Image Blending/Compositing

(f(alpha)I_src) (OP) (g(alpha)I_dest) = I_dest
where
OP = add, minus, etc.

The order of operations is important when doing alpha blending.

Defintion: image processing = discrete signal processing in 2D

Combining images using interpolation - there are 2 methods of interpolation used (Nearest Neighbor and Bilinear)

Nearest Neighbor
I(x,y) where x and y are float values

Round the values to the nearest integer
x_r = round(x)
y_r = round(y)

Then reset the pixel to the rounded value
output_value = I(x_r, y_r)


Bilinear Interpolation. 
This is linear interpolation. It is often called a lerp()

function lerp(v_0, v_1, t) {
	return (1-t)*v_0 + t*v_1
}

Step 1
	linear interpolation between (x_f, y_f) and (x_c, y_f)

Step 2
	linear interpolation between x_f and x_c at y_c

Step 3
	interpolate the results of the two linear interpolations in x in the y direction


I_y_f = lerp( I[x_f, y_f], I[x_c, y_f], x-x_f )
I_y_c = lerp( I[x_f,y_c], I[x_c, y_c], x-x_f )
I_xy = lerp( I_y_f, I_y_c, y-y_f )

x_f = floor(x)
x_c = x_f + 1
y_f = floor(y) 
y_c = y_f + 1