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#!/usr/bin/env python
"""
Minimal disk
References::
None
"""
from numpy import array, pi, inf, vstack, linspace
from numpy import random, sin, cos, sqrt
random.seed(123)
def disk_coverage(data, cx, cy, r,
area_penalty=1, visibility_penalty=1, distance_penalty=1):
"""
cost function for minimum enclosing circle for a 2D set of points
There are three penalty terms:
- *area_penalty* is the cost per unit area of the disk
- *visibility_penalty* is the cost per point not covered by the disk
- *distance_penalty* is the weight on the sum squared costs of
each point to the disk
"""
if r<0: return inf
x,y = data
d = sqrt((x-cx)**2 + (y-cy)**2)
return area_penalty*pi*r*2 + distance_penalty*sum((d[d>r]-r)**2) + visibility_penalty*sum(d>r)
def outline(N=200, cx=0, cy=0, r=1):
"""
generate the outline of a circle using N steps.
"""
theta = linspace(0, 2*pi, N)
return vstack( (r*cos(theta)+cx, r*sin(theta)+cy) )
def simulate_disk(N, cx=0, cy=0, r=1):
"""
Generate N random points in a disk
"""
data = array(list(_disk_generator(N)))
return vstack( (r*data[:,0]+cx, r*data[:,1]+cy) )
def simulate_circle(N, cx=0, cy=0, r=1):
"""
generate N random points on a circle
"""
theta = random.uniform(0,2*pi,size=N)
return vstack((r*cos(theta)+cx,r*sin(theta)+cy))
def _disk_generator(N):
for _ in range(N):
while True:
x = random.random()*2.-1.
y = random.random()*2.-1.
if x*x + y*y <= 1:
break
yield x,y
# End of file
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