IcoSphereCreator.py

#!/usr/bin/python3
import math

class IcoSphereCreator:
    class MeshGeometry3D:
        positions = []
        TriangleIndices = []

    class TriangleIndices:
        def __init__(self, v1, v2, v3):
            self.v1 = v1
            self.v2 = v2
            self.v3 = v3

    class Point3D:
        def __init__(self, X, Y, Z):
            self.X = X
            self.Y = Y
            self.Z = Z

    geometry = MeshGeometry3D()
    index = -1
    middlePointIndexCache = {}

    def addVertex(self, p):
            length = math.sqrt(p.X * p.X + p.Y * p.Y + p.Z * p.Z)
            self.geometry.positions.append(self.Point3D(p.X/length, p.Y/length, p.Z/length))
            self.index += 1
            return self.index

    def getMiddlePoint(self, p1, p2):
        firstIsSmaller = p1 < p2
        smallerIndex = p1 if firstIsSmaller else p2
        greaterIndex = p2 if firstIsSmaller else p1
        key = (smallerIndex << 32) + greaterIndex;

        if key in self.middlePointIndexCache:
            return self.middlePointIndexCache[key]

        point1 = self.geometry.positions[p1]
        point2 = self.geometry.positions[p2]
        middle = self.Point3D(
            (point1.X + point2.X) / 2.0,
            (point1.Y + point2.Y) / 2.0,
            (point1.Z + point2.Z) / 2.0
            )

        i = self.addVertex(middle)
        self.middlePointIndexCache[key] = i
        return i

    def create(self, recursionLevel):
        # create 12 vertices of a icosahedron
        t = (1.0 + math.sqrt(5.0)) / 2.0

        self.addVertex(self.Point3D(-1,  t,  0))
        self.addVertex(self.Point3D( 1,  t,  0))
        self.addVertex(self.Point3D(-1, -t,  0))
        self.addVertex(self.Point3D( 1, -t,  0))

        self.addVertex(self.Point3D( 0, -1,  t))
        self.addVertex(self.Point3D( 0,  1,  t))
        self.addVertex(self.Point3D( 0, -1, -t))
        self.addVertex(self.Point3D( 0,  1, -t))

        self.addVertex(self.Point3D( t,  0, -1))
        self.addVertex(self.Point3D( t,  0,  1))
        self.addVertex(self.Point3D(-t,  0, -1))
        self.addVertex(self.Point3D(-t,  0,  1))

        # create 20 triangles of the icosahedron
        faces = []

        # 5 faces around point 0
        faces.append(self.TriangleIndices(0, 11, 5))
        faces.append(self.TriangleIndices(0, 5, 1))
        faces.append(self.TriangleIndices(0, 1, 7))
        faces.append(self.TriangleIndices(0, 7, 10))
        faces.append(self.TriangleIndices(0, 10, 11))

        # 5 adjacent faces
        faces.append(self.TriangleIndices(1, 5, 9))
        faces.append(self.TriangleIndices(5, 11, 4))
        faces.append(self.TriangleIndices(11, 10, 2))
        faces.append(self.TriangleIndices(10, 7, 6))
        faces.append(self.TriangleIndices(7, 1, 8))

        # 5 faces around point 3
        faces.append(self.TriangleIndices(3, 9, 4))
        faces.append(self.TriangleIndices(3, 4, 2))
        faces.append(self.TriangleIndices(3, 2, 6))
        faces.append(self.TriangleIndices(3, 6, 8))
        faces.append(self.TriangleIndices(3, 8, 9))

        # 5 adjacent faces
        faces.append(self.TriangleIndices(4, 9, 5))
        faces.append(self.TriangleIndices(2, 4, 11))
        faces.append(self.TriangleIndices(6, 2, 10))
        faces.append(self.TriangleIndices(8, 6, 7))
        faces.append(self.TriangleIndices(9, 8, 1))

        for i in range(0, recursionLevel):
            faces2 = []
            for tri in faces:
                 # replace triangle by 4 triangles
                 a = self.getMiddlePoint(tri.v1, tri.v2)
                 b = self.getMiddlePoint(tri.v2, tri.v3)
                 c = self.getMiddlePoint(tri.v3, tri.v1)

                 faces2.append(self.TriangleIndices(tri.v1, a, c))
                 faces2.append(self.TriangleIndices(tri.v2, b, a))
                 faces2.append(self.TriangleIndices(tri.v3, c, b))
                 faces2.append(self.TriangleIndices(a, b, c))

            faces = faces2

        for tri in faces:
            self.geometry.TriangleIndices.append(tri.v1)
            self.geometry.TriangleIndices.append(tri.v2)
            self.geometry.TriangleIndices.append(tri.v3)

        return self.geometry