   ==========================================


SCALE2X ALGORITHM
=================

The effect works repeating a computation pattern for every
pixel of the original image.
The pattern starts from a square of 9 pixels and expands the
central pixel computing 4 new pixels.

Starting from this pattern :

    A B C
    D E F
    G H I

The central pixel E is expanded in 4 new pixels:

    E0 E1
    E2 E3

with these rules (in C language) :

    E0 = D == B && B != F && D != H ? D : E;
    E1 = B == F && B != D && F != H ? F : E;
    E2 = D == H && D != B && H != F ? D : E;
    E3 = H == F && D != H && B != F ? F : E;

which can be rewritten as :

    E0 = D == B && B != H && D != F ? D : E;
    E1 = B == F && B != H && D != F ? F : E;
    E2 = D == H && B != H && D != F ? D : E;
    E3 = H == F && B != H && D != F ? F : E;

and optimized as:

    if (B != H && D != F) {
    	E0 = D == B ? D : E;
    	E1 = B == F ? F : E;
    	E2 = D == H ? D : E;
    	E3 = H == F ? F : E;
    } else {
    	E0 = E;
    	E1 = E;
    	E2 = E;
    	E3 = E;
    }

The image border is computed reusing the value of the nearest pixel
on the border when the value of a pixel over the border is required.


SCALE3X ALGORITHM
=================

Starting from this pattern :

    A B C
    D E F
    G H I

The central pixel E is expanded in 9 new pixels:

    E0 E1 E2
    E3 E4 E5
    E6 E7 E8

with these rules (in C language) :

    E0 = D == B && B != F && D != H ? D : E;
    E1 = (D == B && B != F && D != H && E != C) || (B == F && B != D && F != H && E != A) ? B : E;
    E2 = B == F && B != D && F != H ? F : E;
    E3 = (D == B && B != F && D != H && E != G) || (D == H && D != B && H != F && E != A) ? D : E;
    E4 = E
    E5 = (B == F && B != D && F != H && E != I) || (H == F && D != H && B != F && E != C) ? F : E;
    E6 = D == H && D != B && H != F ? D : E;
    E7 = (D == H && D != B && H != F && E != I) || (H == F && D != H && B != F && E != G) ? H : E;
    E8 = H == F && D != H && B != F ? F : E;

and optimized as:

    if (B != H && D != F) {
    	E0 = D == B ? D : E;
    	E1 = (D == B && E != C) || (B == F && E != A) ? B : E;
    	E2 = B == F ? F : E;
    	E3 = (D == B && E != G) || (D == H && E != A) ? D : E;
    	E4 = E;
    	E5 = (B == F && E != I) || (H == F && E != C) ? F : E;
    	E6 = D == H ? D : E;
    	E7 = (D == H && E != I) || (H == F && E != G) ? H : E;
    	E8 = H == F ? F : E;
    } else {
    	E0 = E;
    	E1 = E;
    	E2 = E;
    	E3 = E;
    	E4 = E;
    	E5 = E;
    	E6 = E;
    	E7 = E;
    	E8 = E;
    }


SCALE4X ALGORITHM
=================

The Scale4x effect is simply the Scale2x effect applied two times.
