A python package to fill N-sided holes using combined subdivision schemes, based on Catmull-Clark subdivison.
See Levin, Adi. “Filling N-sided Holes Using Combined Subdivision Schemes.” (2000).
Use PyPI to install subdivision-hole-filler:
pip install subdivision-hole-filler
Run the following script to fill a hole.
import numpy as np
from subdivision_hole_filler import Boundary, NsidedHoleFiller
r = 1
R = 1
boundaries = [None, None, None, None, None, None]
for d in range(3):
def coord(u: float, d=d):
phi = (1.0 - u / 2.0) * np.pi / 2.0
x = r * np.cos(phi)
y = r * np.sin(phi)
z = r + R
c = np.zeros(3)
c[d] = z
c[(d + 1) % 3] = x
c[(d + 2) % 3] = y
return c
def deriv(u: float, d=d):
vec = np.zeros(3)
vec[d] = -1
return np.array(vec)
bd = Boundary()
bd.coord = coord # A function of parametric coord `u` in [0.0, 2.0], which defines the coordinate of a point on the boundary
bd.deriv = deriv # A function of parametric coord `u` in [0.0, 2.0], which defines the cross boundary derivative of a point on the boundary, poining to the inside
boundaries[d*2] = bd
for d in range(3):
def coord(u: float, d=d):
phi = (1.0 - u / 2.0) * np.pi / 2.0
x = R + r - R * np.cos(phi)
y = R + r - R * np.sin(phi)
z = 0
c = np.zeros(3)
c[d] = z
c[(d + 1) % 3] = x
c[(d + 2) % 3] = y
return c
def deriv(u: float, d=d):
vec = np.zeros(3)
vec[d] = 1
return np.array(vec)
bd = Boundary()
bd.coord = coord # A function of parametric coord `u` in [0.0, 2.0], which defines the coordinate of a point on the boundary
bd.deriv = deriv # A function of parametric coord `u` in [0.0, 2.0], which defines the cross boundary derivative of a point on the boundary, poining to the inside
boundaries[(d + 1) % 3 * 2 + 1] = bd
filler = NsidedHoleFiller(boundaries)
center_point = np.array([r, r, r])
filler.gen_initial_mesh(center_point)
for iteration in range(3):
filler.cmc_subdiv_for_1step(iteration=iteration)
Here is the ouput.