def create_tiles(self, depth: int):
if depth == 0:
self._draw(depth)
return
self.create_tiles(depth=depth - 1)
print(f"Populating depth {depth}...")
new_boundary = [
self._build_new_tile(self._boundary[0], self._boundary[-1])
]
index = 0
counter = 0
num_tiles = (3 * sqrt(3) * ((2 + sqrt(3))**depth -
(2 - sqrt(3))**depth)).as_int()
while True:
new_vertex = self._build_new_tile(new_boundary[-1],
self._boundary[index])
counter += 1
print(f"created {counter} / {num_tiles} tiles...", end="\r")
if new_vertex in self._boundary:
index += 1
elif new_vertex in new_boundary:
break
else:
new_boundary.append(new_vertex)
self._boundary = new_boundary
self._draw(depth)
print(f"Populated, found {len(self._tiles)} tiles")
def r_euclid(self) -> float:
assert self.z != 0
return (((self.x / self.z)**2 + (self.y / self.z)**2) * sqrt(2) -
1).value**0.5
def from_points(point_1: Point, point_2: Point) -> "Line":
return Line(
x=point_1.y * point_2.z - point_1.z * point_2.y,
y=point_1.z * point_2.x - point_1.x * point_2.z,
z=(point_1.y * point_2.x - point_1.x * point_2.y) * sqrt(2),
)
def product(self, point: Point) -> QuadraticRational:
return self.z * point.z - (self.x * point.x +
self.y * point.y) * sqrt(2)
def norm(self) -> QuadraticRational:
return (self.x**2 + self.y**2) * sqrt(2) - self.z**2
def main():
point_1 = Vertex(0 * sqrt(2) / 1,
sqrt(2) / sqrt(3), (sqrt(2) + 1) / sqrt(3))
point_2 = Vertex(-sqrt(2) / 2, -1 / sqrt(6), (sqrt(2) + 1) / sqrt(3))
point_3 = Vertex(sqrt(2) / 2, -1 / sqrt(6), (sqrt(2) + 1) / sqrt(3))
tiling = Tiling(point_1, point_2, point_3)
tiling.create_tiles(depth=6)
def cosh_distance(point_1: Point, point_2: Point) -> QuadraticRational:
return point_1.z * point_2.z - (point_1.x * point_2.x +
point_1.y * point_2.y) * sqrt(2)