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Ingy döt Net 2023-07-01 11:58:00 -04:00
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56
Task/Total-circles-area/Python/total-circles-area-1.py Normal file
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from collections import namedtuple
Circle = namedtuple("Circle", "x y r")
circles = [
Circle( 1.6417233788, 1.6121789534, 0.0848270516),
Circle(-1.4944608174, 1.2077959613, 1.1039549836),
Circle( 0.6110294452, -0.6907087527, 0.9089162485),
Circle( 0.3844862411, 0.2923344616, 0.2375743054),
Circle(-0.2495892950, -0.3832854473, 1.0845181219),
Circle( 1.7813504266, 1.6178237031, 0.8162655711),
Circle(-0.1985249206, -0.8343333301, 0.0538864941),
Circle(-1.7011985145, -0.1263820964, 0.4776976918),
Circle(-0.4319462812, 1.4104420482, 0.7886291537),
Circle( 0.2178372997, -0.9499557344, 0.0357871187),
Circle(-0.6294854565, -1.3078893852, 0.7653357688),
Circle( 1.7952608455, 0.6281269104, 0.2727652452),
Circle( 1.4168575317, 1.0683357171, 1.1016025378),
Circle( 1.4637371396, 0.9463877418, 1.1846214562),
Circle(-0.5263668798, 1.7315156631, 1.4428514068),
Circle(-1.2197352481, 0.9144146579, 1.0727263474),
Circle(-0.1389358881, 0.1092805780, 0.7350208828),
Circle( 1.5293954595, 0.0030278255, 1.2472867347),
Circle(-0.5258728625, 1.3782633069, 1.3495508831),
Circle(-0.1403562064, 0.2437382535, 1.3804956588),
Circle( 0.8055826339, -0.0482092025, 0.3327165165),
Circle(-0.6311979224, 0.7184578971, 0.2491045282),
Circle( 1.4685857879, -0.8347049536, 1.3670667538),
Circle(-0.6855727502, 1.6465021616, 1.0593087096),
Circle( 0.0152957411, 0.0638919221, 0.9771215985)]
def main():
# compute the bounding box of the circles
x_min = min(c.x - c.r for c in circles)
x_max = max(c.x + c.r for c in circles)
y_min = min(c.y - c.r for c in circles)
y_max = max(c.y + c.r for c in circles)
box_side = 500
dx = (x_max - x_min) / box_side
dy = (y_max - y_min) / box_side
count = 0
for r in xrange(box_side):
y = y_min + r * dy
for c in xrange(box_side):
x = x_min + c * dx
if any((x-circle.x)**2 + (y-circle.y)**2 <= (circle.r ** 2)
for circle in circles):
count += 1
print "Approximated area:", count * dx * dy
main()

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Task/Total-circles-area/Python/total-circles-area-2.py Normal file
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from math import floor, ceil, sqrt
def area_scan(prec, circs):
def sect((cx, cy, r), y):
dr = sqrt(r ** 2 - (y - cy) ** 2)
return (cx - dr, cx + dr)
ys = [a[1] + a[2] for a in circs] + [a[1] - a[2] for a in circs]
mins = int(floor(min(ys) / prec))
maxs = int(ceil(max(ys) / prec))
total = 0
for y in (prec * x for x in xrange(mins, maxs + 1)):
right = -float("inf")
for (x0, x1) in sorted(sect((cx, cy, r), y)
for (cx, cy, r) in circs
if abs(y - cr) < r):
if x1 <= right:
continue
total += x1 - max(x0, right)
right = x1
return total * prec
def main():
circles = [
( 1.6417233788, 1.6121789534, 0.0848270516),
(-1.4944608174, 1.2077959613, 1.1039549836),
( 0.6110294452, -0.6907087527, 0.9089162485),
( 0.3844862411, 0.2923344616, 0.2375743054),
(-0.2495892950, -0.3832854473, 1.0845181219),
( 1.7813504266, 1.6178237031, 0.8162655711),
(-0.1985249206, -0.8343333301, 0.0538864941),
(-1.7011985145, -0.1263820964, 0.4776976918),
(-0.4319462812, 1.4104420482, 0.7886291537),
( 0.2178372997, -0.9499557344, 0.0357871187),
(-0.6294854565, -1.3078893852, 0.7653357688),
( 1.7952608455, 0.6281269104, 0.2727652452),
( 1.4168575317, 1.0683357171, 1.1016025378),
( 1.4637371396, 0.9463877418, 1.1846214562),
(-0.5263668798, 1.7315156631, 1.4428514068),
(-1.2197352481, 0.9144146579, 1.0727263474),
(-0.1389358881, 0.1092805780, 0.7350208828),
( 1.5293954595, 0.0030278255, 1.2472867347),
(-0.5258728625, 1.3782633069, 1.3495508831),
(-0.1403562064, 0.2437382535, 1.3804956588),
( 0.8055826339, -0.0482092025, 0.3327165165),
(-0.6311979224, 0.7184578971, 0.2491045282),
( 1.4685857879, -0.8347049536, 1.3670667538),
(-0.6855727502, 1.6465021616, 1.0593087096),
( 0.0152957411, 0.0638919221, 0.9771215985)]
p = 1e-3
print "@stepsize", p, "area = %.4f" % area_scan(p, circles)
main()

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Task/Total-circles-area/Python/total-circles-area-3.py Normal file
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from __future__ import division
from math import sqrt
from itertools import count
from pprint import pprint as pp
try:
from itertools import izip as zip
except:
pass
# Remove duplicates and sort, largest first.
circles = sorted(set([
# xcenter ycenter radius
(1.6417233788, 1.6121789534, 0.0848270516),
(-1.4944608174, 1.2077959613, 1.1039549836),
(0.6110294452, -0.6907087527, 0.9089162485),
(0.3844862411, 0.2923344616, 0.2375743054),
(-0.2495892950, -0.3832854473, 1.0845181219),
(1.7813504266, 1.6178237031, 0.8162655711),
(-0.1985249206, -0.8343333301, 0.0538864941),
(-1.7011985145, -0.1263820964, 0.4776976918),
(-0.4319462812, 1.4104420482, 0.7886291537),
(0.2178372997, -0.9499557344, 0.0357871187),
(-0.6294854565, -1.3078893852, 0.7653357688),
(1.7952608455, 0.6281269104, 0.2727652452),
(1.4168575317, 1.0683357171, 1.1016025378),
(1.4637371396, 0.9463877418, 1.1846214562),
(-0.5263668798, 1.7315156631, 1.4428514068),
(-1.2197352481, 0.9144146579, 1.0727263474),
(-0.1389358881, 0.1092805780, 0.7350208828),
(1.5293954595, 0.0030278255, 1.2472867347),
(-0.5258728625, 1.3782633069, 1.3495508831),
(-0.1403562064, 0.2437382535, 1.3804956588),
(0.8055826339, -0.0482092025, 0.3327165165),
(-0.6311979224, 0.7184578971, 0.2491045282),
(1.4685857879, -0.8347049536, 1.3670667538),
(-0.6855727502, 1.6465021616, 1.0593087096),
(0.0152957411, 0.0638919221, 0.9771215985),
]), key=lambda x: -x[-1])
def vdcgen(base=2):
'Van der Corput sequence generator'
for n in count():
vdc, denom = 0,1
while n:
denom *= base
n, remainder = divmod(n, base)
vdc += remainder / denom
yield vdc
def vdc_2d():
'Two dimensional Van der Corput sequence generator'
for x, y in zip(vdcgen(base=2), vdcgen(base=3)):
yield x, y
def bounding_box(circles):
'Return minx, maxx, miny, maxy'
return (min(x - r for x,y,r in circles),
max(x + r for x,y,r in circles),
min(y - r for x,y,r in circles),
max(y + r for x,y,r in circles)
)
def circle_is_in_circle(c1, c2):
x1, y1, r1 = c1
x2, y2, r2 = c2
return sqrt((x2 - x1)**2 + (y2 - y1)**2) <= r1 - r2
def remove_covered_circles(circles):
'Takes circles in decreasing radius order. Removes those covered by others'
covered = []
for i, c1 in enumerate(circles):
eliminate = [c2 for c2 in circles[i+1:]
if circle_is_in_circle(c1, c2)]
if eliminate: covered += [c1, eliminate]
for c in eliminate: circles.remove(c)
#pp(covered)
def main(circles):
print('Originally %i circles' % len(circles))
print('Bounding box: %r' % (bounding_box(circles),))
remove_covered_circles(circles)
print(' down to %i due to some being wholly covered by others' % len(circles))
minx, maxx, miny, maxy = bounding_box(circles)
# Shift to 0,0 and compute r**2 once
circles2 = [(x - minx, y - miny, r*r) for x, y, r in circles]
scalex, scaley = abs(maxx - minx), abs(maxy - miny)
pcount, inside, last = 0, 0, ''
for px, py in vdc_2d():
pcount += 1
px *= scalex; py *= scaley
if any((px-cx)**2 + (py-cy)**2 <= cr2 for cx, cy, cr2 in circles2):
inside += 1
if not pcount % 100000:
area = (inside/pcount) * scalex * scaley
print('Points: %8i, Area estimate: %r'
% (pcount, area))
# Hack to check if precision OK
this = '%.4f' % area
if this == last:
break
else:
last = this
print('The value has settled to %s' % this)
if __name__ == '__main__':
main(circles)

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Task/Total-circles-area/Python/total-circles-area-4.py Normal file
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from collections import namedtuple
from functools import partial
from itertools import repeat, imap, izip
from decimal import Decimal, getcontext
# Requires the egg: https://pypi.python.org/pypi/dmath/
from dmath import atan2, asin, sin, cos, pi as piCompute
getcontext().prec = 40 # Set FP precision.
sqrt = Decimal.sqrt
pi = piCompute()
D2 = Decimal(2)
Vec = namedtuple("Vec", "x y")
vcross = lambda (a, b), (c, d): a*d - b*c
vdot = lambda (a, b), (c, d): a*c + b*d
vadd = lambda (a, b), (c, d): Vec(a + c, b + d)
vsub = lambda (a, b), (c, d): Vec(a - c, b - d)
vlen = lambda x: sqrt(vdot(x, x))
vdist = lambda a, b: vlen(vsub(a, b))
vscale = lambda s, (x, y): Vec(x * s, y * s)
def vnorm(v):
l = vlen(v)
return Vec(v.x / l, v.y / l)
vangle = lambda (x, y): atan2(y, x)
def anorm(a):
if a > pi: return a - pi * D2
if a < -pi: return a + pi * D2
return a
Circle = namedtuple("Circle", "x y r")
def circle_cross((x0, y0, r0), (x1, y1, r1)):
d = vdist(Vec(x0, y0), Vec(x1, y1))
if d >= r0 + r1 or d <= abs(r0 - r1):
return []
s = (r0 + r1 + d) / D2
a = sqrt(s * (s - d) * (s - r0) * (s - r1))
h = D2 * a / d
dr = Vec(x1 - x0, y1 - y0)
dx = vscale(sqrt(r0 ** 2 - h ** 2), vnorm(dr))
ang = vangle(dr) if \
r0 ** 2 + d ** 2 > r1 ** 2 \
else pi + vangle(dr)
da = asin(h / r0)
return map(anorm, [ang - da, ang + da])
# Angles of the start and end points of the circle arc.
Angle2 = namedtuple("Angle2", "a1 a2")
Arc = namedtuple("Arc", "c aa")
arcPoint = lambda (x, y, r), a: \
vadd(Vec(x, y), Vec(r * cos(a), r * sin(a)))
arc_start = lambda (c, (a0, a1)): arcPoint(c, a0)
arc_mid = lambda (c, (a0, a1)): arcPoint(c, (a0 + a1) / D2)
arc_end = lambda (c, (a0, a1)): arcPoint(c, a1)
arc_center = lambda ((x, y, r), _): Vec(x, y)
arc_area = lambda ((_0, _1, r), (a0, a1)): r ** 2 * (a1 - a0) / D2
def split_circles(cs):
cSplit = lambda (c, angs): \
imap(Arc, repeat(c), imap(Angle2, angs, angs[1:]))
# If an arc that was part of one circle is inside *another* circle,
# it will not be part of the zero-winding path, so reject it.
in_circle = lambda ((x0, y0), c), (x, y, r): \
c != Circle(x, y, r) and vdist(Vec(x0, y0), Vec(x, y)) < r
def in_any_circle(arc):
return any(in_circle((arc_mid(arc), arc.c), c) for c in cs)
concat_map = lambda f, xs: [y for x in xs for y in f(x)]
f = lambda c: \
(c, sorted([-pi, pi] +
concat_map(partial(circle_cross, c), cs)))
cAngs = map(f, cs)
arcs = concat_map(cSplit, cAngs)
return filter(lambda ar: not in_any_circle(ar), arcs)
# Given a list of arcs, build sets of closed paths from them.
# If one arc's end point is no more than 1e-4 from another's
# start point, they are considered connected. Since these
# start/end points resulted from intersecting circles earlier,
# they *should* be exactly the same, but floating point
# precision may cause small differences, hence the 1e-4 error
# margin. When there are genuinely different intersections
# closer than this margin, the method will backfire, badly.
def make_paths(arcs):
eps = Decimal("0.0001")
def join_arcs(a, xxs):
if not xxs:
return [a]
x, xs = xxs[0], xxs[1:]
if not a:
return join_arcs([x], xs)
if vdist(arc_start(a[0]), arc_end(a[-1])) < eps:
return [a] + join_arcs([], xxs)
if vdist(arc_end(a[-1]), arc_start(x)) < eps:
return join_arcs(a + [x], xs)
return join_arcs(a, xs + [x])
return join_arcs([], arcs)
# Slice N-polygon into N-2 triangles.
def polyline_area(vvs):
tri_area = lambda a, b, c: vcross(vsub(b, a), vsub(c, b)) / D2
v, vs = vvs[0], vvs[1:]
return sum(tri_area(v, v1, v2) for v1, v2 in izip(vs, vs[1:]))
def path_area(arcs):
f = lambda (a, e), arc: \
(a + arc_area(arc), e + [arc_center(arc), arc_end(arc)])
(a, e) = reduce(f, arcs, (0, []))
return a + polyline_area(e)
circles_area = lambda cs: \
sum(imap(path_area, make_paths(split_circles(cs))))
def main():
raw_circles = """\
1.6417233788 1.6121789534 0.0848270516
-1.4944608174 1.2077959613 1.1039549836
0.6110294452 -0.6907087527 0.9089162485
0.3844862411 0.2923344616 0.2375743054
-0.2495892950 -0.3832854473 1.0845181219
1.7813504266 1.6178237031 0.8162655711
-0.1985249206 -0.8343333301 0.0538864941
-1.7011985145 -0.1263820964 0.4776976918
-0.4319462812 1.4104420482 0.7886291537
0.2178372997 -0.9499557344 0.0357871187
-0.6294854565 -1.3078893852 0.7653357688
1.7952608455 0.6281269104 0.2727652452
1.4168575317 1.0683357171 1.1016025378
1.4637371396 0.9463877418 1.1846214562
-0.5263668798 1.7315156631 1.4428514068
-1.2197352481 0.9144146579 1.0727263474
-0.1389358881 0.1092805780 0.7350208828
1.5293954595 0.0030278255 1.2472867347
-0.5258728625 1.3782633069 1.3495508831
-0.1403562064 0.2437382535 1.3804956588
0.8055826339 -0.0482092025 0.3327165165
-0.6311979224 0.7184578971 0.2491045282
1.4685857879 -0.8347049536 1.3670667538
-0.6855727502 1.6465021616 1.0593087096
0.0152957411 0.0638919221 0.9771215985""".splitlines()
circles = [Circle(*imap(Decimal, row.split()))
for row in raw_circles]
print "Total Area:", circles_area(circles)
main()