import scipy.spatial as spatial
import math


""" requires 2 coordinates, calculates euclidean distance between them"""
def distance(a,b):
	return math.sqrt(math.pow(a[0]-b[0],2)+math.pow(a[1]-b[1],2))


""" requires list of ccordinates, returns pairs of coordinates forming triangulation graph"""
def triangulate_set(coords):
	out = spatial.Delaunay(coords)
	alledges = set()
	for i in out.simplices:
		ab =frozenset((coords[i[0]],coords[i[1]]))
		bc =frozenset((coords[i[1]],coords[i[2]]))
		ca =frozenset((coords[i[2]],coords[i[0]]))
		alledges.add(ab)
		alledges.add(bc)
		alledges.add(ca)

	return [list(x) for x in alledges ]

""" requires list of ccordinates, returns pairs of coordinates, by their indexes, forming triangulation graph"""
def triangulate_set_labelling(coords):
	out = spatial.Delaunay(coords)
	alledges = set()
	for i in out.simplices:
		ab =frozenset((i[0],i[1]))
		bc =frozenset((i[1],i[2]))
		ca =frozenset((i[2],i[0]))
		alledges.add(ab)
		alledges.add(bc)
		alledges.add(ca)

	return [list(x) for x in alledges ]

42a042a53be302a5a6b8a6698747a66509480405
<mask token>

<mask token>


def distance(a, b):
    return math.sqrt(math.pow(a[0] - b[0], 2) + math.pow(a[1] - b[1], 2))


<mask token>


def triangulate_set(coords):
    out = spatial.Delaunay(coords)
    alledges = set()
    for i in out.simplices:
        ab = frozenset((coords[i[0]], coords[i[1]]))
        bc = frozenset((coords[i[1]], coords[i[2]]))
        ca = frozenset((coords[i[2]], coords[i[0]]))
        alledges.add(ab)
        alledges.add(bc)
        alledges.add(ca)
    return [list(x) for x in alledges]


<mask token>

<mask token>


def distance(a, b):
    return math.sqrt(math.pow(a[0] - b[0], 2) + math.pow(a[1] - b[1], 2))


<mask token>


def triangulate_set(coords):
    out = spatial.Delaunay(coords)
    alledges = set()
    for i in out.simplices:
        ab = frozenset((coords[i[0]], coords[i[1]]))
        bc = frozenset((coords[i[1]], coords[i[2]]))
        ca = frozenset((coords[i[2]], coords[i[0]]))
        alledges.add(ab)
        alledges.add(bc)
        alledges.add(ca)
    return [list(x) for x in alledges]


<mask token>


def triangulate_set_labelling(coords):
    out = spatial.Delaunay(coords)
    alledges = set()
    for i in out.simplices:
        ab = frozenset((i[0], i[1]))
        bc = frozenset((i[1], i[2]))
        ca = frozenset((i[2], i[0]))
        alledges.add(ab)
        alledges.add(bc)
        alledges.add(ca)
    return [list(x) for x in alledges]

import scipy.spatial as spatial
import math
<mask token>


def distance(a, b):
    return math.sqrt(math.pow(a[0] - b[0], 2) + math.pow(a[1] - b[1], 2))


<mask token>


def triangulate_set(coords):
    out = spatial.Delaunay(coords)
    alledges = set()
    for i in out.simplices:
        ab = frozenset((coords[i[0]], coords[i[1]]))
        bc = frozenset((coords[i[1]], coords[i[2]]))
        ca = frozenset((coords[i[2]], coords[i[0]]))
        alledges.add(ab)
        alledges.add(bc)
        alledges.add(ca)
    return [list(x) for x in alledges]


<mask token>


def triangulate_set_labelling(coords):
    out = spatial.Delaunay(coords)
    alledges = set()
    for i in out.simplices:
        ab = frozenset((i[0], i[1]))
        bc = frozenset((i[1], i[2]))
        ca = frozenset((i[2], i[0]))
        alledges.add(ab)
        alledges.add(bc)
        alledges.add(ca)
    return [list(x) for x in alledges]

import scipy.spatial as spatial
import math


""" requires 2 coordinates, calculates euclidean distance between them"""
def distance(a,b):
	return math.sqrt(math.pow(a[0]-b[0],2)+math.pow(a[1]-b[1],2))


""" requires list of ccordinates, returns pairs of coordinates forming triangulation graph"""
def triangulate_set(coords):
	out = spatial.Delaunay(coords)
	alledges = set()
	for i in out.simplices:
		ab =frozenset((coords[i[0]],coords[i[1]]))
		bc =frozenset((coords[i[1]],coords[i[2]]))
		ca =frozenset((coords[i[2]],coords[i[0]]))
		alledges.add(ab)
		alledges.add(bc)
		alledges.add(ca)

	return [list(x) for x in alledges ]

""" requires list of ccordinates, returns pairs of coordinates, by their indexes, forming triangulation graph"""
def triangulate_set_labelling(coords):
	out = spatial.Delaunay(coords)
	alledges = set()
	for i in out.simplices:
		ab =frozenset((i[0],i[1]))
		bc =frozenset((i[1],i[2]))
		ca =frozenset((i[2],i[0]))
		alledges.add(ab)
		alledges.add(bc)
		alledges.add(ca)

	return [list(x) for x in alledges ]
