HW5Q1 AMS545 2020 Spring Ryan Burgert

#To run this code, please use "pip3 install rp matplotlib numpy"
n=2#Find the nth smallest edge out of N points
N=4

while True:
    from rp import *

    points=random_floats_complex(N)
    points=as_points_array(points)
    points=list(map(tuple,points))

    from scipy.spatial import Delaunay
    d=Delaunay(points)

    edges=[]
    edges+=d.simplices[:,[0,1]].tolist()
    edges+=d.simplices[:,[0,2]].tolist()
    edges+=d.simplices[:,[1,2]].tolist()
    edges+=d.simplices[:,[1,0]].tolist()
    edges+=d.simplices[:,[2,0]].tolist()
    edges+=d.simplices[:,[2,1]].tolist()
    edges=set(map(tuple,edges))
    unique_edges={(x,y) for x,y in edges if x<=y} #Remove duplicate edges where (a,b) is the same as (b,a)
    edges={tuple(points[i] for i in (x,y)) for x,y in edges}

    point_pairs=sorted(combinations(points,2),key=lambda pair:euclidean_distance(*pair))#All possible edges sorted by distance. First is the closest point pair, second is second closest, etc...

    if point_pairs[n] not in edges:
        break

##

display_clear()
scatter_plot(points,dot_size=30)
for edge in edges:
    display_path(as_numpy_array(edge),color='blue',alpha=.1)

def display_edge_length(*edge,color='blue'):
	import matplotlib.pyplot as plt
	edge=as_numpy_array(detuple(edge))
	pos=(edge[0]+edge[1])/2
	plt.text(pos[0],pos[1],str(euclidean_distance(edge[0],edge[1]))[:4],alpha=.5,color=color)

for edge in unique_edges:
	display_edge_length(points[edge[0]],points[edge[1]])

nth_smallest_edge=as_numpy_array(point_pairs[n])
display_edge_length(nth_smallest_edge,color='red')
display_path(as_numpy_array(point_pairs[2]),color='red')
display_update(time=.5)