# cython: language_level=3
# Source: https://github.com/mapbox/earcut
# License: ISC License (MIT compatible)
#
# Copyright (c) 2016, Mapbox
#
# Permission to use, copy, modify, and/or distribute this software for any purpose
# with or without fee is hereby granted, provided that the above copyright notice
# and this permission notice appear in all copies.
#
# THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH
# REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
# FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT,
# INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS
# OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER
# TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
# THIS SOFTWARE.
#
# Cython implementation of module ezdxf.math._mapbox_earcut.py
# Copyright (c) 2022, Manfred Moitzi
# License: MIT License
# type: ignore
from libc.math cimport fmin, fmax, fabs, INFINITY


cdef class Node:
    cdef:
        int i
        double x
        double y
        int z
        bint steiner
        object point
        Node prev
        Node next
        Node prev_z
        Node next_z

    def __cinit__(self, int i, object point):
        self.i = i
        self.point = point
        self.x = point.x
        self.y = point.y
        self.z = 0
        self.steiner = False
        self.prev = None
        self.next = None
        self.prev_z = None
        self.next_z = None

    cdef bint equals(self, Node other):
        return self.x == other.x and self.y == other.y

def node_key(Node node):
    return node.x, node.y

def earcut(list exterior, list holes):
    """Implements a modified ear slicing algorithm, optimized by z-order
    curve hashing and extended to handle holes, twisted polygons, degeneracies
    and self-intersections in a way that doesn't guarantee correctness of
    triangulation, but attempts to always produce acceptable results for
    practical data.

    Source: https://github.com/mapbox/earcut

    Args:
        exterior: outer path as list of points as objects which provide a
            `x`- and a `y`-attribute
        holes: list of holes, each hole is list of points, a hole with
            a single points is a Steiner point

    Returns:
        Returns a list of triangles, each triangle is a tuple of three points,
        the output points are the same objects as the input points.

    """
    cdef:
        Node outer_node
        list triangles = []
        double max_x, max_y, x, y
        double min_x = 0.0
        double min_y = 0.0
        double inv_size = 0.0

    if not exterior:
        return triangles

    outer_node = linked_list(exterior, 0, ccw=True)
    if outer_node is None or outer_node.next is outer_node.prev:
        return triangles

    if holes:
        outer_node = eliminate_holes(holes, len(exterior), outer_node)

    # if the shape is not too simple, we'll use z-order curve hash later
    # calculate polygon bbox
    if len(exterior) > 80:
        min_x = max_x = exterior[0].x
        min_y = max_y = exterior[0].y
        for point in exterior:
            x = point.x
            y = point.y
            min_x = fmin(min_x, x)
            min_y = fmin(min_y, y)
            max_x = fmax(max_x, x)
            max_y = fmax(max_y, y)

        # min_x, min_y and inv_size are later used to transform coords into
        # integers for z-order calculation
        inv_size = fmax(max_x - min_x, max_y - min_y)
        inv_size = 32767 / inv_size if inv_size != 0 else 0

    earcut_linked(outer_node, triangles, min_x, min_y, inv_size, 0)
    return triangles


cdef Node linked_list(list points, int start, bint ccw):
    """Create a circular doubly linked list from polygon points in the specified
    winding order
    """
    cdef:
        Node last = None
        int end

    if ccw is (signed_area(points) < 0):
        for point in points:
            last = insert_node(start, point, last)
            start += 1
    else:
        end = start + len(points)
        for point in reversed(points):
            last = insert_node(end, point, last)
            end -= 1

    # open polygon: where the 1st vertex is not coincident with the last vertex
    if last and last.equals(last.next):
        remove_node(last)
        last = last.next
    return last


cdef double signed_area(list points):
    cdef:
        double s = 0.0
        double point_x, prev_x, point_y, prev_y
    if not len(points):
        return s
    prev = points[-1]
    prev_x = prev.x
    prev_y = prev.y
    for point in points:
        point_x = point.x
        point_y = point.y
        s += (point_x - prev_x) * (point_y + prev_y)
        prev_x = point_x
        prev_y = point_y
    # s < 0 is counter-clockwise
    # s > 0 is clockwise
    return s


cdef double area(Node p, Node q, Node r):
    """Returns signed area of a triangle"""
    return (q.y - p.y) * (r.x - q.x) - (q.x - p.x) * (r.y - q.y)


cdef bint is_valid_diagonal(Node a, Node b):
    """Check if a diagonal between two polygon nodes is valid (lies in polygon
    interior)
    """
    return (
        a.next.i != b.i
        and a.prev.i != b.i
        and not intersects_polygon(a, b)  # doesn't intersect other edges
        and (
            locally_inside(a, b)
            and locally_inside(b, a)
            and middle_inside(a, b)
            and (
                area(a.prev, a, b.prev) or area(a, b.prev, b)
            )  # does not create opposite-facing sectors
            or a.equals(b)
            and area(a.prev, a, a.next) > 0
            and area(b.prev, b, b.next) > 0
        )  # special zero-length case
    )


cdef bint intersects_polygon(Node a, Node b):
    """Check if a polygon diagonal intersects any polygon segments"""
    cdef Node p = a
    while True:
        if (
            p.i != a.i
            and p.next.i != a.i
            and p.i != b.i
            and p.next.i != b.i
            and intersects(p, p.next, a, b)
        ):
            return True
        p = p.next
        if p is a:
            break
    return False


cdef int sign(double num):
    if num < 0.0:
        return -1
    if num > 0.0:
        return 1
    return 0


cdef bint on_segment(p: Node, q: Node, r: Node):
    return fmax(p.x, r.x) >= q.x >= fmin(p.x, r.x) and fmax(
        p.y, r.y
    ) >= q.y >= fmin(p.y, r.y)


cdef bint intersects(Node p1, Node q1, Node p2, Node q2):
    """check if two segments intersect"""
    cdef:
        int o1 = sign(area(p1, q1, p2))
        int o2 = sign(area(p1, q1, q2))
        int o3 = sign(area(p2, q2, p1))
        int o4 = sign(area(p2, q2, q1))

    if o1 != o2 and o3 != o4:
        return True  # general case

    if o1 == 0 and on_segment(p1, p2, q1):
        return True  # p1, q1 and p2 are collinear and p2 lies on p1q1
    if o2 == 0 and on_segment(p1, q2, q1):
        return True  # p1, q1 and q2 are collinear and q2 lies on p1q1
    if o3 == 0 and on_segment(p2, p1, q2):
        return True  # p2, q2 and p1 are collinear and p1 lies on p2q2
    if o4 == 0 and on_segment(p2, q1, q2):
        return True  # p2, q2 and q1 are collinear and q1 lies on p2q2
    return False


cdef Node insert_node(int i, point, Node last):
    """create a node and optionally link it with previous one (in a circular
    doubly linked list)
    """
    cdef Node p = Node(i, point)

    if last is None:
        p.prev = p
        p.next = p
    else:
        p.next = last.next
        p.prev = last
        last.next.prev = p
        last.next = p
    return p


cdef remove_node(Node p):
    p.next.prev = p.prev
    p.prev.next = p.next

    if p.prev_z is not None:
        p.prev_z.next_z = p.next_z
    if p.next_z is not None:
        p.next_z.prev_z = p.prev_z


cdef Node eliminate_holes(list holes, int start, Node outer_node):
    """link every hole into the outer loop, producing a single-ring polygon
    without holes
    """
    cdef:
        list queue = []
        list hole
    for hole in holes:
        if len(hole) < 1:  # skip empty holes
            continue
        # hole vertices in clockwise order
        _list = linked_list(hole, start, ccw=False)
        if _list is _list.next:
            _list.steiner = True
        start += len(hole)
        queue.append(get_leftmost(_list))
    queue.sort(key=node_key)

    # process holes from left to right
    for hole_ in queue:
        outer_node = eliminate_hole(hole_, outer_node)
    return outer_node


cdef Node eliminate_hole(Node hole, Node outer_node):
    """Find a bridge between vertices that connects hole with an outer ring and
    link it
    """
    cdef:
        Node bridge = find_hole_bridge(hole, outer_node)
        Node bridge_reverse

    if bridge is None:
        return outer_node

    bridge_reverse = split_polygon(bridge, hole)

    # filter collinear points around the cuts
    filter_points(bridge_reverse, bridge_reverse.next)
    return filter_points(bridge, bridge.next)


cdef Node filter_points(Node start, Node end = None):
    """eliminate colinear or duplicate points"""
    cdef:
        Node p
        bint again

    if start is None:
        return start
    if end is None:
        end = start

    p = start
    while True:
        again = False
        if not p.steiner and (
            p.equals(p.next) or area(p.prev, p, p.next) == 0
        ):
            remove_node(p)
            p = end = p.prev
            if p is p.next:
                break
            again = True
        else:
            p = p.next
        if not (again or p is not end):
            break
    return end


# main ear slicing loop which triangulates a polygon (given as a linked list)
cdef earcut_linked(
    Node ear,
    list triangles,
    double min_x,
    double min_y,
    double inv_size,
    int pass_,
):
    cdef:
        Node stop, prev, next
        bint _is_ear

    if ear is None:
        return

    # interlink polygon nodes in z-order
    if not pass_ and inv_size:
        index_curve(ear, min_x, min_y, inv_size)

    stop = ear

    # iterate through ears, slicing them one by one
    while ear.prev is not ear.next:
        prev = ear.prev
        next = ear.next

        _is_ear = (
            is_ear_hashed(ear, min_x, min_y, inv_size)
            if inv_size
            else is_ear(ear)
        )
        if _is_ear:
            # cut off the triangle
            triangles.append((prev.point, ear.point, next.point))
            remove_node(ear)

            # skipping the next vertex leads to less sliver triangles
            ear = next.next
            stop = next.next
            continue

        ear = next

        # if we looped through the whole remaining polygon and can't find any more ears
        if ear is stop:
            # try filtering points and slicing again
            if not pass_:
                earcut_linked(
                    filter_points(ear),
                    triangles,
                    min_x,
                    min_y,
                    inv_size,
                    1,
                )

            # if this didn't work, try curing all small self-intersections locally
            elif pass_ == 1:
                ear = cure_local_intersections(filter_points(ear), triangles)
                earcut_linked(ear, triangles, min_x, min_y, inv_size, 2)

            # as a last resort, try splitting the remaining polygon into two
            elif pass_ == 2:
                split_ear_cut(ear, triangles, min_x, min_y, inv_size)
            break


cdef bint is_ear(Node ear):
    """check whether a polygon node forms a valid ear with adjacent nodes"""
    cdef:
        Node a = ear.prev
        Node b = ear
        Node c = ear.next
        Node p
        double x0, x1, y0, y1

    if area(a, b, c) >= 0:
        return False  # reflex, can't be an ear

    # now make sure we don't have other points inside the potential ear
    # triangle bbox
    x0 = fmin(a.x, fmin(b.x, c.x))
    x1 = fmax(a.x, fmax(b.x, c.x))
    y0 = fmin(a.y, fmin(b.y, c.y))
    y1 = fmax(a.y, fmax(b.y, c.y))
    p = c.next

    while p is not a:
        if (
            x0 <= p.x <= x1
            and y0 <= p.y <= y1
            and point_in_triangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y)
            and area(p.prev, p, p.next) >= 0
        ):
            return False
        p = p.next

    return True


cdef bint is_ear_hashed(Node ear, double min_x, double min_y, double inv_size):
    cdef:
        Node a = ear.prev
        Node b = ear
        Node c = ear.next
        double x0, x1, y0, y1, min_z, max_z
        Node p, n

    if area(a, b, c) >= 0:
        return False  # reflex, can't be an ear

    # triangle bbox
    x0 = fmin(a.x, fmin(b.x, c.x))
    x1 = fmax(a.x, fmax(b.x, c.x))
    y0 = fmin(a.y, fmin(b.y, c.y))
    y1 = fmax(a.y, fmax(b.y, c.y))

    # z-order range for the current triangle bbox;
    min_z = z_order(x0, y0, min_x, min_y, inv_size)
    max_z = z_order(x1, y1, min_x, min_y, inv_size)

    p = ear.prev_z
    n = ear.next_z

    # look for points inside the triangle in both directions
    while p and p.z >= min_z and n and n.z <= max_z:
        if (
            x0 <= p.x <= x1
            and y0 <= p.y <= y1
            and p is not a
            and p is not c
            and point_in_triangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y)
            and area(p.prev, p, p.next) >= 0
        ):
            return False
        p = p.prev_z

        if (
            x0 <= n.x <= x1
            and y0 <= n.y <= y1
            and n is not a
            and n is not c
            and point_in_triangle(a.x, a.y, b.x, b.y, c.x, c.y, n.x, n.y)
            and area(n.prev, n, n.next) >= 0
        ):
            return False
        n = n.next_z

    # look for remaining points in decreasing z-order
    while p and p.z >= min_z:
        if (
            x0 <= p.x <= x1
            and y0 <= p.y <= y1
            and p is not a
            and p is not c
            and point_in_triangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y)
            and area(p.prev, p, p.next) >= 0
        ):
            return False
        p = p.prev_z

    # look for remaining points in increasing z-order
    while n and n.z <= max_z:
        if (
            x0 <= n.x <= x1
            and y0 <= n.y <= y1
            and n is not a
            and n is not c
            and point_in_triangle(a.x, a.y, b.x, b.y, c.x, c.y, n.x, n.y)
            and area(n.prev, n, n.next) >= 0
        ):
            return False
        n = n.next_z
    return True


cdef Node get_leftmost(Node start):
    """Find the leftmost node of a polygon ring"""
    cdef:
        Node p = start
        Node leftmost = start

    while True:
        if p.x < leftmost.x or (p.x == leftmost.x and p.y < leftmost.y):
            leftmost = p
        p = p.next
        if p is start:
            break
    return leftmost


cdef bint point_in_triangle(
    double ax,
    double ay,
    double bx,
    double by_,
    double cx,
    double cy,
    double px,
    double py,
):
    """Check if a point lies within a convex triangle"""
    return (
        (cx - px) * (ay - py) >= (ax - px) * (cy - py)
        and (ax - px) * (by_ - py) >= (bx - px) * (ay - py)
        and (bx - px) * (cy - py) >= (cx - px) * (by_ - py)
    )


cdef bint sector_contains_sector(Node m, Node p):
    """Whether sector in vertex m contains sector in vertex p in the same
    coordinates.
    """
    return area(m.prev, m, p.prev) < 0 and area(p.next, m, m.next) < 0


cdef index_curve(Node start, double min_x, double min_y, double inv_size):
    """Interlink polygon nodes in z-order"""
    cdef Node p = start
    while True:
        if p.z == 0:
            p.z = z_order(p.x, p.y, min_x, min_y, inv_size)
        p.prev_z = p.prev
        p.next_z = p.next
        p = p.next
        if p is start:
            break

    p.prev_z.next_z = None
    p.prev_z = None

    sort_linked(p)


cdef int z_order(
    double x0, double y0, double min_x, double min_y, double inv_size
):
    """Z-order of a point given coords and inverse of the longer side of data
    bbox.
    """
    # coords are transformed into non-negative 15-bit integer range
    cdef:
        int x = int((x0 - min_x) * inv_size)
        int y = int ((y0 - min_y) * inv_size)

    x = (x | (x << 8)) & 0x00FF00FF
    x = (x | (x << 4)) & 0x0F0F0F0F
    x = (x | (x << 2)) & 0x33333333
    x = (x | (x << 1)) & 0x55555555

    y = (y | (y << 8)) & 0x00FF00FF
    y = (y | (y << 4)) & 0x0F0F0F0F
    y = (y | (y << 2)) & 0x33333333
    y = (y | (y << 1)) & 0x55555555

    return x | (y << 1)


# Simon Tatham's linked list merge sort algorithm
# http://www.chiark.greenend.org.uk/~sgtatham/algorithms/listsort.html
cdef Node sort_linked(Node head):
    cdef:
        int in_size = 1
        int num_merges, p_size, q_size, i
        Node tail, p, q, e

    while True:
        p = head
        head = None
        tail = None
        num_merges = 0
        while p:
            num_merges += 1
            q = p
            p_size = 0
            for i in range(in_size):
                p_size += 1
                q = q.next_z
                if not q:
                    break
            q_size = in_size
            while p_size > 0 or (q_size > 0 and q):
                if p_size != 0 and (q_size == 0 or not q or p.z <= q.z):
                    e = p
                    p = p.next_z
                    p_size -= 1
                else:
                    e = q
                    q = q.next_z
                    q_size -= 1

                if tail:
                    tail.next_z = e
                else:
                    head = e
                e.prev_z = tail
                tail = e
            p = q
        tail.next_z = None
        in_size *= 2
        if num_merges <= 1:
            break
    return head


cdef Node split_polygon(Node a, Node b):
    """Link two polygon vertices with a bridge.

    If the vertices belong to the same ring, it splits polygon into two.
    If one belongs to the outer ring and another to a hole, it merges it into a
    single ring.
    """
    cdef :
        Node a2 = Node(a.i, a.point)
        Node b2 = Node(b.i, b.point)
        Node an = a.next
        Node bp = b.prev

    a.next = b
    b.prev = a

    a2.next = an
    an.prev = a2

    b2.next = a2
    a2.prev = b2

    bp.next = b2
    b2.prev = bp

    return b2


# go through all polygon nodes and cure small local self-intersections
cdef Node cure_local_intersections(Node start, list triangles):
    cdef:
        Node p = start
        Node a, b
    while True:
        a = p.prev
        b = p.next.next

        if (
            not a.equals(b)
            and intersects(a, p, p.next, b)
            and locally_inside(a, b)
            and locally_inside(b, a)
        ):
            triangles.append((a.point, p.point, b.point))
            # remove two nodes involved
            remove_node(p)
            remove_node(p.next)
            p = start = b

        p = p.next
        if p is start:
            break
    return filter_points(p)


cdef split_ear_cut(
    Node start,
    list triangles,
    double min_x,
    double min_y,
    double inv_size,
):
    """Try splitting polygon into two and triangulate them independently"""
    # look for a valid diagonal that divides the polygon into two
    cdef:
        Node a = start
        Node b, c

    while True:
        b = a.next.next
        while b is not a.prev:
            if a.i != b.i and is_valid_diagonal(a, b):
                # split the polygon in two by the diagonal
                c = split_polygon(a, b)

                # filter colinear points around the cuts
                a = filter_points(a, a.next)
                c = filter_points(c, c.next)

                # run earcut on each half
                earcut_linked(a, triangles, min_x, min_y, inv_size, 0)
                earcut_linked(c, triangles, min_x, min_y, inv_size, 0)
                return
            b = b.next
        a = a.next
        if a is start:
            break


# David Eberly's algorithm for finding a bridge between hole and outer polygon
cdef Node find_hole_bridge(Node hole, Node outer_node):
    cdef:
        Node p = outer_node
        Node m = None
        Node stop
        double hx = hole.x
        double hy = hole.y
        double qx = -INFINITY
        double mx, my, tan_min, tan

    # find a segment intersected by a ray from the hole's leftmost point to the left;
    # segment's endpoint with lesser x will be potential connection point
    while True:
        if p.y >= hy >= p.next.y != p.y:
            x = p.x + (hy - p.y) * (p.next.x - p.x) / (p.next.y - p.y)
            if hx >= x > qx:
                qx = x
                m = p if p.x < p.next.x else p.next
                if x == hx:
                    # hole touches outer segment; pick leftmost endpoint
                    return m
        p = p.next
        if p is outer_node:
            break

    if m is None:
        return None

    # look for points inside the triangle of hole point, segment intersection and endpoint;
    # if there are no points found, we have a valid connection;
    # otherwise choose the point of the minimum angle with the ray as connection point
    stop = m
    mx = m.x
    my = m.y
    tan_min = INFINITY
    p = m

    while True:
        if (
            hx >= p.x >= mx
            and hx != p.x
            and point_in_triangle(
                hx if hy < my else qx,
                hy,
                mx,
                my,
                qx if hy < my else hx,
                hy,
                p.x,
                p.y,
            )
        ):
            tan = fabs(hy - p.y) / (hx - p.x)  # tangential
            if locally_inside(p, hole) and (
                tan < tan_min
                or (
                    tan == tan_min
                    and (
                        p.x > m.x
                        or (p.x == m.x and sector_contains_sector(m, p))
                    )
                )
            ):
                m = p
                tan_min = tan
        p = p.next
        if p is stop:
            break
    return m


cdef bint locally_inside(Node a, Node b):
    """Check if a polygon diagonal is locally inside the polygon"""
    return (
        area(a, b, a.next) >= 0 and area(a, a.prev, b) >= 0
        if area(a.prev, a, a.next) < 0
        else area(a, b, a.prev) < 0 or area(a, a.next, b) < 0
    )


cdef bint middle_inside(Node a, Node b):
    """Check if the middle point of a polygon diagonal is inside the polygon"""
    cdef:
        Node p = a
        bint inside = False
        double px = (a.x + b.x) / 2
        double py = (a.y + b.y) / 2

    while True:
        if (
            ((p.y > py) != (p.next.y > py))
            and p.next.y != p.y
            and (px < (p.next.x - p.x) * (py - p.y) / (p.next.y - p.y) + p.x)
        ):
            inside = not inside
        p = p.next
        if p is a:
            break
    return inside