'''HilbertCurve.py
Demonstrates the use of recursion to produce an image that represents
an approximation of the fractal Hilbert curve. 
'''

WIN = pmNewComputedImage('Hilbert Curve'',256,256,'rgb(255, 200,200)')

XPEN = None; YPEN = None
PENCOLOR = (0,0,128) # Dark blue

# First we define two graphics primitives: moveTo and lineTo.
def moveTo(x,y):
  global XPEN, YPEN
  XPEN = x; YPEN = y

def lineTo(endX,endY):
  if XPEN==None or YPEN==None: moveTo(endX, endY); return
  (R,G,B)=PENCOLOR
  dx = endX-XPEN; dy=endY-YPEN
  if abs(dx)>abs(dy):
    if dx>0: xstart = XPEN; ystart = YPEN
    else: xstart = endX; ystart = endY
    for i in range(abs(dx)+1):
      x = xstart+i
      y = ystart+int(i*dy/dx)
      pmSetPixel(WIN, x, y, R, G, B)
  else:
    if dy>0: ystart = YPEN; xstart = XPEN
    else: ystart = endY; xstart = endX
    for i in range(abs(dy)+1):
      y = ystart+i
      x = xstart+int(i*dx/dy)
      pmSetPixel(WIN, x, y, R, G, B)
  XPEN=endX; YPEN=endY

def hilbert(x, y, ux, uy, vx, vy, k):
  if k==0: lineTo(x + (ux+vx)/2, y + (uy+vy)/2)
  else:
    hilbert(x, y, vx/2, vy/2, ux/2, uy/2, k-1)
    hilbert(x+ux/2, y+uy/2, ux/2, uy/2, vx/2, vy/2, k-1)
    hilbert(x+ux/2+vx/2, y+uy/2+vy/2, ux/2, uy/2, vx/2, vy/2, k-1)
    hilbert(x+ux/2+vx, y+uy/2+vy, -vx/2, -vy/2, -ux/2, -uy/2, k-1)

hilbert(0, 0, 256, 0, 0, 256, 7)