def jarvis(points, cutoff=False):
if cutoff: points = interior_elimination(points)
#removing duplicate points
pts = list(set(points))
P0 = min(pts, key=lambda p: (p[1], p[0]))
H = [P0]
# Since 'for loops' works as generators, 'H' is gonna be
# populated within the loop and 'h' will always be
# the most recent added. In the last iteration, 'H' won't
# be updated (case when P0 is reached again)
# and the 'for loop' ends.
for h in H:
a = h
for b in pts:
if ccw(h, a, b) < 0 or (ccw(h, a, b) == 0 and \
distance(h, b) > distance(h, a)):
a = b
if a is not P0:
H.append(a)
assert is_convex(H)
return H
def half_hull(pts):
h = []
for p in pts:
while len(h) >= 2 and ccw(h[-2], h[-1], p) <= 0:
h.pop()
h.append(p)
return h
def half_hull(pts):
h = []
for p in pts:
while len(h) >= 2 and ccw(h[-2], h[-1], p) <= 0:
h.pop()
h.append(p)
return h
def compare(P0, B, C, to_ignore):
d = ccw(P0, C, B)
if d is not 0: return 1 if d > 0 else -1
if distance(P0, B) > distance(P0, C):
to_ignore[C] = True
return -1
to_ignore[B] = True
return 1
def compare(P0, B, C, to_ignore):
d = ccw(P0, C, B)
if d is not 0: return 1 if d > 0 else -1
if distance(P0, B) > distance(P0, C):
to_ignore[C] = True
return -1
to_ignore[B] = True
return 1
def inside_triangle(n, v1=(500, 500), v2=(1000, 0)):
"http://mathworld.wolfram.com/TrianglePointPicking.html"
#pts = [(0, 0), (500, 500), (1000, 0)]
pts = []
for i in range(n):
while True:
a1 = random.random()
a2 = random.random()
pt = (a1*v1[0]+ a2*v2[0], a1*v1[1] + a2*v2[1])
if ccw(v2, v1, pt) > 0:
break #skipping when it's in the other side of paralelogram
pts.append(pt)
return pts
def graham(points, cutoff=False):
if cutoff: points = interior_elimination(points)
#removing duplicate points
pts = list(set(points))
P0 = min(pts, key=lambda p: (p[1], p[0]))
pts.remove(P0)
# sorting by polar angles and ignoring collinear points
# (keeping the farthest one)
to_ignore = {}
pts.sort(lambda B, C: compare(P0, B, C, to_ignore))
H = [P0] + pts[:2]
for i in range(2, len(pts)):
if pts[i] in to_ignore: continue
while ccw(H[-2], H[-1], pts[i]) <= 0:
H.pop()
H.append(pts[i])
assert is_convex(H)
return H
def graham(points, cutoff=False):
if cutoff: points = interior_elimination(points)
#removing duplicate points
pts = list(set(points))
P0 = min(pts, key=lambda p: (p[1], p[0]))
pts.remove(P0)
# sorting by polar angles and ignoring collinear points
# (keeping the farthest one)
to_ignore = {}
pts.sort(lambda B, C: compare(P0, B, C, to_ignore))
H = [P0] + pts[:2]
for i in range(2, len(pts)):
if pts[i] in to_ignore: continue
while ccw(H[-2], H[-1], pts[i]) <= 0:
H.pop()
H.append(pts[i])
assert is_convex(H)
return H
