# coding=utf-8
"""
Implementation of the straight skeleton algorithm by Felkel and Obdrzalek[1].
[1] Felkel, Petr and Stepan Obdrzalek. 1998. "Straight Skeleton Implementation." In
Proceedings of Spring Conference on Computer Graphics, Budmerice, Slovakia. 210 - 218.
"""

from __future__ import division

import logging
import heapq
from itertools import tee, islice, cycle, chain
from collections import namedtuple
import operator

# Geometry classes
from ladybug_geometry.geometry2d.pointvector import Point2D
from ladybug_geometry.geometry2d.line import LineSegment2D
from ladybug_geometry.geometry2d.ray import Ray2D
from ladybug_geometry import intersection2d

# Polygon sorting classes
_OriginalEdge = namedtuple('_OriginalEdge', 'edge bisector_left, bisector_right')
Subtree = namedtuple('Subtree', 'source, height, sinks')
_SplitEventSubClass = namedtuple('_SplitEvent',
                                 'distance, intersection_point, vertex, opposite_edge')
_EdgeEventSubClass = namedtuple('_EdgeEvent',
                                'distance intersection_point vertex_a vertex_b')

log = logging.getLogger("__name__")
# logging.basicConfig(filename='dg.log',level=logging.DEBUG)


class _Debug:
    """The _Debug class stores the bisectors for each edge event."""

    def __init__(self, image):
        if image is not None:
            self.im = image[0]
            self.draw = image[1]
            self.do = True
        else:
            self.do = False

    def line(self, *args, **kwargs):
        if self.do:
            self.draw.line(*args, **kwargs)

    def rectangle(self, *args, **kwargs):
        if self.do:
            self.draw.rectangle(*args, **kwargs)

    def show(self):
        if self.do:
            self.im.show()


_debug = _Debug(None)


# Debug set function
def set_debug(image):
    global _debug
    _debug = _Debug(image)


class _SplitEvent(_SplitEventSubClass):
    """A Split Event is a reflex vertex that splits an Edge Event.

    They therefore split the entire polygon and create new adjacencies between the split
    edge and each of the two edges incident to the reflex vertex
    (Felkel and Obdrzalek 1998, 1).
    """

    __slots__ = ()

    def __str__(self):
        return "{} Split event @ {} from {} to {}".format(
            self.distance,
            self.intersection_point,
            self.vertex,
            self.opposite_edge)


class _EdgeEvent(_EdgeEventSubClass):
    """
    An Edge Event is an edge extended from a perimeter edge, that shrinks to zero.

    This will make its neighoring edges adjacent (Felkel and Obdrzalek 1998, 2).
    """
    __slots__ = ()

    def __str__(self):
        return "{} Edge event @ {} between {} and {}".format(
            self.distance,
            self.intersection_point,
            self.vertex_a,
            self.vertex_b)


class _LAVertex:
    """A LAVertex is a vertex in a double connected circular list of active vertices."""

    def __init__(self, point, edge_left, edge_right, direction_vectors=None, tol=1e-10):
        self.point = point
        self.edge_left = edge_left
        self.edge_right = edge_right
        self.prev = None
        self.next = None
        self.lav = None
        self.tol = tol
        self.id = None
        # this should be handled better. Maybe membership in lav implies validity?
        self._valid = True
        creator_vectors = (edge_left.v.normalize() * -1, edge_right.v.normalize())
        if direction_vectors is None:
            direction_vectors = creator_vectors
        # The determinant of two 2d vectors equals the sign of their cross product
        # If second vector is to left, then sign of det is pos, else neg
        # So if cw polygon, convex angle will be neg (since second vector to right)
        # In this case, since we flip first vector, concave will be neg
        self._is_reflex = direction_vectors[0].determinant(direction_vectors[1]) < 0.0
        self._bisector = Ray2D(
            self.point,
            operator.add(*creator_vectors) * (-1 if self.is_reflex else 1)
        )
        log.info("Created vertex %s", self.__repr__())
        _debug.line(
            (self.bisector.p.x, self.bisector.p.y,
             self.bisector.p.x + self.bisector.v.x * 100,
             self.bisector.p.y + self.bisector.v.y * 100),
            fill="blue")

    @property
    def bisector(self):
        return self._bisector

    def __eq__(self, other):
        """Equality of this _LAvertex with another."""
        return self.point.is_equivalent(other.point, self.tol) and \
            self.edge_left.is_equivalent(other.edge_left, self.tol) and \
            self.edge_right.is_equivalent(other.edge_right, self.tol) and \
            self.next.point.is_equivalent(other.next.point, self.tol) and \
            self.prev.point.is_equivalent(other.prev.point, self.tol)

    @property
    def is_reflex(self):
        return self._is_reflex

    @property
    def original_edges(self):
        return self.lav._slav._original_edges

    def next_event(self):
        """ Computes the event (change to edge) associated with each polygon vertex.

        Reflex vertices can result in split or edge events, while non-reflex vertices
        will result in only edge events.

        Returns:
            EdgeEvent associated with self.
        """
        events = []
        if self.is_reflex:
            # a reflex vertex may generate a split event
            # split events happen when a vertex hits an opposite edge,
            # splitting the polygon in two.
            log.debug("looking for split candidates for vertex %s", self)
            for edge in self.original_edges:
                cond_1 = edge.edge.is_equivalent(self.edge_left, self.tol)
                if cond_1 or edge.edge.is_equivalent(self.edge_right, self.tol):
                    continue

                log.debug('\tconsidering EDGE %s', edge)

                # A potential b is at the intersection of between our own bisector and
                # the bisector of the angle between the tested edge and any one of our
                # own edges.

                # We choose the 'less parallel' edge (in order to exclude a
                # potentially parallel edge)

                # Make normalized copies of vectors
                norm_edge_left_v = self.edge_left.v.normalize()
                norm_edge_right_v = self.edge_right.v.normalize()
                norm_edge_v = edge.edge.v.normalize()

                # Compute dot
                leftdot = abs(norm_edge_left_v.dot(norm_edge_v))
                rightdot = abs(norm_edge_right_v.dot(norm_edge_v))
                selfedge = self.edge_left if leftdot < rightdot else self.edge_right
                # otheredge = self.edge_left if leftdot > rightdot else self.edge_right

                # Make copies of edges and compute intersection
                self_edge_copy = LineSegment2D(selfedge.p, selfedge.v)
                edge_edge_copy = LineSegment2D(edge.edge.p, edge.edge.v)
                # Ray line intersection
                i = intersection2d.intersect_line2d_infinite(
                    edge_edge_copy,
                    self_edge_copy)

                if (i is not None) and (not i.is_equivalent(self.point, self.tol)):
                    # locate candidate b
                    linvec = (self.point - i).normalize()
                    edvec = edge.edge.v.normalize()
                    if linvec.dot(edvec) < 0:
                        edvec = -edvec

                    bisecvec = edvec + linvec
                    if abs(bisecvec.magnitude) < self.tol:
                        continue
                    bisector = LineSegment2D(i, bisecvec)
                    b = intersection2d.intersect_line2d(self.bisector, bisector)
                    if b is None:
                        continue

                    # check eligibility of b
                    # a valid b should lie within the area limited by the edge and the
                    # bisectors of its two vertices:
                    _left_bisector_norm = edge.bisector_left.v.normalize()
                    _left_to_b_norm = (b - edge.bisector_left.p).normalize()
                    xleft = _left_bisector_norm.determinant(_left_to_b_norm) > 0

                    _right_bisector_norm = edge.bisector_right.v.normalize()
                    _right_to_b_norm = (b - edge.bisector_right.p).normalize()
                    xright = _right_bisector_norm.determinant(_right_to_b_norm) < 0

                    _edge_edge_norm = edge.edge.v.normalize()
                    _b_to_edge_norm = (b - edge.edge.p).normalize()
                    xedge = _edge_edge_norm.determinant(_b_to_edge_norm) < 0

                    if not (xleft and xright and xedge):
                        log.debug(
                            '\t\tDiscarded candidate %s (%s-%s-%s)',
                            b, xleft, xright, xedge)
                        continue

                    log.debug('\t\tFound valid candidate %s', b)
                    _dist_line_to_b = LineSegment2D(
                        edge.edge.p,
                        edge.edge.v).distance_to_point(b)
                    if _dist_line_to_b < self.tol:
                        _dist_line_to_b = 0.0
                    _new_split_event = _SplitEvent(_dist_line_to_b, b, self, edge.edge)
                    events.append(_new_split_event)

        # Intersect line2d with line2d (does not assume lines are infinite)
        i_prev = intersection2d.intersect_line2d_infinite(
            self.prev.bisector, self.bisector)
        i_next = intersection2d.intersect_line2d_infinite(
            self.next.bisector, self.bisector)
        # Make EdgeEvent and append to events
        if i_prev is not None:
            dist_to_i_prev = LineSegment2D(
                self.edge_left.p.duplicate(),
                self.edge_left.v.duplicate()).distance_to_point(i_prev)
            if dist_to_i_prev < self.tol:
                dist_to_i_prev = 0.0
            events.append(_EdgeEvent(dist_to_i_prev, i_prev, self.prev, self))

        if i_next is not None:
            dist_to_i_next = LineSegment2D(
                self.edge_right.p.duplicate(),
                self.edge_right.v.duplicate()).distance_to_point(i_next)
            if dist_to_i_next < self.tol:
                dist_to_i_next = 0.0
            events.append(_EdgeEvent(dist_to_i_next, i_next, self, self.next))

        if not events:
            return None

        ev = min(events,
                 key=lambda event:
                 self.point.distance_to_point(event.intersection_point))

        log.info('Generated new event for %s: %s', self, ev)
        return ev

    def invalidate(self):
        """Mutates invalidate attribute of self.
        """
        if self.lav is not None:
            self.lav.invalidate(self)
        else:
            self._valid = False

    @property
    def is_valid(self):
        return self._valid

    def __str__(self):
        return 'Vertex ({:.2f};{:.2f})'.format(self.point.x, self.point.y)

    def __lt__(self, other):
        if isinstance(other, _LAVertex):
            return self.point.x < other.point.x

    def __repr__(self):
        return 'Vertex ({}) ({:.2f};{:.2f}), bisector {}, edges {} {}'.format(
            'reflex' if self.is_reflex else 'convex',
            self.point.x,
            self.point.y,
            self.bisector,
            self.edge_left,
            self.edge_right)


class _SLAV:
    """ A SLAV is a set of circular lists of active vertices.

    It stores a loop of vertices for the outer boundary, and for all holes and
    sub-polygons created during the straight skeleton computation
    (Felkel and Obdrzalek 1998, 2).
    """

    def __init__(self, polygon, holes, tol):
        self.tol = tol
        contours = [_normalize_contour(polygon, tol)]
        contours.extend([_normalize_contour(hole, tol) for hole in holes])

        self._lavs = [_LAV.from_polygon(contour, self) for contour in contours]

        # Store original polygon edges for calculating split events
        self._original_edges = [
            _OriginalEdge(
                LineSegment2D.from_end_points(vertex.prev.point, vertex.point),
                vertex.prev.bisector,
                vertex.bisector
            ) for vertex in chain.from_iterable(self._lavs)
        ]

    def __iter__(self):
        for lav in self._lavs:
            yield lav

    def __len__(self):
        return len(self._lavs)

    def empty(self):
        return len(self._lavs) == 0

    def handle_edge_event(self, event):
        """Resolves adjacency of new edge event.

        This function resolves the edge event with previous edges, LAV, and then stores
        edge information in a Subtree.

        Args:
            event: EdgeEvent

        Returns:
            Subtree namedTuple
        """
        sinks = []
        events = []

        lav = event.vertex_a.lav
        # Triangle, one sink point
        if event.vertex_a.prev.point.is_equivalent(event.vertex_b.next.point, self.tol):
            log.info('%.2f Peak event at intersection %s from <%s,%s,%s> in %s',
                     event.distance, event.intersection_point, event.vertex_a,
                     event.vertex_b, event.vertex_a.prev, lav)
            self._lavs.remove(lav)
            lst_lav = list(lav)
            for vi, vertex in enumerate(lst_lav):
                sinks.append(vertex.point)
                vertex.invalidate()
        else:
            log.info('%.2f Edge event at intersection %s from <%s,%s> in %s',
                     event.distance, event.intersection_point, event.vertex_a,
                     event.vertex_b, lav)
            new_vertex = lav.unify(event.vertex_a,
                                   event.vertex_b, event.intersection_point)
            if lav.head in (event.vertex_a, event.vertex_b):
                lav.head = new_vertex

            sinks.extend((event.vertex_a.point, event.vertex_b.point))
            next_event = new_vertex.next_event()
            if next_event is not None:
                events.append(next_event)

        return (Subtree(event.intersection_point, event.distance, sinks), events)

    def handle_split_event(self, event):
        """Consumes a split event.

        This function resolves the adjacency of new split event with previous edges, LAV,
        and then stores edge information in a Subtree.

        Args:
            event: EdgeEvent

        Returns:
            Subtree namedTuple
        """
        lav = event.vertex.lav
        log.info(
            '%.2f Split event at intersection %s from vertex %s, for edge %s in %s',
            event.distance,
            event.intersection_point,
            event.vertex,
            event.opposite_edge,
            lav)

        sinks = [event.vertex.point]
        vertices = []
        x = None  # right vertex
        y = None  # left vertex
        norm = event.opposite_edge.v.normalize()
        for v in chain.from_iterable(self._lavs):
            log.debug('%s in %s', v, v.lav)
            equal_to_edge_left_p = event.opposite_edge.p.is_equivalent(
                v.edge_left.p, self.tol)
            equal_to_edge_right_p = event.opposite_edge.p.is_equivalent(
                v.edge_right.p, self.tol)

            _pnorm = Point2D(norm.x, norm.y)
            if _pnorm.is_equivalent(v.edge_left.v.normalize(), self.tol) \
                    and equal_to_edge_left_p:
                x = v
                y = x.prev
            elif _pnorm.is_equivalent(v.edge_right.v.normalize(), self.tol) \
                    and equal_to_edge_right_p:
                y = v
                x = y.next

            if x:
                xleft = y.bisector.v.normalize().determinant(
                    (event.intersection_point - y.point).normalize()) >= 0

                xright = x.bisector.v.normalize().determinant(
                    (event.intersection_point - x.point).normalize()) <= 0

                log.debug(
                    'Vertex %s holds edge as %s edge (%s, %s)', v,
                    ('left' if x == v else 'right'), xleft, xright)

                if xleft and xright:
                    break
                else:
                    x = None
                    y = None

        if x is None:
            log.info(
                'Failed split event %s (equivalent edge event is expected to follow)',
                event
            )
            return (None, [])

        v1 = _LAVertex(
            event.intersection_point,
            event.vertex.edge_left,
            event.opposite_edge,
            tol=self.tol
        )
        v2 = _LAVertex(
            event.intersection_point,
            event.opposite_edge,
            event.vertex.edge_right,
            tol=self.tol
        )

        v1.prev = event.vertex.prev
        v1.next = x
        event.vertex.prev.next = v1
        x.prev = v1

        v2.prev = y
        v2.next = event.vertex.next
        event.vertex.next.prev = v2
        y.next = v2

        new_lavs = None
        self._lavs.remove(lav)
        if lav != x.lav:
            # the split event actually merges two lavs
            self._lavs.remove(x.lav)
            new_lavs = [_LAV.from_chain(v1, self)]
        else:
            new_lavs = [_LAV.from_chain(v1, self), _LAV.from_chain(v2, self)]

        for lv in new_lavs:
            log.debug(lv)
            if len(lv) > 2:
                self._lavs.append(lv)
                vertices.append(lv.head)
            else:
                log.info(
                    'LAV %s has collapsed into the line %s--%s',
                    lv, lv.head.point, lv.head.next.point
                )
                sinks.append(lv.head.next.point)
                for v in list(lv):
                    v.invalidate()

        events = []
        for vertex in vertices:
            next_event = vertex.next_event()
            if next_event is not None:
                events.append(next_event)

        event.vertex.invalidate()
        return (Subtree(event.intersection_point, event.distance, sinks), events)


class _LAV:
    """A single circular list of active vertices.

    Stored in a SLAV (Felkel and Obdrzalek 1998, 2).
    """

    def __init__(self, slav):
        self.head = None
        self._slav = slav
        self._len = 0
        self.tol = slav.tol
        log.debug('Created LAV %s', self)

    @classmethod
    def from_polygon(cls, polygon, slav):
        """Construct a LAV from a list of point coordinates representing a polygon.

        Args:
            polygon: list of points (tuple of x,y coordinates).
            slav: SLAV (a set of circular lists of active vertices).
            tol: tolerance for point equality.

        Returns:
            LAV (single circular list of active vertices).
        """
        lav = cls(slav)
        for prev, point, next in _window(polygon):
            lav._len += 1
            vertex = _LAVertex(
                point,
                LineSegment2D.from_end_points(prev, point),
                LineSegment2D.from_end_points(point, next),
                tol=slav.tol
            )
            vertex.lav = lav
            if lav.head is None:
                lav.head = vertex
                vertex.prev = vertex.next = vertex
            else:
                vertex.next = lav.head
                vertex.prev = lav.head.prev
                vertex.prev.next = vertex
                lav.head.prev = vertex
        return lav

    @classmethod
    def from_chain(cls, head, slav):
        """Creates new LAV from consumed _LAVertex, and reference _SLAV.

        Args:
            head: Head _LAVertex that creates new _LAV loop.
            slav: Reference SLAV (a set of circular lists of active vertices).

        Returns:
            LAV (a single circular list of active vertices).
        """
        lav = cls(slav)
        lav.head = head
        for vertex in lav:
            lav._len += 1
            vertex.lav = lav
        return lav

    def invalidate(self, vertex):
        """Sets vertex validity to False, and handles head relationship.

        Args:
            vertex: _LAVertex to be invalidated.
        """
        assert vertex.lav is self, 'Tried to invalidate a vertex thats not mine'
        log.debug('Invalidating %s', vertex)
        vertex._valid = False
        if self.head == vertex:
            self.head = self.head.next
        vertex.lav = None

    def unify(self, vertex_a, vertex_b, point):
        """Generate a new _LAVertex from input Point2D and then resolves adjacency to old edges.

        Args:
            vertex_a = _LAVertex
            vertex_b = _LAVertex
            point = intersection point from angle bisectors from vertex_a
                and vertex_b as a Point2D.
        Returns:
            _LAVertex of intersection point.
        """
        normed_b_bisector = vertex_b.bisector.v.normalize()
        normed_a_bisector = vertex_a.bisector.v.normalize()
        replacement = _LAVertex(
            point,
            vertex_a.edge_left,
            vertex_b.edge_right,
            (normed_b_bisector, normed_a_bisector),
            tol=vertex_a.tol,
        )
        replacement.lav = self

        if self.head in [vertex_a, vertex_b]:
            self.head = replacement

        vertex_a.prev.next = replacement
        vertex_b.next.prev = replacement
        replacement.prev = vertex_a.prev
        replacement.next = vertex_b.next

        vertex_a.invalidate()
        vertex_b.invalidate()

        self._len -= 1
        return replacement

    def __str__(self):
        return 'LAV {}'.format(id(self))

    def __repr__(self):
        return '{} = {}'.format(str(self), [vertex for vertex in self])

    def __len__(self):
        return self._len

    def __iter__(self):
        cur = self.head
        while True:
            yield cur
            try:
                cur = cur.next
                if cur == self.head:
                    raise StopIteration
            except StopIteration:
                return

    def _show(self):
        """ Iterates through _LAV linked list and prints _LAVertex."""
        cur = self.head
        while True:
            print(cur.__repr__())
            cur = cur.next
            if cur == self.head:
                break


class _EventQueue:
    """
    An EventQueue is a priority queue that stores vertices of the polygon.
    """

    def __init__(self):
        self.__data = []

    def put(self, item):
        if item is not None:
            heapq.heappush(self.__data, item)

    def put_all(self, iterable):
        for item in iterable:
            heapq.heappush(self.__data, item)

    def get(self):
        return heapq.heappop(self.__data)

    def empty(self):
        return len(self.__data) == 0

    def peek(self):
        return self.__data[0]

    def show(self):
        for item in self.__data:
            print(item)


# Skeleton Code
def _window(lst):
    """
    Window operator for lists.

    Consume a list of items, and returns a zipped list of the previous, current and next
    items in the list, accessible by the same index.

    Args:
        lst: list

    Returns:
        Zipped list of previous, current and next items in list.
    """
    prevs, items, nexts = tee(lst, 3)
    prevs = islice(cycle(prevs), len(lst) - 1, None)
    nexts = islice(cycle(nexts), 1, None)
    return zip(prevs, items, nexts)


def _normalize_contour(contour, tol):
    """
    Consumes list of x,y coordinate tuples and returns list of Point2Ds.

    Args:
        contour: list of x,y tuples from contour.
        tol: Number for point equivalence tolerance.
    Return:
         list of Point2Ds of contour.
    """
    contour = [Point2D(float(x), float(y)) for (x, y) in contour]
    normed_contour = []
    for prev, point, next in _window(contour):
        normed_prev = (point - prev).normalize()
        normed_next = (next - point).normalize()

        if not point.is_equivalent(next, tol) or \
                normed_prev.is_equivalent(normed_next, tol):
            normed_contour.append(point)

    return normed_contour


def _skeletonize(slav):
    """
    Compute polygon straight skeleton from a Set of List of Active vertex (SLAV).

    The SLAV will represent the polygon as a double linked list of vertices in
    counter-clockwise order. Holes is a similar list with the vertices of which
    should be in clockwise order.

    Args:
        slav: SLAV object.
    Returns:
        List of subtrees.
    """
    output = []
    prioque = _EventQueue()

    for lav in slav:
        for vertex in lav:
            v = vertex.next_event()
            prioque.put(v)

    # While the priority queue or SLAV is not empty, compute the intersection of
    # bisectors at edge. The 'handle_edge_event' method computes the next event
    # from the new intersection via the next_event method. Thus, this while loop
    # iteratively adds new events without recursion.
    while not (prioque.empty() or slav.empty()):
        log.debug('SLAV is %s', [repr(lav) for lav in slav])
        i = prioque.get()  # vertex a, b is self or next vertex

        # Handle edge or split events.
        # arc: subtree(event.intersection_point, event.distance, sinks)
        # events: updated events with new vertex
        if isinstance(i, _EdgeEvent):
            if not i.vertex_a.is_valid or not i.vertex_b.is_valid:
                log.info('%.2f Discarded outdated edge event %s', i.distance, i)
                continue
            (arc, events) = slav.handle_edge_event(i)
        elif isinstance(i, _SplitEvent):
            if not i.vertex.is_valid:
                log.info('%.2f Discarded outdated split event %s', i.distance, i)
                continue
            (arc, events) = slav.handle_split_event(i)
        prioque.put_all(events)
        # As we traverse priorque, output list of "subtrees", which are in the form
        # of (source, height, sinks) where source is the highest points, height is
        # its distance to an edge, and sinks are the point connected to the source.
        if arc is not None:
            output.append(arc)
            for sink in arc.sinks:
                _debug.line((arc.source.x, arc.source.y, sink.x, sink.y), fill='red')
            _debug.show()

    return output


def skeleton_as_subtree_list(polygon, holes=None, tol=1e-10):
    """Compute polygon straight skeleton as a list of subtree source and sink points.

    Args:
        polygon: nested list of endpoint coordinates in counter-clockwise order.
            Example square: [[0,0], [1,0], [1,1], [0,1]]
        holes: list of polygons representing holes in clockwise order.
            Example hole: [[.25,.75], [.75,.75], [.75,.25], [.25,.25]]
        tol: Tolerance for point equivalence. (Default: 1e-10).

    Returns:
        List of subtrees.
    """

    # Reverse order to ensure cw order for input
    holes = [] if holes is None else [reversed(hole) for hole in holes]
    slav = _SLAV(reversed(polygon), holes, tol)

    subtree_list = _skeletonize(slav)

    return subtree_list


def skeleton_as_edge_list(polygon, holes=None, tol=1e-10):
    """Compute the straight skeleton of a polygon and returns skeleton as list of edges.

    Args:
        polygon: list of list of point coordinates in counter-clockwise order.
            Example square: [[0,0], [1,0], [1,1], [0,1]]
        holes: list of polygons representing holes in clockwise order.
            Example hole: [[.25,.75], [.75,.75], [.75,.25], [.25,.25]].
        tol: Tolerance for point equivalence. (Default: 1e-10).

    Returns:
        list of lines as coordinate tuples.
    """
    edge_lst = []

    # Reverse order to ensure cw order for input
    holes = [] if holes is None else[hole[::-1] for hole in holes]
    slav = _SLAV(polygon[::-1], holes, tol)
    subtree_list = _skeletonize(slav)

    for subtree in subtree_list:
        source_pt = subtree.source
        for sink_pt in subtree.sinks:
            edge_arr = ((source_pt.x, source_pt.y), (sink_pt.x, sink_pt.y))
            edge_lst.append(edge_arr)

    return edge_lst
