Traversing grid in a snake like pattern

I have a rectangle defined by its four corners on a Cartesian coordinate system. The rectangle consist of identically sized cells.

Given one of the corner cells as a starting point and a direction (either along x or y axis) how can I traverse this grid in snake like pattern?

For example, here (x4, y4) is the starting cell and direction is defined to be along the x axis. Blue line depicts the desired path.

Thanks!

Try the 4 pair of points to find the opposite point that defines the box. Then you have a Start and an Opposite pair of points. In your case, followAlongX will be an input so it's not needed to test the direction but I added a classic decision text otherwise.

In the end, try something like (Java, written in Notepad, not tested):

int stepY, stepX, yMin, yMax, yOpposite, yStart, xMin, xMax, xOpposite, xStart;
if (yOpposite > yStart) {
    stepY = 1;
    yMin = yStart;
    yMax = yOpposite;
}
else {
    stepY = -1;
    yMax = yStart;
    yMin = yOpposite;
}

if (xOpposite > xStart) {
    stepX = -1;
    xMin = xStart;
    xMax = xOpposite;
}
else {
    stepX = 1;
    xMin = xOpposite;
    xMax = xStart;
}

// boolean followAlongX = false;
// if (xMax-xMin>yMax-yMin) {
//     loopOnX = true;
// }

List<Points> path = new ArrayList<>();
if (followAlongX) {
    for (int i=yMin; i!=yMax; i+=stepY) {
        for (int j=xmin; j!=xmax; j+=stepX) {
            path.add(new Point(i,j));
        }
        stepX = -stepX;
        int temp = xMin;
        xMin = xMax;
        xMax = temp;
    }
}
else {
    for (int j=xmin; j!=xmax; j+=stepX) {
        for (int i=yMin; i!=yMax; i+=stepY) {
            path.add(new Point(i,j));
        }
        stepY = -stepY;
        int temp = yMin;
        yMin = yMax;
        yMax = temp;
    }
}
return path.toArray(new Point[path.size()]);