// Generalized Integer Bresenham's Algorithm for all quadrants
// all variables are assumed integer
// sign function returns -1, 0, 1 as its argument is < 0, = 0 or > 0
bresenham_algorithm(x1, y1, x2, y2)

    // initialize variables
    x = x1
    y = y1
    delta_x = abs(x2 - x1)
    delta_y = abs(y2 - y1)
    s1 = sign(x2 - x1)
    s2 = sign(y2 - y1)

    // interchange delta_x and delta_y, depending on the slope of the line
    if delta_y > delta_x then
        interchange(delta_x, delta_y)
        interchanged is true
    else interchanged is false
    end if

    // initialize the error term to compensate for a nonzero intercept
    error = 2 * delta_y - delta_x

    for i = 0 to delta_x
        set_pixel(x, y)

        while error > 0
            if interchanged is true then x = x + s1
            else y = y + s2
            end if
            error = error - 2 * delta_x
        end while

        if interchanged is true then y = y + s2
        else x = x + s1
        end if

        error = error + 2 * delta_y
    end for
end