Filler for N-sided holes

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).

Install

Use PyPI to install subdivision-hole-filler:

pip install subdivision-hole-filler

Usage

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.