def ngon_to_triangles(face: Iterable['Vertex']) -> Iterable[Sequence[Vec3]]:
face = [Vec3(v) for v in face]
if face[0].isclose(face[-1]): # closed shape
center = Vec3.sum(face[:-1]) / (len(face) - 1)
else:
center = Vec3.sum(face) / len(face)
face.append(face[0])
for v1, v2 in zip(face[:-1], face[1:]):
yield v1, v2, center
def ngon_to_triangles(face: Iterable["Vertex"]) -> Iterable[Sequence[Vec3]]:
_face = Vec3.list(face)
if _face[0].isclose(_face[-1]): # closed shape
center = Vec3.sum(_face[:-1]) / (len(_face) - 1)
else:
center = Vec3.sum(_face) / len(_face)
_face.append(_face[0])
for v1, v2 in zip(_face[:-1], _face[1:]):
yield v1, v2, center
def subdivide_face(face: Sequence[Union[Vec3, Vec2]],
quads=True) -> Iterable[List[Vec3]]:
""" Yields new subdivided faces. Creates new faces from subdivided edges and the face midpoint by linear
interpolation.
Args:
face: a sequence of vertices, :class:`Vec2` and :class:`Vec3` objects supported.
quads: create quad faces if ``True`` else create triangles
"""
if len(face) < 3:
raise ValueError('3 or more vertices required.')
len_face = len(face)
mid_pos = Vec3.sum(face) / len_face
subdiv_location = [
face[i].lerp(face[(i + 1) % len_face]) for i in range(len_face)
]
for index, vertex in enumerate(face):
if quads:
yield vertex, subdiv_location[index], mid_pos, subdiv_location[
index - 1]
else:
yield subdiv_location[index - 1], vertex, mid_pos
yield vertex, subdiv_location[index], mid_pos
def spherical_envelope(points: Sequence["Vertex"]) -> Tuple[Vec3, float]:
"""Calculate the spherical envelope for the given points. Returns the
centroid (a.k.a. geometric center) and the radius of the enclosing sphere.
.. note::
The result does not represent the minimal bounding sphere!
.. versionadded:: 0.18
"""
centroid = Vec3.sum(points) / len(points)
radius = max(centroid.distance(p) for p in points)
return centroid, radius
def subdivide_ngons(
faces: Iterable[Sequence[Union[Vec3, Vec2]]]) -> Iterable[List[Vec3]]:
""" Yields only triangles or quad faces, subdivides ngons into triangles.
Args:
faces: iterable of faces as sequence of :class:`Vec2` and
:class:`Vec3` objects
"""
for face in faces:
if len(face) < 5:
yield face
else:
mid_pos = Vec3.sum(face) / len(face)
for index, vertex in enumerate(face):
yield face[index - 1], vertex, mid_pos
def recenter() -> Iterator[AnyVec]:
for cluster_points in clusters.values():
yield Vec3.sum(cluster_points) / len(cluster_points)
if len(clusters) < k: # refill centroids if required
yield from random.sample(points, k - len(clusters))
