def unique_signature(pts):
"""Similar to signature, it produces a string associated to the point set,
but it is independent of the labelling of the point set.
It runs in O(n^3 \logn) time"""
pts=[x[:] for x in pts]
D=points_index(pts)
ch=convexhull.CH(pts)
S=[]
for p in ch:
idx=D[tuple(p)]
pts2=pts[:idx]
pts2.extend(pts[idx+1:])
pts2=geometricbasics.sort_around_point(p,pts2)
pts2.append(p)
S.append(signature(pts2))
print S
return min(S)
def lambda_matrix(pts):
"""M[i,j] is the number of points of pts that lie to the LEFT
of the edge (pts[i],pts[j])."""
M=[[0 for i in xrange(len(pts))] for j in xrange(len(pts))]
D=points_index(pts)
n=len(pts)
for i in xrange(n):
tpts=pts[:i]
tpts.extend(pts[i+1:])
p=pts[i]
#check whether we have the C++ version running correctly
pts_sorted=geometricbasics.sort_around_point(p,tpts)
k=0
for j in xrange(n-1):
while (geometricbasics.turn(p,pts_sorted[j],pts_sorted[(k+1)%(n-1)])<=0 and
(k+1)%(n-1)!=j):
k=k+1
ni=(k-j)%(n-1)
M[D[tuple(p)]][D[tuple(pts_sorted[j])]]=ni
return M
def _visible_points(n):
"""Returns the first n points visibible from
the origin in the integer grid."""
V=[[1,0],[-1,0],[0,1],[0,-1]]
gcd=_gcd_dict(n)
k=2
while len(V)<n:
for i in range(1,k):
j=k-i
if gcd[i][j]==1:
#V=V+[[i,j],[-i,-j]]
V.append([i,j])
V.append([-i,-j])
if len(V)==n:
break
#V=V+[[-i,j],[i,-j]]
V.append([-i,j])
V.append([i,-j])
if len(V)==n:
break
k=k+1
#print k
V=V[:n]
return geometricbasics.sort_around_point([0,0],V)