php - Bresenham lines w/o diagonal movement

Question

Is there a modified Bresenham algorithm, where the step from one pixel to the next one isn't allowed to be diagonally, just horizontally or vertically? Or any other algorithm which does that? (PHP preferred)

Right:
0 0 0 1
0 0 1 1
0 1 1 0
1 1 0 0

Wrong:
0 0 0 1
0 0 1 0
0 1 0 0
1 0 0 0

Answer 1

James' answer is pretty cool, but as he commented, it skews the line a bit. Another simple modification of the original Bresenham draws a line without diagonal steps that is closer to the "real" line.

This is an implementation of the original Bresenham algorithm:

public void line(int x0, int y0, int x1, int y1, int value) {
    int xDist =  Math.abs(x1 - x0);
    int yDist = -Math.abs(y1 - y0);
    int xStep = (x0 < x1 ? +1 : -1);
    int yStep = (y0 < y1 ? +1 : -1);
    int error = xDist + yDist;

    plot(x0, y0, value);

    while (x0 != x1 || y0 != y1) {
        if (2*error > yDist) {
            // horizontal step
            error += yDist;
            x0 += xStep;
        }

        if (2*error < xDist) {
            // vertical step
            error += xDist;
            y0 += yStep;
        }

        plot(x0, y0, value);
    }
}

The modification is simply to do either a horizontal or vertical step, not both, depending on whether the error indicator is nearer to a horizontal or vertical step:

public void lineNoDiag(int x0, int y0, int x1, int y1, int value) {
    int xDist =  Math.abs(x1 - x0);
    int yDist = -Math.abs(y1 - y0);
    int xStep = (x0 < x1 ? +1 : -1);
    int yStep = (y0 < y1 ? +1 : -1);
    int error = xDist + yDist;

    plot(x0, y0, value);

    while (x0 != x1 || y0 != y1) {
        if (2*error - yDist > xDist - 2*error) {
            // horizontal step
            error += yDist;
            x0 += xStep;
        } else {
            // vertical step
            error += xDist;
            y0 += yStep;
        }

        plot(x0, y0, value);
    }
}

This effectively chooses the kind of step that minimizes the error, thus resulting in a line that is closer to the real line.

The code is in Java, but it should be easily portable to PHP. I haven't thoroughly tested it, but it should work just as well as the original Bresenham. It may even be a tad faster.