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 andrew(points, cutoff=False):
if cutoff: points = interior_elimination(points)
pts = sorted(set(points))
H = half_hull(pts)[:-1] + \
half_hull(reversed(pts))[:-1]
assert is_convex(H)
return H
def andrew(points, cutoff=False):
if cutoff: points = interior_elimination(points)
pts = sorted(set(points))
H = half_hull(pts)[:-1] + \
half_hull(reversed(pts))[:-1]
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
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 plot(points):
SIZE = (1024, 768)
BLACK = (0, 0, 0)
WHITE = (255, 255, 255)
GREEN = (0, 255, 0)
RED = (255, 0, 0)
BLUE = (0, 0, 255)
GRAY = (100, 100, 100)
MARGIN = 50
PANELW = 200
SAMPLE = 100
LIMIT = 1000
ZOOM = 10
CIRCLE = 2
up_sample = False
down_sample = False
x, y = 0, 0
pygame.init()
# ch = graham(points[:])
# ch = jarvis(points[:])
# ch = andrew(points[:])
ch = graham(points[:])
screen = pygame.display.set_mode(SIZE)
def scale(points):
xmax = max(points, key=lambda p: p[0])[0]
xmin = min(points, key=lambda p: p[0])[0]
ymin = min(points, key=lambda p: p[1])[1]
ymax = max(points, key=lambda p: p[1])[1]
dx = float(xmax - xmin)
dy = float(ymax - ymin)
# preventing division per zero
if dy == 0:
dy = 0.0001
if dx == 0:
dx = 0.0001
wx = float(1024 - 2 * MARGIN - PANELW)
hy = float(768 - 2 * MARGIN)
pts = map(lambda p: (p[0] + -xmin, ymax - p[1]), points)
pts = map(lambda p: (p[0] * 724.0 / dx, p[1] * 668.0 / dy), pts)
xmaxk = max(pts, key=lambda p: p[0])[0]
xmink = min(pts, key=lambda p: p[0])[0]
ymaxk = max(pts, key=lambda p: p[1])[1]
ymink = min(pts, key=lambda p: p[1])[1]
dxk = (MARGIN + wx / 2.0) - (xmaxk - xmink) / 2.0
dyk = (MARGIN + hy / 2.0) - (ymaxk - ymink) / 2.0
pts = map(lambda p: (p[0] + dxk, p[1] + dyk), pts)
pts = map(lambda p: (int(p[0]), int(p[1])), pts)
# pygame.draw.circle(screen, (0, 255, 0), (MARGIN + int(wx/2.), MARGIN + int(hy/2.)), 2)
return pts
def random_points():
wx = float(1024 - 2 * MARGIN - PANELW)
hy = float(768 - 2 * MARGIN)
# return [(random.randrange(-wx, wx), random.randrange(-hy, hy)) for i in range(SAMPLE)]
# return inside_rectangle(SAMPLE)
# return inside_circle(SAMPLE)
# return on_circle(SAMPLE)
return inside_triangle(SAMPLE)
while 1:
for event in pygame.event.get():
if event.type == pygame.MOUSEMOTION:
x, y = event.pos
elif event.type == pygame.KEYDOWN:
if event.key == pygame.K_ESCAPE:
sys.exit()
elif event.key == pygame.K_UP:
up_sample = True
elif event.key == pygame.K_DOWN and SAMPLE > 3:
down_sample = True
elif event.key == pygame.K_r:
restart = True
points = random_points()
# ch = graham(points[:])
# ch = jarvis(points[:])
# ch = andrew(points[:])
ch = graham(points[:])
print len(ch)
# print ch
elif event.key == pygame.K_e:
pts = interior_elimination(points)
print len(points), len(pts)
points = pts
elif event.type == pygame.KEYUP:
if event.key == pygame.K_UP:
up_sample = False
elif event.key == pygame.K_DOWN:
down_sample = False
if up_sample:
SAMPLE += 1
if down_sample and SAMPLE > 3:
SAMPLE -= 1
screen.fill(WHITE)
def draw_ch():
# plot axis lines
pygame.draw.aaline(screen, GRAY, (0, SIZE[1] / 2), (SIZE[0] - PANELW, SIZE[1] / 2), 2)
pygame.draw.aaline(screen, GRAY, ((SIZE[0] - PANELW) / 2, 0), ((SIZE[0] - PANELW) / 2, SIZE[1]), 2)
# plot convex hull edges
pts = scale(ch)
for p in range(1, len(pts)):
pygame.draw.aaline(screen, BLUE, pts[p - 1], pts[p], 2)
pygame.draw.aaline(screen, BLUE, pts[-1], pts[0], 2)
# plot points
pts = scale(points)
for point in pts:
pygame.draw.circle(screen, RED, point, CIRCLE)
pygame.draw.rect(screen, GRAY, (SIZE[0] - PANELW, 0, PANELW, SIZE[1]))
# plot convex hull vertices
pts = scale(ch)
for p in pts:
pygame.draw.circle(screen, BLACK, p, CIRCLE + 1)
draw_ch()
# plot text
text = pygame.font.SysFont("", 20)
label = text.render("Commands", 1, WHITE)
screen.blit(label, (SIZE[0] - PANELW + 20, 0.5 * MARGIN))
text = pygame.font.SysFont("", 15)
label = text.render("r: randomize points", 1, WHITE)
screen.blit(label, (SIZE[0] - PANELW + 20, MARGIN))
text = pygame.font.SysFont("", 15)
label = text.render("e: eliminate points", 1, WHITE)
screen.blit(label, (SIZE[0] - PANELW + 20, 1.5 * MARGIN))
label = text.render("up arrow: increase sample size", 1, WHITE)
screen.blit(label, (SIZE[0] - PANELW + 20, 2 * MARGIN))
label = text.render("down arrow: decrease sample size", 1, WHITE)
screen.blit(label, (SIZE[0] - PANELW + 20, 2.5 * MARGIN))
label = text.render("Sample size: %d" % SAMPLE, 1, WHITE)
screen.blit(label, (SIZE[0] - PANELW + 20, 3 * MARGIN))
label = text.render("Mouse position: %d, %d" % (x, y), 1, WHITE)
screen.blit(label, (SIZE[0] - PANELW + 20, 15 * MARGIN))
pygame.display.flip()
def plot(points):
SIZE = (1024, 768)
BLACK = (0, 0, 0)
WHITE = (255, 255, 255)
GREEN = (0, 255, 0)
RED = (255, 0, 0)
BLUE = (0, 0, 255)
GRAY = (100, 100, 100)
MARGIN = 50
PANELW = 200
SAMPLE = 100
LIMIT = 1000
ZOOM = 10
CIRCLE = 2
up_sample = False
down_sample = False
x, y = 0, 0
pygame.init()
#ch = graham(points[:])
#ch = jarvis(points[:])
#ch = andrew(points[:])
ch = graham(points[:])
screen = pygame.display.set_mode(SIZE)
def scale(points):
xmax = max(points, key=lambda p: p[0])[0]
xmin = min(points, key=lambda p: p[0])[0]
ymin = min(points, key=lambda p: p[1])[1]
ymax = max(points, key=lambda p: p[1])[1]
dx = float(xmax - xmin)
dy = float(ymax - ymin)
# preventing division per zero
if dy == 0: dy = 0.0001
if dx == 0: dx = 0.0001
wx = float(1024 - 2*MARGIN - PANELW)
hy = float(768 - 2*MARGIN)
pts = map(lambda p: (p[0] + -xmin, ymax - p[1]), points)
pts = map(lambda p: (p[0]*724./dx, p[1]*668./dy), pts)
xmaxk = max(pts, key=lambda p: p[0])[0]
xmink = min(pts, key=lambda p: p[0])[0]
ymaxk = max(pts, key=lambda p: p[1])[1]
ymink = min(pts, key=lambda p: p[1])[1]
dxk = (MARGIN + wx/2.) - (xmaxk - xmink)/2.
dyk = (MARGIN + hy/2.) - (ymaxk - ymink)/2.
pts = map(lambda p: (p[0] + dxk, p[1] + dyk), pts)
pts = map(lambda p: (int(p[0]), int(p[1])), pts)
#pygame.draw.circle(screen, (0, 255, 0), (MARGIN + int(wx/2.), MARGIN + int(hy/2.)), 2)
return pts
def random_points():
wx = float(1024 - 2*MARGIN - PANELW)
hy = float(768 - 2*MARGIN)
#return [(random.randrange(-wx, wx), random.randrange(-hy, hy)) for i in range(SAMPLE)]
#return inside_rectangle(SAMPLE)
#return inside_circle(SAMPLE)
#return on_circle(SAMPLE)
return inside_triangle(SAMPLE)
while 1:
for event in pygame.event.get():
if event.type == pygame.MOUSEMOTION:
x, y = event.pos
elif event.type == pygame.KEYDOWN:
if event.key == pygame.K_ESCAPE:
sys.exit()
elif event.key == pygame.K_UP:
up_sample = True
elif event.key == pygame.K_DOWN and SAMPLE > 3:
down_sample = True
elif event.key == pygame.K_r:
restart = True
points = random_points()
#ch = graham(points[:])
#ch = jarvis(points[:])
#ch = andrew(points[:])
ch = graham(points[:])
print len(ch)
#print ch
elif event.key == pygame.K_e:
pts = interior_elimination(points)
print len(points), len(pts)
points = pts
elif event.type == pygame.KEYUP:
if event.key == pygame.K_UP:
up_sample = False
elif event.key == pygame.K_DOWN:
down_sample = False
if up_sample: SAMPLE += 1
if down_sample and SAMPLE > 3: SAMPLE -= 1
screen.fill(WHITE)
def draw_ch():
#plot axis lines
pygame.draw.aaline(screen, GRAY, (0, SIZE[1]/2), (SIZE[0] - PANELW, SIZE[1]/2), 2)
pygame.draw.aaline(screen, GRAY, ((SIZE[0] - PANELW)/2, 0), ((SIZE[0] - PANELW)/2, SIZE[1]), 2)
#plot convex hull edges
pts = scale(ch)
for p in range(1, len(pts)):
pygame.draw.aaline(screen, BLUE, pts[p-1], pts[p], 2)
pygame.draw.aaline(screen, BLUE, pts[-1], pts[0], 2)
#plot points
pts = scale(points)
for point in pts:
pygame.draw.circle(screen, RED, point, CIRCLE)
pygame.draw.rect(screen, GRAY, (SIZE[0] - PANELW, 0, PANELW, SIZE[1]))
#plot convex hull vertices
pts = scale(ch)
for p in pts:
pygame.draw.circle(screen, BLACK, p, CIRCLE + 1)
draw_ch()
#plot text
text = pygame.font.SysFont("", 20)
label = text.render("Commands", 1, WHITE)
screen.blit(label, (SIZE[0] - PANELW + 20, 0.5*MARGIN))
text = pygame.font.SysFont("", 15)
label = text.render("r: randomize points", 1, WHITE)
screen.blit(label, (SIZE[0] - PANELW + 20, MARGIN))
text = pygame.font.SysFont("", 15)
label = text.render("e: eliminate points", 1, WHITE)
screen.blit(label, (SIZE[0] - PANELW + 20, 1.5*MARGIN))
label = text.render("up arrow: increase sample size", 1, WHITE)
screen.blit(label, (SIZE[0] - PANELW + 20, 2*MARGIN))
label = text.render("down arrow: decrease sample size", 1, WHITE)
screen.blit(label, (SIZE[0] - PANELW + 20, 2.5*MARGIN))
label = text.render("Sample size: %d" % SAMPLE, 1, WHITE)
screen.blit(label, (SIZE[0] - PANELW + 20, 3*MARGIN))
label = text.render("Mouse position: %d, %d" % (x, y), 1, WHITE)
screen.blit(label, (SIZE[0] - PANELW + 20, 15*MARGIN))
pygame.display.flip()
