"""
Icosphere
=========
Generates a mesh of a icosphere.
"""
__author__ = 'Christoph Kirst <christoph.kirst.ck@gmail.com>'
__license__ = 'GPLv3 - GNU General Pulic License v3 (see LICENSE)'
__copyright__ = 'Copyright © 2020 by Christoph Kirst'
__webpage__ = 'http://idisco.info'
__download__ = 'http://www.github.com/ChristophKirst/ClearMap2'
import numpy as np
[docs]
def icosphere(radius = 1.0, center = (0,0,0), n_refinements = 0):
#construct icosahedron
r = (1.0 + np.sqrt(5.0)) / 2.0;
vertices = np.array([
[-1.0, r, 0.0],
[ 1.0, r, 0.0],
[-1.0, -r, 0.0],
[ 1.0, -r, 0.0],
[0.0, -1.0, r],
[0.0, 1.0, r],
[0.0, -1.0, -r],
[0.0, 1.0, -r],
[ r, 0.0, -1.0],
[ r, 0.0, 1.0],
[ -r, 0.0, -1.0],
[ -r, 0.0, 1.0],
], dtype=float);
vertices = list(vertices)
faces = [
[0, 11, 5],
[0, 5, 1],
[0, 1, 7],
[0, 7, 10],
[0, 10, 11],
[1, 5, 9],
[5, 11, 4],
[11, 10, 2],
[10, 7, 6],
[7, 1, 8],
[3, 9, 4],
[3, 4, 2],
[3, 2, 6],
[3, 6, 8],
[3, 8, 9],
[5, 4, 9],
[2, 4, 11],
[6, 2, 10],
[8, 6, 7],
[9, 8, 1],
];
for n in range(n_refinements):
vertices, faces = _sub_divide_faces(vertices, faces);
length = np.linalg.norm(vertices, axis=1);
vertices = (np.array(vertices).T / length * radius).T + center;
faces = np.array(faces);
return vertices, faces
def _sub_divide_faces(vertices, faces):
new_vertices = list(vertices);
new_faces = [];
n = len(new_vertices);
for face in faces:
new_vertices += [0.5 * (vertices[face[i]] + vertices[face[j]]) for i,j in zip([0,1,2],[1,2,0])];
new_faces += [[face[0], n, n+2], [n, face[1], n+1], [n+1, face[2], n+2],[n, n+1, n+2]];
n += 3;
return new_vertices, new_faces;
def _test():
import ClearMap.Visualization.Mesh.IcoSphere as ics
from importlib import reload
reload(ics)
vertices, faces = ics.icosphere(n_refinements = 2);
import ClearMap.Visualization.Plot3d as p3d
p3d.plot_mesh_3d(vertices, faces)
