What does the variable D do inside the while in this Bresenham's line drawing algorithm?

Question

I've found this Generalized Bresenham's Line Drawing Algorithm and I'm having a hard time understanding what the while is doing here.

Any help is greatly appreciated.

the code:

#define sign(x) ((x > 0)? 1 : ((x < 0)? -1: 0))

x = x1; 
y = y1;
dx = abs(x2 - x1); 
dy = abs(y2 - y1);
s1 = sign(x2 - x1); 
s2 = sign(y2 - y1);
swap = 0;

if (dy > dx) {
    temp = dx;
    dx = dy;
    dy = temp;
    swap = 1;
}

D = 2*dy - dx;
for (i = 0; i < dx; i++) {
    display_pixel (x, y); 
    while (D >= 0) { 
        D = D - 2*dx;
        if (swap)
            x += s1;
        else
            y += s2;
    } 
    D = D + 2*dy;
    if (swap)
        y += s2;
    else
        x += s1; 
} 

Answer 1

D is the scaled distance from the line to the candidate x, y coordinate.

Better: D is scaled difference of the distance from the line to the candidates x+1, y+0 and x+1, y+1.

That is, as x increments, the sign of D indicates should the closer y increment by 0 or 1?

(The role of x, y interchanges depending on which octant the algorithm is applied.)

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I expected while (D >= 0) { as if (D >= 0) {. Bresenham's line algorithm

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Note that OP's code is subject to overflow in abs(x2 - x1) and 2*dy - dx. Alternates exist that do not rely on wider math.