291 lines
8.1 KiB
Python
291 lines
8.1 KiB
Python
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#!/usr/bin/env python3
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import sys
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# This script generates a configuration of 3-staircases in which there is a
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# grid of particles in one phase, and the rest of space is filled with
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# particles in another phase.
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# size of grid
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L1=100
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L2=100
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# grid of particles in phase 1
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N11=12
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N12=12
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# position of lower left particle in phase 1
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x01=30+N12
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x02=30
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# only print from here to there
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l11=16
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l12=16
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l21=80
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l22=88
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# R2 of the model
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R2=3
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def main():
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# particles in phase 1
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particles1=[]
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# particles in phase 2
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particles2=[]
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fill_particles1(particles1)
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fill_particles2(particles2,particles1)
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# join particles
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particles=particles1+particles2
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# compute which particles have a Voronoi cells containing a given site
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voronoi_index=particles_in_voronoi(particles)
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# compute the Voronoi cells of each particle
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voronois=voronoi_of_particles(voronoi_index,particles)
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# check whether the particles are in the GFc
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GFc=particles_in_GFc(voronois,particles1,particles2)
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# boundary of GFc
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support=GFc_support(GFc,voronois)
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GFc_boundary=boundary(support)
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# print
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print_headers()
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print_particles(particles1,particles2,GFc)
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print_boundary(GFc_boundary)
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print_footers()
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# generate grid of particles in phase 1
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def fill_particles1(particles1):
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for k1 in range(N11):
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for k2 in range(N12):
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particles1.append((x01+2*k1-k2,x02+k1+3*k2,1))
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# fill the rest of space with particles in phase 2
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def fill_particles2(particles2, particles1):
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for x1 in range(L1):
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for x2 in range(L2):
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# index of particle
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k1=(x1+3*x2)/7
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k2=(2*x1-x2)/7
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# check the indices are integers:
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if k1 != int(k1) or k2 != int(k2):
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continue
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# check overlap with particles in phase 1
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if check_overlap_1((x1,x2),particles1):
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continue
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particles2.append((x1,x2,2))
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# check overlap with particles in phase 1
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def check_overlap_1(x,particles1):
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for p in particles1:
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if check_overlap(x,p):
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return True
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return False
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# check overlap between two 3-staircases
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def check_overlap(x,y):
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if max(abs(y[0]-x[0]),abs(y[1]-x[1]))>2:
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return False
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if abs((y[1]-x[1])+(y[0]-x[0]))<=2:
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return True
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return False
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# given a site, compute the particles whose Voronoi cell the site is in
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def particles_in_voronoi(particles):
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out=[]
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for x1 in range(L1):
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for x2 in range(L2):
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# minimize distance
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mindist=L1+L2+1
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candidate_list=[]
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for p in particles:
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dd=dist_support((x1,x2),p)
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if dd<mindist:
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# reset candidate list
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candidate_list=[p]
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mindist=dd
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elif dd==mindist:
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# append candidate
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candidate_list.append(p)
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# add list to output (keep x1,x2 as index)
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out.append(((x1,x2),candidate_list))
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return out
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# distance between a point and the support of a particle
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def dist_support(x,p):
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# if x is in support then 0
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if abs(p[0]-x[0])+abs(p[1]-x[1])<=2 and x[0]>=p[0] and x[1]>=p[1]:
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return 0
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# base
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out=abs(x[0]-p[0])+abs(x[1]-p[1])
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# correct this depending on which site in \sigma_p is actually closest
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# lower left quadrant: p is the closest
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if x[0]-p[0]<=0 and x[1]-p[1]<=0:
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return out
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# lines next to lower left quadrant: neighbor of p closest
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if x[0]-p[0]==1 and x[1]-p[1]<=0 or x[1]-p[1]==1 and x[0]-p[0]<=0:
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return out-1
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# otherwise: second neightbor of p closest
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return out-2
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# from a table associating sites to voronoi cells, get particles
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def voronoi_of_particles(voronoi_index,particles):
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out=[]
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# output is indexed in the same order as particles
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for p in particles:
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vois=[]
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for v in voronoi_index:
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if p in v[1]:
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vois.append(v[0])
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out.append((p,vois))
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return out
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# find which particles are in the GFc
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def particles_in_GFc(voronois,particles1,particles2):
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out=[]
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# loop over particles
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for v in voronois:
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# check all other particles
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for w in voronois:
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# skip v
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if v==w:
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continue
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# check whether the distance between the cells is <=R2
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if set_dist(v[1],w[1])>R2:
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continue
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# check whether w is #-correct
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if not ((w[0][2]==1 and sharp_correct1(w[0],particles1)) or (w[0][2]==2 and sharp_correct2(w[0],particles2))):
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# in GFc
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out.append(v[0])
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break
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return out
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# distance between two sets
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def set_dist(s1,s2):
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if len(s1)==0 or len(s2)==0:
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print("error: computing the distance between two sets, one of which is empty",file=sys.stderr)
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exit(-1)
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return -1
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mind=abs(s1[0][0]-s2[0][0])+abs(s1[0][1]-s2[0][1])
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for x in s1:
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for y in s2:
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if abs(x[0]-y[0])+abs(x[1]-y[1])<mind:
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mind=abs(x[0]-y[0])+abs(x[1]-y[1])
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return mind
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# check whether a particle of type 1 is #-correct:
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def sharp_correct1(x,particles1):
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if (x[0]+2,x[1]+1,1) not in particles1:
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return False
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if (x[0]-2,x[1]-1,1) not in particles1:
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return False
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if (x[0]-3,x[1]+2,1) not in particles1:
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return False
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if (x[0]+3,x[1]-2,1) not in particles1:
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return False
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if (x[0]+1,x[1]-3,1) not in particles1:
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return False
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if (x[0]-1,x[1]+3,1) not in particles1:
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return False
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return True
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# check whether a particle of type 2 is #-correct:
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def sharp_correct2(x,particles2):
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if (x[0]+1,x[1]+2,2) not in particles2:
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return False
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if (x[0]-1,x[1]-2,2) not in particles2:
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return False
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if (x[0]+2,x[1]-3,2) not in particles2:
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return False
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if (x[0]-2,x[1]+3,2) not in particles2:
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return False
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if (x[0]-3,x[1]+1,2) not in particles2:
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return False
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if (x[0]+3,x[1]-1,2) not in particles2:
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return False
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return True
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# support of a GFc
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def GFc_support(GFc,voronois):
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out=[]
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for p in GFc:
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# find Voronoi cell
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for v in voronois:
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if p==v[0]:
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out=out+v[1]
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break
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# remove duplicates
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return list(set(out))
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# boundary of a set
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def boundary(S):
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out=[]
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for s in S:
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if (s[0]+1,s[1]) not in S:
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out.append(((s[0]+0.5,s[1]-0.5),(s[0]+0.5,s[1]+0.5)))
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if (s[0]-1,s[1]) not in S:
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out.append(((s[0]-0.5,s[1]-0.5),(s[0]-0.5,s[1]+0.5)))
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if (s[0],s[1]+1) not in S:
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out.append(((s[0]-0.5,s[1]+0.5),(s[0]+0.5,s[1]+0.5)))
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if (s[0],s[1]-1) not in S:
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out.append(((s[0]-0.5,s[1]-0.5),(s[0]+0.5,s[1]-0.5)))
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return out
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# print particles
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def print_headers():
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print(r'''\documentclass{standalone}
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\usepackage{tikz}
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\usepackage{shapes}
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\begin{document}
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\begin{tikzpicture}
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''')
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# print grid
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print(r'\grid{'+str(l21-l11+1+3)+'}{'+str(l22-l12+1+3)+'}{('+str(l11-1)+','+str(l12-1)+')}')
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def print_particles(particles1,particles2,GFc):
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for p in particles1:
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if p[0]>=l11 and p[0]<=l21 and p[1]>=l12 and p[1]<=l22:
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if p in GFc:
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print(r'\staircase{green}{('+str(p[0])+','+str(p[1])+')}')
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else:
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print(r'\staircase{cyan}{('+str(p[0])+','+str(p[1])+')}')
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for p in particles2:
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if p[0]>=l11 and p[0]<=l21 and p[1]>=l12 and p[1]<=l22:
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if p in GFc:
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print(r'\staircase{yellow}{('+str(p[0])+','+str(p[1])+')}')
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else:
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print(r'\staircase{red}{('+str(p[0])+','+str(p[1])+')}')
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def print_boundary(boundary):
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for seg in boundary:
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if seg[0][0]>=l11 and seg[0][0]<=l21 and seg[0][1]>=l12 and seg[0][1]<=l22:
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if seg[1][0]>=l11 and seg[1][0]<=l21 and seg[1][1]>=l12 and seg[1][1]<=l22:
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print(r'\draw[line width=8pt]('+str(seg[0][0])+','+str(seg[0][1])+')--('+str(seg[1][0])+','+str(seg[1][1])+');')
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def print_footers():
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print(r'''
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\end{tikzpicture}
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\end{document}''')
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main()
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