Get all pixels a ray passses through

Question

I have a 2 dimensional space and a ray in that space.

I need to get the coordinates of the red rectangles in the order of the numbers.

My attempt: I have the starting of the ray which is a double.
I have a value yaw which is the direction in radians.
The I did this to get the coordinate of the next red square.

double tanyaw = Math.tan(yaw);
if ((int) (x + 1/tanyaw) == (int) x) {
    x += 1/tanyaw;
    z += Math.signum(tanyaw);
} else {
    x += Math.signum(tanyaw);
    z += tanyaw;
}

However:

That was with yaw = 3*pi/8 note that the line was made in a drawing program and is only approximatly correct.

Answer 1

Line equation is:

x = x0 + t*xd
y = y0 + t*yd

For simplicity define that begin of shot leaves at t=0 and the last position to test is at t=1. Then you can simple define step sizes with (assuming that you can simple calculate the end position x1,y1):

xstep = 1/(x1 - x0)
ystep = 1/(y1 - y0)
xpos = x0
ypos = y0

And then simple loop until you hit the intersection or end using:

while(!hitsomething()) {
    if (xpos + xstep - x0 < ypos + ystep - y0) {
           xpos += xstep;
           visit(xpos, ypos);
    } else {
           ypos += ystep;
           visit(xpos, ypos);
    }
}