My implementation of Breshenem's algorithm fails for lines at certain angles

Question

I wrote an implementation of the Breshenem algorithm in Python (after the Wikipedia article ), and it works correctly, except for lines at certain angles. All lines that should extend from 45 to 90 degrees, or from 135 to 270 degrees, will expand along the line y = x.

Here is my code:

def bresenham(origin, dest):
    # debug code
    print origin
    print dest
    # end debug code
    x0 = origin[0]; y0 = origin[1]
    x1 = dest[0]; y1 = dest[1]
    steep = abs(y1 - y0) > abs(x1 - x0)
    backward = x0 > x1

    if steep:
        x0, y0 = y0, x0
        x1, y1 = y1, x1
    if backward:
        x0, x1 = x1, x0
        y0, y1 = y1, y0

    dx = x1 - x0
    dy = abs(y1 - y0)
    error = dx / 2
    y = y0

    if y0 < y1: ystep = 1 
    else: ystep = -1

    result = []
    #if x0 > x1: xstep = -1
    #else: xstep = 1
    # debug code
    print "x0 = %d" % (x0)
    print "x1 = %d" % (x1)
    print "y0 = %d" % (y0)
    print "y1 = %d" % (y1)
    for x in range(x0, x1):
        if steep: result.append((y,x))
        else: result.append((x,y))
        error -= dy
        if error < 0:
            y += ystep
            error += dx 
    # ensure the line extends from the starting point to the destination
    # and not vice-versa
    if backward: result.reverse()
    print result
    return result

Does anyone see me screwing up?

---

EDIT:

I added some print code to the function.

(0,0) is located in the upper left corner of the display.

My test framework is pretty simple. This is a standalone function, so I just pass two points to it:

  

= (416, 384)
    dest = (440, 347)
    bresenham (, dest)
    (416, 384)
    (440, 347)
    x0 = 384
    x1 = 347
    y0 = 416
    y1 = 440
    []

  

Answer 1

, xstep. , .

@Gabe: xstep, , x0 > x1, for , Python for 1.

, xstep, , , ( if backward: ), , -.

:

result = []

for x in range(x0, x1):
    if steep: result.append((y, x))
    else: result.append((x, y))
    error -= dy
    if error < 0:
        y += ystep
        error += dx

return result

, :

if backward: return result.reverse()
else: return result

. , backward , . steep, , backward . , backward boolean, :

if x0 > x1:
    # swapping here

, , :

backward = x0 > x1

if backward:

Answer 2

, x0 > x1 , x y.

:

backward = x0 > x1 

if steep: 
    x0, y0 = y0, x0 
    x1, y1 = y1, x1 
if backward: 
    x0, x1 = x1, x0 
    y0, y1 = y1, y0 

:

if steep: 
    x0, y0 = y0, x0 
    x1, y1 = y1, x1 

backward = x0 > x1 
if backward: 
    x0, x1 = x1, x0 
    y0, y1 = y1, y0