```"""

from: https://github.com/linuxlewis/tripy/blob/master/tripy.py
"""

from __future__ import annotations

from typing import List, Tuple

[docs]
def earclip(polygon: PointList) -> List[Tuple[Tuple[float, float], Tuple[float, float], Tuple[float, float]]]:
"""
Simple earclipping algorithm for a given polygon p.
polygon is expected to be an array of 2-tuples of the cartesian points of the polygon
For a polygon with n points it will return n-2 triangles.
The triangles are returned as an array of 3-tuples where each item in the tuple is a 2-tuple of the cartesian point.

Implementation Reference:
- https://www.geometrictools.com/Documentation/TriangulationByEarClipping.pdf
"""
ear_vertex = []
triangles = []

polygon = list(polygon)

if _is_clockwise(polygon):
polygon.reverse()

point_count = len(polygon)
for i in range(point_count):
prev_index = i - 1
prev_point = polygon[prev_index]
point = polygon[i]
next_index = (i + 1) % point_count
next_point = polygon[next_index]

if _is_ear(prev_point, point, next_point, polygon):
ear_vertex.append(point)

while ear_vertex and point_count >= 3:
ear = ear_vertex.pop(0)
i = polygon.index(ear)
prev_index = i - 1
prev_point = polygon[prev_index]
next_index = (i + 1) % point_count
next_point = polygon[next_index]

polygon.remove(ear)
point_count -= 1
triangles.append(((prev_point[0], prev_point[1]), (ear[0], ear[1]), (next_point[0], next_point[1])))
if point_count > 3:
prev_prev_point = polygon[prev_index - 1]
next_next_index = (i + 1) % point_count
next_next_point = polygon[next_next_index]

groups = [
(prev_prev_point, prev_point, next_point, polygon),
(prev_point, next_point, next_next_point, polygon)
]
for group in groups:
p = group[1]
if _is_ear(*group):
if p not in ear_vertex:
ear_vertex.append(p)
elif p in ear_vertex:
ear_vertex.remove(p)
return triangles

def _is_clockwise(polygon: List[Point]) -> bool:
s = 0.0
polygon_count = len(polygon)
for i in range(polygon_count):
point = polygon[i]
point2 = polygon[(i + 1) % polygon_count]
s += (point2[0] - point[0]) * (point2[1] + point[1])
return s > 0

def _is_convex(prev: Point, point: Point, next_point: Point) -> bool:
return _triangle_sum(prev[0], prev[1], point[0], point[1], next_point[0], next_point[1]) < 0

def _is_ear(p1: Point, p2: Point, p3: Point, polygon: List[Point]) -> bool:
return _contains_no_points(p1, p2, p3, polygon) and \
_is_convex(p1, p2, p3) and \
_triangle_area(p1[0], p1[1], p2[0], p2[1], p3[0], p3[1]) > 0

def _contains_no_points(p1: Point, p2: Point, p3: Point, polygon: List[Point]) -> bool:
for pn in polygon:
if pn in (p1, p2, p3):
continue
elif _is_point_inside(pn, p1, p2, p3):
return False
return True

def _is_point_inside(p: Point, a: Point, b: Point, c: Point) -> bool:
area = _triangle_area(a[0], a[1], b[0], b[1], c[0], c[1])
area1 = _triangle_area(p[0], p[1], b[0], b[1], c[0], c[1])
area2 = _triangle_area(p[0], p[1], a[0], a[1], c[0], c[1])
area3 = _triangle_area(p[0], p[1], a[0], a[1], b[0], b[1])
return area == sum([area1, area2, area3])

def _triangle_area(x1: float, y1: float, x2: float, y2: float, x3: float, y3: float) -> float:
return abs((x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)) / 2.0)

def _triangle_sum(x1: float, y1: float, x2: float, y2: float, x3: float, y3: float) -> float:
return x1 * (y3 - y2) + x2 * (y1 - y3) + x3 * (y2 - y1)
```