def computeHull (points):
"""
Compute the convex hull for given points and return as polygon.
Returned polygon is in 'counter-clockwise' fashion, with the
interior "to the left" of each edge.
"""
# sort by x coordinate (and if ==, by y coordinate).
n = len(points)
points = sorted(points, key=lambda pt:[pt.x(), pt.y()])
if n < 3:
return Polygon(points)
# Compute upper hull by starting with rightmost two points
upper = Polygon ([points[-1], points[-2]])
for i in range(n-3, -1, -1):
upper.add (points[i].x(), points[i].y())
while upper.numPoints() >=3 and lastThreeNonLeft(upper):
upper.remove(-2)
# Compute lower hull by starting with leftmost two points
lower = Polygon ([points[0], points[1]])
for i in range(2, n):
lower.add (points[i].x(), points[i].y())
while lower.numPoints() >=3 and lastThreeNonLeft(lower):
lower.remove(-2)
# Merge into upper (skip first and last to avoid duplication) and return.
upper.remove(-1)
upper.remove(0)
for pt in upper:
lower.add(pt.x(), pt.y())
return lower
def convexIntersect(p, q):
"""
Compute and return polygon resulting from the intersection of
two convext polygons, p and q.
"""
intersection = Polygon()
pn = p.numEdges()
qn = q.numEdges()
k = 1
inside = None # can't know inside until intersection
first = None # remember 1st intersection to know when to stop
firstp = pe = p.edges()[0] # get first edge of p and q
firstq = qe = q.edges()[0]
while k < 2*(pn + qn):
pt = pe.intersect(qe)
if pt is not None:
if first == None:
first = pt
elif pt == first:
# stop when find first intersection again
break
intersection.add(pt.x(), pt.y())
if inhalfplane(pe.tail(), qe):
inside = p
else:
inside = q
# Identify relationship between edges; either we advance
# p or we advance q, based on whether p's current edge
# is aiming at qe (or vice versa).
advancep = advanceq = False
if (aim(pe,qe) and aim(qe,pe)) or (not aim(pe,qe) and not aim(qe,pe)):
if inside is p:
advanceq = True
elif inside is q:
advancep = True
else:
# no intersection yet. Choose based on
# which one is "outside"
if inhalfplane(pe.tail(), qe):
advanceq = True
else:
advancep = True
elif aim(pe, qe):
advancep = True
elif aim(qe, pe):
advanceq = True
## if aim(pe, qe):
## if aim(qe, pe):
## if inside is p:
## advanceq = True
## elif inside is q:
## advancep = True
## else:
## advancep = True # arbitrary pick
## else:
## advancep = True
## else:
## if aim(qe, pe):
## advanceq = True
## else:
## if inside is p:
## advanceq = True
## elif inside is q:
## advancep = True
## else:
## advancep = True # arbitrary pick
if advancep:
if inside is p:
intersection.add(pe.tail().x(), pe.tail().y())
pe = pe.next()
elif advanceq:
if inside is q:
intersection.add(qe.tail().x(), qe.tail().y())
qe = qe.next()
k += 1
if intersection.numPoints() == 0:
if containedWithin(firstp.tail(), q):
return p
elif containedWithin(firstq.tail(), p):
return q
else:
return None
# Return computed intersection
return intersection