Based on Wikipedia's article on Bresenham's line algorithm I've implemented the simplified version described there, my Java implementation looks like this:
int dx = Math.abs(x2 - x1);
int dy = Math.abs(y2 - y1);
int sx = (x1 < x2) ? 1 : -1;
int sy = (y1 < y2) ? 1 : -1;
int err = dx - dy;
while (true) {
framebuffer.setPixel(x1, y1, Vec3.one);
if (x1 == x2 && y1 == y2) {
break;
}
int e2 = 2 * err;
if (e2 > -dy) {
err = err - dy;
x1 = x1 + sx;
}
if (e2 < dx) {
err = err + dx;
y1 = y1 + sy;
}
}
Now I do understand that err
controls the ratio between steps on the x-axis compared to steps on the y-axis - but now that I'm supposed to document what the code is doing I fail to clearly express, what it is for, and why exactly the if-statements are, how they are, and why err
is changed in the way as seen in the code.
Wikipedia doesn't point to any more detailled explanations or sources, so I'm wondering:
What precisely does err
do and why are dx
and dy
used in exactly the shown way to maintain the correct ratio between horizontal and vertical steps using this simplified version of Bresenham's line algorithm?