This part I understand
The values can be determined by an elegant incremental algorithm opoerating on a single integer D represented by a machine word of n bits. The integer increment involved is d = floor(k*2 + 0.5)"
This I'm a little fuzzy about. What is a module 2^n addition?
The operation D <- D + d is a module 2^n addition with the overflow recorded.
This is essentially a classical DDA method... For the following analysis we may consider D as a fixed point number with the decimal point before its most significant bit, or conceptually percieve the proposed integer arithmetic as fixed point arithmetic. Thus the error between the real DDA increment and our integer DDA increment is e = k - d*2^(-n)
This I don't understand at all. How does he come up with that error. k is the slope and d is the increment, n is the number of bits in D. But how does he come up with a negative exponent and why is he subtracting.
Here he lost me completely. I understand that 2^m - 1 is the alpha basically, usually set to 255. But how did he tie in D and the error e? He goes on:
All gray-scale raster devices have 2^m, for some m > 1 discrete intensity levels from 0 to 2^m - 1. The intensity interpolation between the two vertically adjacent pixels becomes a bi-partition of the integer I, the maximum intensity. The intensity of the upper pixel for the line is
I( x, ceil(k*x) ) = (2^m - 1) * (D*2^(-n) + ex) = D*2^(m-n) + ....
The approximated I(x, ceil(k*x) ) ~ D*2^(m - n) is simply presented by the m most significant bits of D... Now we see that the integer D controls both the pixel positions and intensities
Can anyone tell me what the heck is he talking about?