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 algorit

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.