Subdivide Icosahedrons to make nice spheres

divided_icosahedron.py

#!/usr/bin/env python
from itertools import combinations, chain
import numpy as np
from pyhull.convex_hull import ConvexHull
from stl import Mode
from stl.mesh import Mesh


def subdivide(shape):
    ''' Take a triangulated sphere and subdivide each face. '''
    # https://gamedevdaily.io/d7956b825db4 - Icosahedron section
    hull = ConvexHull(shape)  # Use this to get a list of vertices (faces).
    radius = np.mean(np.linalg.norm(shape, axis=1))  # Estimate radius
    edges = set(chain(*[combinations(v, 2) for v in hull.vertices]))
    midpoints = np.mean(hull.points.take(list(edges), axis=0), axis=1)
    newpoints = midpoints / np.linalg.norm(midpoints, axis=1)[:, None] * radius
    return np.vstack((hull.points, newpoints))  # Add new points to old points


def points_to_mesh(points):
    ''' Given a set points, make a STL mesh of the convex hull. '''
    hull = ConvexHull(points)
    mesh = Mesh(np.zeros(len(hull.vertices), dtype=Mesh.dtype))
    for i, vertex in enumerate(hull.vertices):
        mesh.vectors[i] = hull.points[vertex][::-1]  # Turn it inside out
    return mesh


# Construct Icosahedron from 3 Golden Rectangles
phi = (1 + 5 ** .5) / 2  # Golden ratio
plane = np.dstack(np.meshgrid([1, -1], [phi, -phi], [0])).reshape(-1, 3)
icosahedron = np.vstack([np.roll(plane, i) for i in range(3)])

# Save to STL files so we can view in GitHub
sphere = icosahedron
for i in range(4):
    points_to_mesh(sphere).save('sphere{}.stl'.format(i), mode=Mode.ASCII)
    sphere = subdivide(sphere)  # Finer spheres by subdividing

sphere0.stl

sphere1.stl

sphere2.stl

sphere3.stl