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nickponline/geometry.py Secret

Created Sep 20, 2016
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import sys
import random
import pylab
import math
import flow
import viz
import collections
N = 200
D = 20
RANGE = 20
random.seed(1)
points = [ (random.uniform(-RANGE, RANGE), random.uniform(-RANGE, RANGE)) for _ in xrange(N) ]
viz.figure()
viz.plot_points(points)
viz.show(RANGE)
def max_bipartite_independent(top, bot):
graph = collections.defaultdict(dict)
top_set = set( [i for i in xrange( len(top)) ])
bot_set = set( [i for i in xrange( len(bot)) ])
for i in xrange(len(top)):
for j in xrange(len(bot)):
xi, yi = top[i]
xj, yj = bot[j]
if distance(xi, yi, xj, yj) > F:
node_i = 'TOP' + str(i)
node_j = 'BOT' + str(j)
src = 'SOURCE-NODE'
snk = 'SINK-NODE'
graph[node_i][node_j] = 1
graph[src][node_i] = sys.maxint
graph[node_j][snk] = sys.maxint
top_set.discard(i)
bot_set.discard(j)
f = flow.max_flow(graph, 'SOURCE-NODE', 'SINK-NODE')
solution = f + len(top_set) + len(bot_set) + 2
return solution
def area(a, b, c):
return (b[0] - a[0]) * (c[1] - a[1]) - (c[0] - a[0]) * (b[1] - a[1])
def distance(xi, yi, xj, yj):
return math.hypot(xi - xj, yi - yj)
best = 0
for i in xrange(N):
for j in xrange(i + 1, N):
xi, yi = points[i]
xj, yj = points[j]
if distance(xi, yi, xj, yj) > D: continue
# Furthest pair in our thing
F = distance(xi, yi, xj, yj)
viz.figure()
viz.plot_points(points)
viz.plot_line(xi, yi, xj, yj)
viz.plot_circle(xi, yi, D)
viz.plot_circle(xj, yj, D)
viz.show(RANGE)
lens = []
for k in xrange(N):
if k == i: continue
if k == j: continue
xk, yk = points[k]
if distance(xi, yi, xk, yk) > F: continue
if distance(xj, yj, xk, yk) > F: continue
lens.append(points[k])
viz.figure()
if len(lens) > 0: viz.plot_points(lens)
viz.plot_line(xi, yi, xj, yj)
viz.plot_circle(xi, yi, F)
viz.plot_circle(xj, yj, F)
viz.show(RANGE)
top, bot = [], []
M = len(lens)
for k in xrange(M):
xk, yk = lens[k]
if area((xi, yi), (xj, yj), (xk, yk)) >= 0:
top.append(lens[k])
else:
bot.append(lens[k])
viz.figure()
for t in top:
for b in bot:
if distance(t[0], t[1], b[0], b[1]) > D:
viz.plot_line(t[0], t[1], b[0], b[1], color='k')
if len(top) > 0: viz.plot_points(top, color='bo')
if len(bot) > 0: viz.plot_points(bot, color='ro')
viz.plot_line(xi, yi, xj, yj)
viz.plot_circle(xi, yi, F)
viz.plot_circle(xj, yj, F)
viz.show(RANGE)
solution = max_bipartite_independent(top, bot)
best = max(best, solution)
print 'MAXIMUM: ', best
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