def calculate_surface_normal(p1: Point, p2: Point, p3: Point) -> Point:
u = vector(p1, p2)
v = vector(p1, p3)
return Point(
u.y * v.z - u.z * v.y,
u.z * v.x - u.x * v.z,
u.x * v.y - u.y * v.x
)
def get_centroid(self, clear: bool = False) -> Point:
"""Get the centroid of the triangle"""
if self.centroid and not clear:
return self.centroid
x = (self.points[0].x + self.points[1].x + self.points[2].x) / 3
y = (self.points[0].y + self.points[1].y + self.points[2].y) / 3
z = (self.points[0].z + self.points[1].z + self.points[2].z) / 3
centroid = Point(x, y, z)
self.centroid = centroid
return centroid
def normalize_vector(v: Point) -> Point:
magnitude = math.sqrt(
math.pow(v.x, 2)
+ math.pow(v.y, 2)
+ math.pow(v.z, 2)
)
return Point(
v.x / magnitude,
v.y / magnitude,
v.z / magnitude
)
def get_point_if_exists(point: Point) -> Point:
"""Check if a suitable point already exists and use it
otherwise create one"""
for p in points.keys():
if point.common_point(p):
print("Point already exists!")
return p
else:
print("Create point")
points[point] = point
return point
def __init__(self,
point1: Point,
point2: Point,
point3: Point,
register: bool = True):
self.id = next(_id)
self.points = [point1, point2, point3]
self.centroid: Point = self.get_centroid(True)
if register:
point1.register_face(self)
point2.register_face(self)
point3.register_face(self)
def __init__(self, centre_point: Point, hex_size: float = 1):
hex_size = max(0.01, min(1.0, hex_size))
self.centre_point = centre_point
self.faces: List[Face] = centre_point.get_ordered_faces()
self.boundary: List[Point] = []
self.neighbour_ids: List[Point] = []
self.neighbours: List[Tile] = []
neighbour_hash: Dict[Point, int] = {}
for f in self.faces:
centroid_point = f.get_centroid()
self.boundary.append(
centroid_point.segment(self.centre_point, hex_size))
other_points = f.get_other_points(self.centre_point)
for other in other_points:
neighbour_hash[other] = 1
self.neighbour_ids = list(neighbour_hash.keys())
normal = calculate_surface_normal(*self.boundary[:3])
if not pointing_away_from_origin(self.centre_point, normal):
self.boundary.reverse()
def vector(p1: Point, p2: Point) -> Point:
return Point(p2.x - p1.x,
p2.y - p1.y,
p2.z - p1.z)
def get_corners(self):
tao = 1.61803399
size = 1000
return [
Point(size, tao * size, 0),
Point(-size, tao * size, 0),
Point(size, -tao * size, 0),
Point(-size, -tao * size, 0),
Point(0, size, tao * size),
Point(0, -size, tao * size),
Point(0, size, -tao * size),
Point(0, -size, -tao * size),
Point(tao * size, 0, size),
Point(-tao * size, 0, size),
Point(tao * size, 0, -size),
Point(-tao * size, 0, -size)
]