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.

Answer 2

I have found that Franz D's answer produces lines that do not closely match the original when close to the horizontal or vertical. While the function below is not perfect, I have found it produces nicer results.

Function BresenhamLineNew : Void( x0 : Int, y0 : Int, x1 : Int, y1 : Int )

    Local dx : Int = Abs( x1 - x0 )
    Local dy : Int = Abs( y1 - y0 )

    Local sx : Int = -1
    Local sy : Int = -1

    If x0 < x1 Then sx = 1
    If y0 < y1 Then sy = 1

    Local err : Int = dx - dy
    Local e2 : Int

    While True

        DrawRect x0, y0, 1, 1

        If x0 = x1 And y0 = y1 Then Exit

        e2 = 2 * err

        If dy > dx
            If e2 > -dy
                err = err - dy
                x0 = x0 + sx
            Elseif e2 < dx
                err = err + dx
                y0 = y0 + sy
            Endif
        Else
            If e2 < dx
                err = err + dx
                y0 = y0 + sy
            Elseif e2 > -dy
                err = err - dy
                x0 = x0 + sx
            Endif
        Endif

    Wend

End Function

Answer 3

Should be a trivial modification - let's say you're in the quadrant I - i.e. going up and to the right. Instead of doing a diagonal, do an up... and then a right.

Instead of:

  for x from x0 to x1
             plot(x,y)
             error := error + deltaerr
             if error ≥ 0.5 then
                 y := y + 1
                 error := error - 1.0

Something like this:

for x from x0 to x1
         plot(x,y)
         error := error + deltaerr
         if error ≥ 0.5 then
             y := y + 1
             plot(x,y)
             error := error - 1.0