"""
Quad Tree Structure Class for PySAL_core/cg/shapes.Ring, PySAL_core/cg/shapes.Polygon
This structure could speed up the determining of point in polygon process
"""
__author__ = "Hu Shao"

from .shapes import Ring
import math


def cwt(a, b, tolerance=1e-9):
    """compare_with_tolerance

    For the float value comparing, there are some situlation that two values
    are actually the same but been shown differently, e.g 1.230 and
    1.2300000000000001. Especially after some calculation. This function is
    used to compare two float value with some tolerance

    Parameters
    ----------
    a : float
        The first value

    b : float
        The second value

    tolerance : float
        Tolerance for the comparing

    Returns
    -------
    if_bigger_than  : int
        if a is bigger than b 1: a > b 0: a == b -1: a < b

    """
    tolerance = math.fabs(tolerance)
    if a - b > tolerance:
        return 1
    elif a - b < -tolerance:
        return -1
    else:
        return 0


class Cell(object):
    """Basic rectangle geometry used for dividing research area (polygon) into quadtree structure

    Attributes
    ----------
    level : int
        Quadtree level this cell belongs to. Begins with 0

    min_x : float
        min x coordinate of this cell

    min_y : float
        min y coordinate of this cell

    length_x : float
        width of this cell

    length_y : float
        height of this cell

    arcs : list
        detected arc list which are within this cell

    status : str
        enum status of this cell, indicating this cell's spatial relationship with the research area
                  "in"      : this cell lies totally inside of the research area
                  "out"     : this cell lies totally outside of the research area
                  "maybe"   : this cell intersects with the research area's boundary

    children_l_b : Cell
        children of current cell, left-bottom

    children_l_t : Cell
        children of current cell, left-top

    children_r_b : Cell
        children of current cell, right-bottom

    children_t_t : Cell
        children of current cell, right-top

    """

    def __init__(self, level, min_x, min_y, length_x, length_y, arcs, status):
        """

        Parameters
        ----------
        level : int
            on which quadtree level this cell belongs to. Begins with 0

        min_x : float
            min x coordinate of this cell

        min_y : float
            min y coordinate of this cell

        length_x : float
            width of this cell

        length_y : float
            height of this cell

        arcs : list
            detected arc list which are within this cell

        status : str
            enum status of this cell, indicating this cell's spatial relationship with the research area
                      "in"      : this cell lies totally inside of the research area
                      "out"     : this cell lies totally outside of the research area
                      "maybe"   : this cell intersects with the research area's boundary
        """
        self.level = level
        self.min_x = min_x
        self.min_y = min_y
        self.length_x = length_x
        self.length_y = length_y
        self.arcs = arcs
        self.status = status
        self.zero_tolerance = 1e-9
        self._rings = None
        self.children_l_b = None
        self.children_l_t = None
        self.children_r_b = None
        self.children_r_t = None

    @property
    def rings(self):
        """ the list of rings which are formed by the intersection of this cell and the arcs pass them

        Returns
        -------

        rings : list

        """
        if self._rings is None:
            if self.status == "in" or self.status == "out":
                self._rings = []
            else:
                self._rings = []
                extract_result = extract_segments_from_cell_with_arcs(
                    [self.min_x, self.min_y],
                    self.length_x,
                    self.length_y,
                    self.arcs,
                    self.zero_tolerance,
                )
                for point_list in extract_result[0]:
                    self._rings.append(Ring(point_list))

        return self._rings

    def split(self):
        """equally split current cell into 4 sub cells

        if this cell in needed to be splitted into four parts, add the result cells as children to current cell
        """

        if self.status == "in" or self.status == "out":
            # no need to conduct the splitting
            return

        level = self.level + 1
        length_x = self.length_x / 2
        length_y = self.length_y / 2
        middle_x = self.min_x + length_x
        middle_y = self.min_y + length_y
        """
        Do the splitting work here.
        Some properties of the arc:
        - Point order of the arcs MUST be clockwise
        - The two end-points of each arc MUST lie on the borders of the cell
        - When a arc goes in a cell, it MUST goes out from the same one
        - The intersection points MUST be lying on the inner-boundaries which are used to divide the cell into 4 sub-cells
        - Use the intersection points to split the arcs into small ones
        - No need to store cell boundaries as arcs, store the intersection points, points' relative location from
        """
        if self.level == 0:
            if len(self.arcs) != 1:
                raise LookupError(
                    "Unexpected arc number! Only single ring can be assigned to the root cell"
                )
                return
            # Do some initialize work, find one point lies on the border of the rectangle(cell) and begin with this point
            arc = self.arcs[0]
            if (
                arc[0] == arc[len(arc) - 1]
            ):  # remove the duplicated points the the end of the arc
                arc = arc[0 : len(arc) - 1]
            min_x = arc[0][0]
            min_x_index = 0
            for index in range(0, len(arc)):
                if arc[index][0] < min_x:
                    min_x = arc[index][0]
                    min_x_index = index
            arc = arc[min_x_index : len(arc)] + arc[0 : min_x_index + 1]
            self.arcs[0] = arc

        # l: left, r: right, b: bottom, t: top
        cell_arcs_l_b = []
        cell_arcs_r_b = []
        cell_arcs_l_t = []
        cell_arcs_r_t = []
        for arc in self.arcs:
            temp_arc = []
            temp_arc_belonging = None
            for index in range(0, len(arc) - 1):
                x0 = arc[index][0]
                y0 = arc[index][1]
                x1 = arc[index + 1][0]
                y1 = arc[index + 1][1]
                if temp_arc_belonging is None:
                    """
                    In this section, determine which sub-cell does the current temp_arc belong to
                    Although every single arc must begin and end on the cell's outer boundaries, when the split
                    process begin, there might be some sub-arcs begin at the split-line. So here we should
                    consider all possible situations
                    See the image cell_boundary_category_rule to better understand the process
                    """
                    if cwt(x0, self.min_x, self.zero_tolerance) == 0:  # left border
                        if cwt(y0, middle_y, self.zero_tolerance) == -1:  # position 1
                            temp_arc_belonging = "l_b"
                        elif cwt(y0, middle_y, self.zero_tolerance) == 1:  # position 2
                            temp_arc_belonging = "l_t"
                        else:  # just by chance at the middle point
                            if cwt(y1, y0, self.zero_tolerance) == -1:  # going down
                                temp_arc_belonging = "l_b"
                            elif cwt(y1, y0, self.zero_tolerance) == 1:  # going up
                                temp_arc_belonging = "l_t"
                            else:  # just by chance this segment lies on split_line_h, throw it
                                continue
                    elif (
                        cwt(x0, self.min_x + self.length_x, self.zero_tolerance) == 0
                    ):  # right border
                        if cwt(y0, middle_y, self.zero_tolerance) == -1:  # position 6
                            temp_arc_belonging = "r_b"
                        elif cwt(y0, middle_y, self.zero_tolerance) == 1:  # position 5
                            temp_arc_belonging = "r_t"
                        else:  # just by chance at the middle point
                            if cwt(y1, y0, self.zero_tolerance) == -1:  # going down
                                temp_arc_belonging = "r_b"
                            elif cwt(y1, y0, self.zero_tolerance) == 1:  # going up
                                temp_arc_belonging = "r_t"
                            else:  # just by chance this segment lies on split_line_h, throw it
                                continue
                    elif cwt(y0, self.min_y, self.zero_tolerance) == 0:  # bottom border
                        if cwt(x0, middle_x, self.zero_tolerance) == -1:  # position 8
                            temp_arc_belonging = "l_b"
                        elif cwt(x0, middle_x, self.zero_tolerance) == 1:  # position 7
                            temp_arc_belonging = "r_b"
                        else:  # just by chance at the middle point
                            if cwt(x1, x0, self.zero_tolerance) == -1:  # going left
                                temp_arc_belonging = "l_b"
                            elif cwt(x1, x0, self.zero_tolerance) == 1:  # going right
                                temp_arc_belonging = "r_b"
                            else:  # just by chance this segment lies on split_line_v, throw it
                                continue
                    elif (
                        cwt(y0, self.min_y + self.length_y, self.zero_tolerance) == 0
                    ):  # top border
                        if cwt(x0, middle_x, self.zero_tolerance) == -1:  # position 3
                            temp_arc_belonging = "l_t"
                        elif cwt(x0, middle_x, self.zero_tolerance) == 1:  # position 4
                            temp_arc_belonging = "r_t"
                        else:  # just by chance at the middle point
                            if cwt(x1, x0, self.zero_tolerance) == -1:  # going left
                                temp_arc_belonging = "l_t"
                            elif cwt(x1, x0, self.zero_tolerance) == 1:  # going right
                                temp_arc_belonging = "r_t"
                            else:  # just by chance this segment lies on split_line_v, throw it
                                continue
                    elif cwt(x0, middle_x, self.zero_tolerance) == 0:  # split_line_v
                        if cwt(y0, middle_y, self.zero_tolerance) == 1:  # position c
                            if cwt(x1, x0, self.zero_tolerance) == 1:
                                temp_arc_belonging = "r_t"
                            elif cwt(x1, x0, self.zero_tolerance) == -1:
                                temp_arc_belonging = "l_t"
                            else:  # x1==x0, just by chance on the split_line_v
                                continue
                        elif cwt(y0, middle_y, self.zero_tolerance) == -1:  # position d
                            if cwt(x1, x0, self.zero_tolerance) == 1:
                                temp_arc_belonging = "r_b"
                            elif cwt(x1, x0, self.zero_tolerance) == -1:
                                temp_arc_belonging = "l_b"
                            else:  # x1==x0, just by chance on the split_line_v
                                continue
                        else:  # in condition that p0 lies at the cross point of two split lines
                            if (
                                cwt(x1, x0, self.zero_tolerance) == 0
                                or cwt(y1, y0, self.zero_tolerance) == 0
                            ):  # on one of the split_line
                                continue
                            elif cwt(x1, x0, self.zero_tolerance) == 1:
                                if cwt(y1, y0, self.zero_tolerance) == 1:
                                    temp_arc_belonging = "r_t"
                                else:
                                    temp_arc_belonging = "r_b"
                            else:  # on condition that x1 < x0
                                if cwt(y1, y0, self.zero_tolerance) == 1:
                                    temp_arc_belonging = "l_t"
                                else:
                                    temp_arc_belonging = "l_b"
                    elif cwt(y0, middle_y, self.zero_tolerance) == 0:  # split_line_h
                        if cwt(x0, middle_x, self.zero_tolerance) == 1:  # position r
                            if cwt(y1, y0, self.zero_tolerance) == 1:
                                temp_arc_belonging = "r_t"
                            elif cwt(y1, y0, self.zero_tolerance) == -1:
                                temp_arc_belonging = "r_b"
                            else:  # y1==y0, just by chance on the split_line_h
                                continue
                        else:  # on condition that x0 < middle_x, position a
                            if cwt(y1, y0, self.zero_tolerance) == 1:
                                temp_arc_belonging = "l_t"
                            elif cwt(y1, y0, self.zero_tolerance) == -1:
                                temp_arc_belonging = "l_b"
                            else:  # y1==y0, just by chance on the split_line_h
                                continue
                if temp_arc_belonging is None:
                    raise Exception("Error on cell split!!!")

                # At this point, the belonging sub-cell of current segment is already known.
                # Let's begin the splitting!
                """
                Firstly determine if the segment totally lies on the split_lines.
                p1 (x1, y1) could lie on the split_lines
                This situation is not the same with previous ones which "both points lie on the same split_line"
                In previous situation, the p1 is the begin point of a sub arc, we can just throw that segment if
                it totally lie on split_line. However, in current situation, the segment is in the middle of the
                sub-arc. So if the segment is detected totally lie on the split_line, we should split the sub_arc
                here.
                """
                if (
                    cwt(x0, x1, self.zero_tolerance)
                    == cwt(x0, middle_x, self.zero_tolerance)
                    == 0
                    or cwt(y0, y1, self.zero_tolerance)
                    == cwt(y0, middle_y, self.zero_tolerance)
                    == 0
                ):  # split the arc here, throw current segment
                    if len(temp_arc) != 0:
                        if temp_arc_belonging == "l_b":
                            cell_arcs_l_b.append(temp_arc)
                        elif temp_arc_belonging == "l_t":
                            cell_arcs_l_t.append(temp_arc)
                        elif temp_arc_belonging == "r_b":
                            cell_arcs_r_b.append(temp_arc)
                        elif temp_arc_belonging == "r_t":
                            cell_arcs_r_t.append(temp_arc)
                    temp_arc = []
                    temp_arc_belonging = None
                    continue

                intersect_point_h = None
                intersect_point_v = None
                # Check if the segment intersects with split_line_h
                if (
                    cwt(y0, middle_y, self.zero_tolerance) == -1
                    and cwt(middle_y, y1, self.zero_tolerance) <= 0
                ) or (
                    cwt(y0, middle_y, self.zero_tolerance) == 1
                    and cwt(middle_y, y1, self.zero_tolerance) >= 0
                ):
                    if (
                        cwt(x0, x1, self.zero_tolerance) == 0
                    ):  # the segments is vertical
                        intersect_point_h = [x0, middle_y]
                    else:
                        a = (y1 - y0) / (x1 - x0)
                        b = y0 - a * x0
                        x_new = (middle_y - b) / a
                        intersect_point_h = [x_new, middle_y]
                # Check if the segment intersects with split_line_v
                if (
                    cwt(x0, middle_x, self.zero_tolerance) == -1
                    and cwt(middle_x, x1, self.zero_tolerance) <= 0
                ) or (
                    cwt(x0, middle_x, self.zero_tolerance) == 1
                    and cwt(middle_x, x1, self.zero_tolerance) >= 0
                ):
                    if (
                        cwt(y0, y1, self.zero_tolerance) == 0
                    ):  # the segments is horizontal
                        intersect_point_v = [middle_x, y0]
                    else:
                        a = (y1 - y0) / (x1 - x0)
                        b = y0 - a * x0
                        y_new = a * middle_x + b
                        intersect_point_v = [middle_x, y_new]
                # check if the intersect point(s) exist
                intersect_point = None
                intersect_point_mark = None
                if (intersect_point_h is not None) and (intersect_point_v is not None):
                    # In this situation, the current segment cannot be vertical nor horizontal.
                    # Find the closer intersection point to p0
                    if math.fabs(intersect_point_h[0] - x0) < math.fabs(
                        intersect_point_v[0] - x0
                    ):
                        intersect_point = intersect_point_h
                        intersect_point_mark = "h"
                    else:
                        intersect_point = intersect_point_v
                        intersect_point_mark = "v"
                elif intersect_point_h is not None:
                    intersect_point = intersect_point_h
                    intersect_point_mark = "h"
                elif intersect_point_v is not None:
                    intersect_point = intersect_point_v
                    intersect_point_mark = "v"

                if intersect_point is not None:  # split the arc here
                    if len(temp_arc) == 0:
                        temp_arc.append([x0, y0])
                    temp_arc.append(intersect_point)
                    if temp_arc_belonging == "l_b":
                        cell_arcs_l_b.append(temp_arc)
                    elif temp_arc_belonging == "l_t":
                        cell_arcs_l_t.append(temp_arc)
                    elif temp_arc_belonging == "r_b":
                        cell_arcs_r_b.append(temp_arc)
                    elif temp_arc_belonging == "r_t":
                        cell_arcs_r_t.append(temp_arc)

                    if temp_arc_belonging == "l_b":
                        if intersect_point_mark == "h":
                            if (intersect_point_h is not None) and (
                                intersect_point_v is not None
                            ):
                                # under the situation that a single segment intersects with both split lines,
                                # here need carefully process
                                small_arc = [intersect_point_h, intersect_point_v]
                                if (
                                    cwt(
                                        intersect_point_h[0],
                                        intersect_point_v[0],
                                        self.zero_tolerance,
                                    )
                                    != 0
                                ):  # deal with the situation that the segment just goes through center point
                                    cell_arcs_l_t.append(small_arc)
                                temp_arc = [intersect_point_v, [x1, y1]]
                                temp_arc_belonging = "r_t"
                            else:
                                temp_arc = [intersect_point, [x1, y1]]
                                temp_arc_belonging = "l_t"
                        else:
                            if (intersect_point_h is not None) and (
                                intersect_point_v is not None
                            ):
                                # under the situation that a single segment intersects with both split lines,
                                # here need carefully process
                                small_arc = [intersect_point_v, intersect_point_h]
                                if (
                                    cwt(
                                        intersect_point_h[0],
                                        intersect_point_v[0],
                                        self.zero_tolerance,
                                    )
                                    != 0
                                ):  # deal with the situation that the segment just goes through center point
                                    cell_arcs_r_b.append(small_arc)
                                temp_arc = [intersect_point_h, [x1, y1]]
                                temp_arc_belonging = "r_t"
                            else:
                                temp_arc = [intersect_point, [x1, y1]]
                                temp_arc_belonging = "r_b"

                    elif temp_arc_belonging == "l_t":
                        if intersect_point_mark == "h":
                            if (intersect_point_h is not None) and (
                                intersect_point_v is not None
                            ):
                                # under the situation that a single segment intersects with both split lines,
                                # here need carefully process
                                small_arc = [intersect_point_h, intersect_point_v]
                                if (
                                    cwt(
                                        intersect_point_h[0],
                                        intersect_point_v[0],
                                        self.zero_tolerance,
                                    )
                                    != 0
                                ):  # deal with the situation that the segment just goes through center point
                                    cell_arcs_l_b.append(small_arc)
                                temp_arc = [intersect_point_v, [x1, y1]]
                                temp_arc_belonging = "r_b"
                            else:
                                temp_arc = [intersect_point, [x1, y1]]
                                temp_arc_belonging = "l_b"
                        else:
                            if (intersect_point_h is not None) and (
                                intersect_point_v is not None
                            ):
                                # under the situation that a single segment intersects with both split lines,
                                # here need carefully process
                                small_arc = [intersect_point_v, intersect_point_h]
                                if (
                                    cwt(
                                        intersect_point_h[0],
                                        intersect_point_v[0],
                                        self.zero_tolerance,
                                    )
                                    != 0
                                ):  # deal with the situation that the segment just goes through center point
                                    cell_arcs_r_t.append(small_arc)
                                temp_arc = [intersect_point_h, [x1, y1]]
                                temp_arc_belonging = "r_b"
                            else:
                                temp_arc = [intersect_point, [x1, y1]]
                                temp_arc_belonging = "r_t"

                    elif temp_arc_belonging == "r_b":
                        if intersect_point_mark == "h":
                            if (intersect_point_h is not None) and (
                                intersect_point_v is not None
                            ):
                                # under the situation that a single segment intersects with both split lines,
                                # here need carefully process
                                small_arc = [intersect_point_h, intersect_point_v]
                                if (
                                    cwt(
                                        intersect_point_h[0],
                                        intersect_point_v[0],
                                        self.zero_tolerance,
                                    )
                                    != 0
                                ):  # deal with the situation that the segment just goes through center point
                                    cell_arcs_r_t.append(small_arc)
                                temp_arc = [intersect_point_v, [x1, y1]]
                                temp_arc_belonging = "l_t"
                            else:
                                temp_arc = [intersect_point, [x1, y1]]
                                temp_arc_belonging = "r_t"
                        else:
                            if (intersect_point_h is not None) and (
                                intersect_point_v is not None
                            ):
                                # under the situation that a single segment intersects with both split lines,
                                # here need carefully process
                                small_arc = [intersect_point_v, intersect_point_h]
                                if (
                                    cwt(
                                        intersect_point_h[0],
                                        intersect_point_v[0],
                                        self.zero_tolerance,
                                    )
                                    != 0
                                ):  # deal with the situation that the segment just goes through center point
                                    cell_arcs_l_b.append(small_arc)
                                temp_arc = [intersect_point_h, [x1, y1]]
                                temp_arc_belonging = "l_t"
                            else:
                                temp_arc = [intersect_point, [x1, y1]]
                                temp_arc_belonging = "l_b"

                    elif temp_arc_belonging == "r_t":
                        if intersect_point_mark == "h":
                            if (intersect_point_h is not None) and (
                                intersect_point_v is not None
                            ):
                                # under the situation that a single segment intersects with both split lines,
                                # here need carefully process
                                small_arc = [intersect_point_h, intersect_point_v]
                                if (
                                    cwt(
                                        intersect_point_h[0],
                                        intersect_point_v[0],
                                        self.zero_tolerance,
                                    )
                                    != 0
                                ):  # deal with the situation that the segment just goes through center point
                                    cell_arcs_r_b.append(small_arc)
                                temp_arc = [intersect_point_v, [x1, y1]]
                                temp_arc_belonging = "l_b"
                            else:
                                temp_arc = [intersect_point, [x1, y1]]
                                temp_arc_belonging = "r_b"
                        else:
                            if (intersect_point_h is not None) and (
                                intersect_point_v is not None
                            ):
                                # under the situation that a single segment intersects with both split lines,
                                # here need carefully process
                                small_arc = [intersect_point_v, intersect_point_h]
                                if (
                                    cwt(
                                        intersect_point_h[0],
                                        intersect_point_v[0],
                                        self.zero_tolerance,
                                    )
                                    != 0
                                ):  # deal with the situation that the segment just goes through center point
                                    cell_arcs_l_t.append(small_arc)
                                temp_arc = [intersect_point_h, [x1, y1]]
                                temp_arc_belonging = "l_b"
                            else:
                                temp_arc = [intersect_point, [x1, y1]]
                                temp_arc_belonging = "l_t"
                    if (
                        cwt(temp_arc[0][0], temp_arc[1][0], self.zero_tolerance) == 0
                        and cwt(temp_arc[0][1], temp_arc[1][1], self.zero_tolerance)
                        == 0
                    ):
                        # to deal with the situation that p1 just lied on one of the split-lines
                        temp_arc = []
                        temp_arc_belonging = None
                else:  # simply append the point to current arc
                    if len(temp_arc) == 0:
                        temp_arc.append([x0, y0])
                    temp_arc.append([x1, y1])
            # Allocate the last left arc to a sub-cell
            if len(temp_arc) > 0:
                if temp_arc_belonging == "l_b":
                    cell_arcs_l_b.append(temp_arc)
                elif temp_arc_belonging == "l_t":
                    cell_arcs_l_t.append(temp_arc)
                elif temp_arc_belonging == "r_b":
                    cell_arcs_r_b.append(temp_arc)
                elif temp_arc_belonging == "r_t":
                    cell_arcs_r_t.append(temp_arc)
        status_l_b = "maybe"
        status_l_t = "maybe"
        status_r_b = "maybe"
        status_r_t = "maybe"
        """
        At this point, all the arcs in this cell have been split into sub-arcs and allocated to 4 sub-cells.
        So, we can try to create the cells on left-bottom, right-bottom, left-top and right-top.
        Before doing that, we need to determine the status of each sub-cell, especially those who are totally
        within or out of the study area.
        These two kind of sub-cell have the same property: they don't have arc allocated. So, If here exists
        cell(s) who don't have arcs allocated, we need to begin the check
        """
        if (
            len(cell_arcs_l_b)
            * len(cell_arcs_l_t)
            * len(cell_arcs_r_b)
            * len(cell_arcs_r_t)
            == 0
        ):
            extract_result = extract_segments_from_cell_with_arcs(
                [self.min_x, self.min_y],
                self.length_x,
                self.length_y,
                self.arcs,
                self.zero_tolerance,
            )
            construct_rings = []
            for arc in extract_result[0]:
                construct_rings.append(Ring(arc))
            # determine the totally within and out-of sub cells
            if len(cell_arcs_l_b) == 0:
                center = [self.min_x + length_x / 2, self.min_y + length_y / 2]
                is_in = False
                for ring in construct_rings:
                    if ring.contains_point(center):
                        is_in = True
                if is_in:
                    status_l_b = "in"
                else:
                    status_l_b = "out"
            if len(cell_arcs_l_t) == 0:
                center = [self.min_x + length_x / 2, middle_y + length_y / 2]
                is_in = False
                for ring in construct_rings:
                    if ring.contains_point(center):
                        is_in = True
                if is_in:
                    status_l_t = "in"
                else:
                    status_l_t = "out"
            if len(cell_arcs_r_b) == 0:
                center = [middle_x + length_x / 2, self.min_y + length_y / 2]
                is_in = False
                for ring in construct_rings:
                    if ring.contains_point(center):
                        is_in = True
                if is_in:
                    status_r_b = "in"
                else:
                    status_r_b = "out"
            if len(cell_arcs_r_t) == 0:
                center = [middle_x + length_x / 2, middle_y + length_y / 2]
                is_in = False
                for ring in construct_rings:
                    if ring.contains_point(center):
                        is_in = True
                if is_in:
                    status_r_t = "in"
                else:
                    status_r_t = "out"

        cells_l_b = Cell(
            level, self.min_x, self.min_y, length_x, length_y, cell_arcs_l_b, status_l_b
        )
        cells_l_t = Cell(
            level, self.min_x, middle_y, length_x, length_y, cell_arcs_l_t, status_l_t
        )
        cells_r_b = Cell(
            level, middle_x, self.min_y, length_x, length_y, cell_arcs_r_b, status_r_b
        )
        cells_r_t = Cell(
            level, middle_x, middle_y, length_x, length_y, cell_arcs_r_t, status_r_t
        )
        self.children_l_b = cells_l_b
        self.children_l_t = cells_l_t
        self.children_r_b = cells_r_b
        self.children_r_t = cells_r_t

    #     ===================

    def contains_point(self, point):
        """Decide if this cell (rectangle) contains a given point

        Parameters
        ----------
        point : list
            Point structure, like [x, y]

        Returns
        -------
        if_contains : bool

        """
        if self.status == "out":
            return False
        if (
            point[0] < self.min_x
            or point[0] > self.min_x + self.length_x
            or point[1] < self.min_y
            or point[1] > self.min_y + self.length_y
        ):
            return False
        if self.status == "in":
            return True
        else:
            is_in = False
            for ring in self.rings:
                if ring.contains_point(point):
                    is_in = True
            return is_in


def extract_connecting_borders_between_points(
    cell_min_point, cell_length_x, cell_length_y, point_begin, point_end, zero_tolerance
):

    """There is an rectangle and two points on the border, this function is
    used to extract the borders connecting these two points. The segments must
    be clockwise

    Parameters
    ----------
    cell_min_point : list
        the bottom-left point of the cell, like [x0, y0]

    cell_length_x : float
        width of the cell

    cell_length_y : float
        height of the cell

    point_begin  : list
        the first point on the cell's border. like [xa, ya]

    point_end : list
        the second point on the cell's border. like [xb, yb]

    result_type : str
        MUST be one of ["segments", "border_ids"]. Indicts which kind of result
        will return. "segments": return the segments list which connecting
        these two points "border_ids" return a list of ids of the orders of the
        cell connecting these two points

    zero_tolerance : float
        value of zero_tolerance for determining if two float values are equal

    Returns
    -------
    segments_and_ids : tuple
        like (segments, involved_border_ids) 1. list of points, including the
        start and end points 2. list of border ids being involved in the
        segments, not necessary to be in the original order

    """
    if point_begin == point_end:
        return ([], [])
    # Determine which borders do the point_begin and point_end belong
    border_id_p_begin = -1
    border_id_p_end = -1
    if cwt(point_begin[0], cell_min_point[0], zero_tolerance) == 0:
        border_id_p_begin = 0
    elif cwt(point_begin[1], cell_min_point[1] + cell_length_y, zero_tolerance) == 0:
        border_id_p_begin = 1
    elif cwt(point_begin[0], cell_min_point[0] + cell_length_x, zero_tolerance) == 0:
        border_id_p_begin = 2
    elif cwt(point_begin[1], cell_min_point[1], zero_tolerance) == 0:
        border_id_p_begin = 3

    if cwt(point_end[0], cell_min_point[0], zero_tolerance) == 0:
        border_id_p_end = 0
    elif cwt(point_end[1], cell_min_point[1] + cell_length_y, zero_tolerance) == 0:
        border_id_p_end = 1
    elif cwt(point_end[0], cell_min_point[0] + cell_length_x, zero_tolerance) == 0:
        border_id_p_end = 2
    elif cwt(point_end[1], cell_min_point[1], zero_tolerance) == 0:
        border_id_p_end = 3

    if border_id_p_begin == -1 or border_id_p_end == -1:
        print(
            (
                cell_min_point,
                cell_min_point[0] + cell_length_x,
                cell_min_point[1] + cell_length_y,
                point_begin,
                point_end,
                cell_length_x,
                cell_length_y,
            )
        )
        raise Exception("Error! begin/end point doesn't lie on the cell border!!!")

    # Now, move forward from point_begin to point_end
    segments = [point_begin]
    involved_border_ids = [border_id_p_begin]
    border_id_p_search = border_id_p_begin
    if (
        border_id_p_search == border_id_p_end
    ):  # first check if they lie on the same border at the beginning
        if border_id_p_search == 0:
            if cwt(point_begin[1], point_end[1], zero_tolerance) == -1:
                segments.append(point_end)
                return (segments, involved_border_ids)
            else:
                segments.append([cell_min_point[0], cell_min_point[1] + cell_length_y])
                border_id_p_search = (border_id_p_search + 1) % 4
        elif border_id_p_search == 1:
            if cwt(point_begin[0], point_end[0], zero_tolerance) == -1:
                segments.append(point_end)
                return (segments, involved_border_ids)
            else:
                segments.append(
                    [
                        cell_min_point[0] + cell_length_x,
                        cell_min_point[1] + cell_length_y,
                    ]
                )
                border_id_p_search = (border_id_p_search + 1) % 4
        elif border_id_p_search == 2:
            if cwt(point_begin[1], point_end[1], zero_tolerance) == 1:
                segments.append(point_end)
                return (segments, involved_border_ids)
            else:
                segments.append([cell_min_point[0] + cell_length_x, cell_min_point[1]])
                border_id_p_search = (border_id_p_search + 1) % 4
        elif border_id_p_search == 3:
            if cwt(point_begin[0], point_end[0], zero_tolerance) == 1:
                segments.append(point_end)
                return (segments, involved_border_ids)
            else:
                segments.append([cell_min_point[0], cell_min_point[1]])
                border_id_p_search = (border_id_p_search + 1) % 4
    while True:
        involved_border_ids.append(border_id_p_search)
        if border_id_p_search != border_id_p_end:  # add a whole border
            if border_id_p_search == 0:
                segments.append([cell_min_point[0], cell_min_point[1] + cell_length_y])
            elif border_id_p_search == 1:
                segments.append(
                    [
                        cell_min_point[0] + cell_length_x,
                        cell_min_point[1] + cell_length_y,
                    ]
                )
            elif border_id_p_search == 2:
                segments.append([cell_min_point[0] + cell_length_x, cell_min_point[1]])
            elif border_id_p_search == 3:
                segments.append([cell_min_point[0], cell_min_point[1]])
            border_id_p_search = (border_id_p_search + 1) % 4
        else:  # add the border segment according to the enc point
            segments.append(point_end)
            return (segments, list(set(involved_border_ids)))


def get_relative_location_on_cell_border(
    cell_min_point, cell_length_x, cell_length_y, point, zero_tolerance
):
    """When a point is on the border of a cell, this function can be used to
    calculate the relative location of the point

    to cell's left-bottom corner.
    Parameters
    ----------
    cell_min_point : list
        the bottom-left point of the cell, like [x0, y0]

    cell_length_x : float
        width of the cell

    cell_length_y : float
        height of the cell

    point : list
         the point on the cell's border. like [x, y]

    zero_tolerance : float
        value of zero_tolerance for determining if two float values are equal

    Returns
    -------
    distance : float
        range from 0 to 4

    """
    border_id_p = -1
    if cwt(point[0], cell_min_point[0], zero_tolerance) == 0:
        border_id_p = 0
        border_id_p += (point[1] - cell_min_point[1]) / cell_length_y
    elif cwt(point[1], cell_min_point[1] + cell_length_y, zero_tolerance) == 0:
        border_id_p = 1
        border_id_p += (point[0] - cell_min_point[0]) / cell_length_x
    elif cwt(point[0], cell_min_point[0] + cell_length_x, zero_tolerance) == 0:
        border_id_p = 2
        border_id_p += 1 - (point[1] - cell_min_point[1]) / cell_length_y
    elif cwt(point[1], cell_min_point[1], zero_tolerance) == 0:
        border_id_p = 3
        border_id_p += 1 - (point[0] - cell_min_point[0]) / cell_length_x
    return border_id_p


def extract_segments_from_cell_with_arcs(
    cell_min_point, cell_length_x, cell_length_y, arcs, zero_tolerance
):
    """At the end of study area quadtree dividing, there will be some node
    cells intersect with arcs. The arcs are segments of original study border
    and the begin and end points of the arcs MUST lie on node cell border. This
    function can intersect the node cell and

    Parameters
    ----------
    cell_min_point : array
        the bottom-left point of the cell, like [x0, y0]

    cell_length_x : float
        width of the cell

    cell_length_y : float
        height of the cell

    arcs : array
        array of point lists

    zero_tolerance : float
        value of zero_tolerance for determining if two float values are equal

    Returns
    -------
    rings_and_border_ids : tuple
        like (rings, involved_border_ids) 1. the list of rings extracted, each
        ring contains a sequence of points - the begin and end points are the
        same. Note that there might be multiple rings extracted in a cell. 2.
        the ids of borders of the cell who are involved in the ring. Duplicated
        ids are removed and they may not be in the original order

    """
    arc_begin_points = []  # beginning points of each arc
    arc_begin_points_location = []  # location of beginning points of each arc
    arc_end_points = []  # ending points of each arc
    arc_end_points_location = []  # location of ending points of each arc
    for single_arc in arcs:
        arc_begin_points.append(single_arc[0])
        arc_end_points.append(single_arc[len(single_arc) - 1])
        arc_begin_points_location.append(
            get_relative_location_on_cell_border(
                cell_min_point,
                cell_length_x,
                cell_length_y,
                single_arc[0],
                zero_tolerance,
            )
        )
        arc_end_points_location.append(
            get_relative_location_on_cell_border(
                cell_min_point,
                cell_length_x,
                cell_length_y,
                single_arc[len(single_arc) - 1],
                zero_tolerance,
            )
        )

    rings = []
    involved_border_ids = []
    used_arc_ids = []
    # every time find an unused arc with minimum begin-point-location, and begin the track form here
    new_ring = []  # the point list
    new_ring_end_point = None
    new_ring_end_point_location = -1
    selected_arc_ids = []
    while len(used_arc_ids) < len(arcs):
        if len(selected_arc_ids) == 0:
            # init the process of constructing a new ring
            # find the unused arc with min begin point location
            arc_id_with_min_begin_location = -1
            for i in range(0, len(arcs)):
                if i in used_arc_ids:
                    continue
                if (
                    arc_id_with_min_begin_location == -1
                    or cwt(
                        arc_begin_points_location[arc_id_with_min_begin_location],
                        arc_begin_points_location[i],
                        zero_tolerance,
                    )
                    == 1
                ):
                    arc_id_with_min_begin_location = i
            new_ring_end_point = arc_end_points[arc_id_with_min_begin_location]
            new_ring_end_point_location = arc_end_points_location[
                arc_id_with_min_begin_location
            ]
            selected_arc_ids.append(arc_id_with_min_begin_location)
            for point in arcs[arc_id_with_min_begin_location]:
                new_ring.append(point)
        else:
            # there is already a selected arc, find the next available arc(maybe itself) and add the borders between
            # these two arcs
            arc_id_with_relatively_min_begin_location = -1
            for i in range(0, len(arcs)):
                if i in used_arc_ids:
                    continue
                if arc_id_with_relatively_min_begin_location == -1:
                    arc_id_with_relatively_min_begin_location = i
                else:
                    distance_to_end_point_min = (
                        arc_begin_points_location[
                            arc_id_with_relatively_min_begin_location
                        ]
                        - new_ring_end_point_location
                    )
                    if distance_to_end_point_min < 0:
                        distance_to_end_point_min += 4
                    distance_to_end_point_now = (
                        arc_begin_points_location[i] - new_ring_end_point_location
                    )
                    if distance_to_end_point_now < 0:
                        distance_to_end_point_now += 4
                    if (
                        cwt(
                            distance_to_end_point_min,
                            distance_to_end_point_now,
                            zero_tolerance,
                        )
                        == 1
                    ):
                        arc_id_with_relatively_min_begin_location = i
            extract_result = extract_connecting_borders_between_points(
                cell_min_point,
                cell_length_x,
                cell_length_y,
                new_ring_end_point,
                arc_begin_points[arc_id_with_relatively_min_begin_location],
                zero_tolerance,
            )
            point_list = extract_result[0]
            border_id_list = extract_result[1]
            for i in range(0, len(point_list)):
                if i == 0 and point_list[i] == new_ring[len(new_ring) - 1]:
                    continue
                new_ring.append(point_list[i])
            for border_id in border_id_list:
                if border_id not in involved_border_ids:
                    involved_border_ids.append(border_id)
            new_ring_end_point = arc_end_points[
                arc_id_with_relatively_min_begin_location
            ]
            new_ring_end_point_location = arc_end_points_location[
                arc_id_with_relatively_min_begin_location
            ]
            if arc_id_with_relatively_min_begin_location not in selected_arc_ids:
                #  find a new arc, add the point sequence in this arc to the ring, and continue the searching further
                selected_arc_ids.append(arc_id_with_relatively_min_begin_location)
                single_arc = arcs[arc_id_with_relatively_min_begin_location]
                for i in range(0, len(single_arc)):
                    if i == 0 and single_arc[i] == new_ring[len(new_ring) - 1]:
                        continue
                    new_ring.append(single_arc[i])
            else:
                # the newly found arc is exactly the beginning one, a whole closed ring is formed. stop here
                rings.append(new_ring)
                new_ring = []
                new_ring_end_point = None
                new_ring_end_point_location = -1
                for arc_id in selected_arc_ids:
                    used_arc_ids.append(arc_id)
                selected_arc_ids = []
    if len(new_ring) > 0:
        raise Exception("Error in extract_segments_from_cell_with_arcs!!!")
    return (rings, involved_border_ids)


class QuadTreeStructureSingleRing(object):
    """This class is the main manager of cells.

    By giving a study area. This class can construct a cell list depicting the
    study area. When given a new point. This class could rapidly determine
    whether the point lies in the study area

    Attributes
    __________
    root_cell : Cell
        The Cell structure for storing the quad-tree for this ring
    """

    def __init__(self, ring):
        """
        Parameters
        ----------
        ring : Ring
            the point list of study area. But in the class of Ring in PySAL
            Example: Ring([[0.0, 0.0], [3.0, 2.0], [5.0, 1.0]])

        """
        self.ring = ring
        self.root_cell = Cell(
            0,
            ring.bounding_box.left,
            ring.bounding_box.lower,
            ring.bounding_box.width,
            ring.bounding_box.height,
            [ring.vertices],
            "maybe",
        )

        # here build the quad tree structure
        # The criterion of stopping splitting the tree:
        #    1. The status is "in" or "out"
        #    2. The level >= 5 and the the number of current cell only contains one ring and all segments of the ring is no more than 4
        #    3. The level >= 8
        cells_for_processing = [self.root_cell]
        total_cell_count = 1
        for i in range(0, 8):  # 10
            result_cell_list = []
            while len(cells_for_processing) > 0:
                cell = cells_for_processing.pop()
                cell.split()
                total_cell_count += 4
                children_cells = [
                    cell.children_l_b,
                    cell.children_l_t,
                    cell.children_r_b,
                    cell.children_r_t,
                ]
                for child in children_cells:
                    if child.status == "out" or child.status == "in":
                        continue
                    if child.level >= 5:  # 6
                        if len(child.rings) == 1 and child.rings[0].len <= 5:
                            continue
                    result_cell_list.append(child)
            cells_for_processing = result_cell_list

    def contains_point(self, point):
        """Quickly determine if the study area contains a point

        Parameters
        ----------
        point : list
            the point structure, like [x, y]

        Returns
        -------
        if_contains : bool

        """

        # bbox check
        if (
            point[0] < self.min_x
            or point[0] > self.min_x + self.region_width
            or point[1] < self.min_y
            or point[1] > self.min_y + self.region_height
        ):
            return False
        # find the leaf cell for checking
        cell_to_check = self.root_cell
        while True:
            if cell_to_check.children_l_b is None:
                break
            middle_x = cell_to_check.min_x + cell_to_check.length_x / 2
            middle_y = cell_to_check.min_y + cell_to_check.length_y / 2
            if point[0] <= middle_x and point[1] <= middle_y:
                cell_to_check = cell_to_check.children_l_b
            elif point[0] <= middle_x and point[1] > middle_y:
                cell_to_check = cell_to_check.children_l_t
            elif point[0] > middle_x and point[1] <= middle_y:
                cell_to_check = cell_to_check.children_r_b
            else:
                cell_to_check = cell_to_check.children_r_t

        return cell_to_check.contains_point(point)

    @property
    def region_width(self):
        return self.ring.bounding_box.width

    @property
    def region_height(self):
        return self.ring.bounding_box.height

    @property
    def min_x(self):
        return self.ring.bounding_box.left

    @property
    def min_y(self):
        return self.ring.bounding_box.lower
