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Subdivide Icosahedrons to make nice spheres
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| #!/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 |
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| vertex -0.809017 -1.118034 -1.309017 | |
| endloop | |
| endfacet | |
| facet normal -0.190983 -0.190983 -0.190983 | |
| outer loop | |
| vertex -1.118034 -1.309017 -0.809017 | |
| vertex -1.309017 -0.809017 -1.118034 | |
| vertex -0.809017 -1.118034 -1.309017 | |
| endloop | |
| endfacet | |
| facet normal -0.083260 -0.186062 -0.167271 | |
| outer loop | |
| vertex -0.305521 -1.319649 -1.335372 | |
| vertex -0.587785 -1.538842 -0.951057 | |
| vertex -0.809017 -1.118034 -1.309017 | |
| endloop | |
| endfacet | |
| facet normal -0.142040 -0.221232 -0.172288 | |
| outer loop | |
| vertex -1.118034 -1.309017 -0.809017 | |
| vertex -0.809017 -1.118034 -1.309017 | |
| vertex -0.587785 -1.538842 -0.951057 | |
| endloop | |
| endfacet | |
| facet normal -0.108700 -0.119459 -0.208434 | |
| outer loop | |
| vertex -0.494344 -0.825305 -1.640893 | |
| vertex -0.809017 -1.118034 -1.309017 | |
| vertex -0.951057 -0.587785 -1.538842 | |
| endloop | |
| endfacet | |
| facet normal -0.172288 -0.142040 -0.221232 | |
| outer loop | |
| vertex -1.309017 -0.809017 -1.118034 | |
| vertex -0.951057 -0.587785 -1.538842 | |
| vertex -0.809017 -1.118034 -1.309017 | |
| endloop | |
| endfacet | |
| facet normal -0.186062 -0.167271 0.083260 | |
| outer loop | |
| vertex -1.538842 -0.951057 0.587785 | |
| vertex -1.319649 -1.335372 0.305521 | |
| vertex -1.118034 -1.309017 0.809017 | |
| endloop | |
| endfacet | |
| facet normal -0.212080 -0.151191 0.041163 | |
| outer loop | |
| vertex -1.618034 -1.000000 0.000000 | |
| vertex -1.319649 -1.335372 0.305521 | |
| vertex -1.538842 -0.951057 0.587785 | |
| endloop | |
| endfacet | |
| facet normal -0.158805 -0.210831 0.074626 | |
| outer loop | |
| vertex -0.825305 -1.640893 0.494344 | |
| vertex -1.118034 -1.309017 0.809017 | |
| vertex -1.319649 -1.335372 0.305521 | |
| endloop | |
| endfacet | |
| facet normal -0.146716 -0.211389 0.042073 | |
| outer loop | |
| vertex -0.825305 -1.640893 0.494344 | |
| vertex -1.319649 -1.335372 0.305521 | |
| vertex -1.000000 -1.618034 0.000000 | |
| endloop | |
| endfacet | |
| facet normal -0.204926 -0.182326 0.000000 | |
| outer loop | |
| vertex -1.618034 -1.000000 0.000000 | |
| vertex -1.319649 -1.335372 -0.305521 | |
| vertex -1.319649 -1.335372 0.305521 | |
| endloop | |
| endfacet | |
| facet normal -0.172719 -0.195319 0.000000 | |
| outer loop | |
| vertex -1.319649 -1.335372 -0.305521 | |
| vertex -1.000000 -1.618034 0.000000 | |
| vertex -1.319649 -1.335372 0.305521 | |
| endloop | |
| endfacet | |
| endsolid sphere2.stl |
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