PythonicGeodynamicsMorra/Example Ch02 3d Sphere Packing.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.spatial import ConvexHull"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def writeVTKSurface(outFileName,x,y,z,triangles):\n",
    "    nodesNumber=x.size\n",
    "    trianglesNumber=int(triangles.size/3)\n",
    "    m=open(outFileName,'w')\n",
    "    m.write('# vtk DataFile Version 2.0\\n')\n",
    "    m.write('Moebius surface\\n')\n",
    "    m.write('ASCII\\n')\n",
    "    m.write('DATASET POLYDATA\\n')\n",
    "    m.write('POINTS '+str(nodesNumber)+' float\\n')\n",
    "    for node in np.arange(nodesNumber):\n",
    "        m.write(str(x[node])+' '+str(y[node])+' '+str(z[node])+' \\n')\n",
    "\n",
    "    m.write('POLYGONS '+str(trianglesNumber)+' '+str(trianglesNumber*4)+'\\n')\n",
    "    for triangle in np.arange(trianglesNumber):\n",
    "        m.write('3 '+str(triangles[triangle,0])+' '+str(triangles[triangle,1])+' '+str(triangles[triangle,2])+' \\n')\n",
    "\n",
    "    m.close()\n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def writeVTKSurfaceField(outFileName,x,y,z,triangles,field):\n",
    "    nodesNumber=x.size\n",
    "    trianglesNumber=int(triangles.size/3)\n",
    "    m=open(outFileName,'w')\n",
    "    m.write('# vtk DataFile Version 2.0\\n')\n",
    "    m.write('Moebius surface\\n')\n",
    "    m.write('ASCII\\n')\n",
    "    m.write('DATASET POLYDATA\\n')\n",
    "    m.write('POINTS '+str(nodesNumber)+' float\\n')\n",
    "    for node in np.arange(nodesNumber):\n",
    "        m.write(str(x[node])+' '+str(y[node])+' '+str(z[node])+' \\n')\n",
    "\n",
    "    m.write('POLYGONS '+str(trianglesNumber)+' '+str(trianglesNumber*4)+'\\n')\n",
    "    for triangle in np.arange(trianglesNumber):\n",
    "        m.write('3 '+str(triangles[triangle,0])+' '+str(triangles[triangle,1])+' '+str(triangles[triangle,2])+' \\n')\n",
    "\n",
    "    a=field.shape\n",
    "    m.write('CELL_DATA '+str(trianglesNumber)+'\\n')\n",
    "    m.write('FIELD FieldData 1\\n')\n",
    "    m.write('FIEfaceAttributes '+str(a[1])+' '+str(trianglesNumber)+' float\\n')\n",
    "    for triangle in np.arange(trianglesNumber):\n",
    "        for i in np.arange(a[1]): m.write(str(field[triangle,i])+' ')\n",
    "        m.write('\\n')\n",
    "\n",
    "    m.close()\n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def writeVTKDatasetStructure(outFileName,xNum, yNum, zNum, xMin, yMin, zMin, xSpacing, ySpacing, zSpacing, dataInteriors):\n",
    "    outFile=open(outFileName,'w')\n",
    "    outFile.write('# vtk DataFile Version 2.0\\n')\n",
    "    outFile.write('corrected flow of stream with boundary elements\\n')\n",
    "    outFile.write('\\n')\n",
    "    outFile.write('ASCII\\n')\n",
    "    outFile.write('DATASET STRUCTURED_POINTS\\n')\n",
    "    outFile.write('DIMENSIONS '+str(xNum)+' '+str(yNum)+' '+str(zNum)+'\\n')\n",
    "    outFile.write('ORIGIN '+str(xMin)+' '+str(yMin)+' '+str(zMin)+'\\n')\n",
    "    outFile.write('SPACING '+str(xSpacing)+' '+str(ySpacing)+' '+str(zSpacing)+'\\n')\n",
    "    outFile.write('\\n')\n",
    "    outFile.write('POINT_DATA '+str(xNum*yNum*zNum)+'\\n')\n",
    "    outFile.write('SCALARS scalar_name float 1\\n')\n",
    "    outFile.write('LOOKUP_TABLE default\\n')\n",
    "        \n",
    "    numberOfPoints = xNum*yNum*zNum\n",
    "    for i in np.arange(numberOfPoints):\n",
    "        outFile.write(str(dataInteriors[i])+'\\n')\n",
    "    outFile.close()\n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# mesh of one sphere\n",
    "def fibonacci_covering(samples):\n",
    "\n",
    "    increment = np.pi * ( 3 - 5**0.5 ) #fibonacci number\n",
    "    points = np.zeros((samples,3))\n",
    "\n",
    "    phi = np.arange(samples) * increment\n",
    "    points[:,1] = ( 2. * np.arange(samples) + 1 )/samples - 1.\n",
    "    r = ( 1 - points[:,1]**2 )**0.5      \n",
    "    points[:,0] = np.cos(phi) * r\n",
    "    points[:,2] = np.sin(phi) * r\n",
    "      \n",
    "    return(points,ConvexHull(points))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Sphere packing\n",
    "rMin = np.float64(0.03)\n",
    "rMax = np.float64(0.2)\n",
    "packingTarget = 0.50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#first sphere:\n",
    "centers = np.random.random((1,3))*(1.0-2*rMin)+rMin\n",
    "radii = np.array([rMin])\n",
    "packing=4/3*radii[0]**3*np.pi\n",
    "attempt=0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "sphere 1003 58988 0.03 0.2 [0.65610021 0.23614967 0.4151567 ] 0.030379555281504017 0.49952544453516967\n",
      "sphere 1004 61510 0.03 0.2 [0.89833023 0.91456724 0.82026929] 0.030052090588453026 0.4996391320249058\n",
      "sphere 1005 62048 0.03 0.2 [0.77791524 0.31363834 0.79625986] 0.03003008203168575 0.4997525699214622\n",
      "sphere 1006 62375 0.03 0.2 [0.31561685 0.17446154 0.88157034] 0.032119242073638234 0.49989136832631426\n",
      "sphere 1007 62746 0.03 0.2 [0.95577963 0.76865472 0.75427656] 0.032252893409773234 0.5000319066125244\n"
     ]
    }
   ],
   "source": [
    "while packing<packingTarget:\n",
    "    attempt+=1\n",
    "    #rMin=(1./attempt)**0.333\n",
    "    #rMax=np.min([rMin*100,0.3])\n",
    "    newCenter = np.random.rand(3)*(1.0-2*rMin)+rMin\n",
    "    \n",
    "    #check that it does not exit the box boundaries    \n",
    "    maxRadius = np.min(np.concatenate(([rMax],newCenter[0:3],1.0-newCenter[0:3])))\n",
    "\n",
    "    # expand the sphere up to touching the wall or another sphere\n",
    "    distances = np.linalg.norm(newCenter-centers,axis=1)\n",
    "    newRadius = np.min([np.min(distances - radii),maxRadius])\n",
    "    if newRadius>rMin:\n",
    "        centers = np.append(centers,np.array([newCenter]),axis=0)\n",
    "        radii = np.append(radii,newRadius)\n",
    "        packing+=4/3*newRadius**3*np.pi\n",
    "        print('sphere',radii.size,attempt,rMin,rMax,newCenter,newRadius,packing) \n",
    "nSpheres = radii.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# write a VTK file with the surfaces\n",
    "nPoints=500\n",
    "(points,oneSphereMesh) = fibonacci_covering(nPoints)        \n",
    "allPoints = np.zeros((0,3),dtype=np.float64)\n",
    "connectivity = np.zeros((0,3),dtype=np.int64)\n",
    "for thisSphere in np.arange(nSpheres):\n",
    "    allPoints=np.append(allPoints, points*radii[thisSphere]+centers[thisSphere], axis=0)\n",
    "    connectivity=np.append(connectivity, oneSphereMesh.simplices+thisSphere*nPoints,axis=0)\n",
    "\n",
    "writeVTKSurface('sphere_packing.vtk',allPoints[:, 0], allPoints[:, 1], allPoints[:, 2],connectivity)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "calculating the sphere 2\n",
      "calculating the sphere 10\n",
      "calculating the sphere 25\n",
      "calculating the sphere 31\n",
      "calculating the sphere 41\n",
      "calculating the sphere 46\n",
      "calculating the sphere 50\n",
      "calculating the sphere 58\n",
      "calculating the sphere 61\n",
      "calculating the sphere 68\n",
      "calculating the sphere 76\n",
      "calculating the sphere 94\n",
      "calculating the sphere 95\n",
      "calculating the sphere 109\n",
      "calculating the sphere 133\n",
      "calculating the sphere 139\n",
      "calculating the sphere 146\n",
      "calculating the sphere 147\n",
      "calculating the sphere 154\n",
      "calculating the sphere 161\n",
      "calculating the sphere 175\n",
      "calculating the sphere 176\n",
      "calculating the sphere 180\n",
      "calculating the sphere 185\n",
      "calculating the sphere 191\n",
      "calculating the sphere 196\n",
      "calculating the sphere 197\n",
      "calculating the sphere 214\n",
      "calculating the sphere 233\n",
      "calculating the sphere 236\n",
      "calculating the sphere 239\n",
      "calculating the sphere 241\n",
      "calculating the sphere 244\n",
      "calculating the sphere 260\n",
      "calculating the sphere 262\n",
      "calculating the sphere 268\n",
      "calculating the sphere 277\n",
      "calculating the sphere 279\n",
      "calculating the sphere 285\n",
      "calculating the sphere 323\n",
      "calculating the sphere 345\n",
      "calculating the sphere 366\n",
      "calculating the sphere 381\n",
      "calculating the sphere 399\n",
      "calculating the sphere 401\n",
      "calculating the sphere 402\n",
      "calculating the sphere 413\n",
      "calculating the sphere 442\n",
      "calculating the sphere 448\n",
      "calculating the sphere 479\n",
      "calculating the sphere 484\n",
      "calculating the sphere 491\n",
      "calculating the sphere 543\n",
      "calculating the sphere 562\n",
      "calculating the sphere 566\n",
      "calculating the sphere 569\n",
      "calculating the sphere 585\n",
      "calculating the sphere 610\n",
      "calculating the sphere 625\n",
      "calculating the sphere 649\n",
      "calculating the sphere 668\n",
      "calculating the sphere 680\n",
      "calculating the sphere 688\n",
      "calculating the sphere 692\n",
      "calculating the sphere 693\n",
      "calculating the sphere 703\n",
      "calculating the sphere 722\n",
      "calculating the sphere 724\n",
      "calculating the sphere 725\n",
      "calculating the sphere 731\n",
      "calculating the sphere 744\n",
      "calculating the sphere 806\n",
      "calculating the sphere 807\n",
      "calculating the sphere 810\n",
      "calculating the sphere 823\n",
      "calculating the sphere 841\n",
      "calculating the sphere 865\n",
      "calculating the sphere 880\n",
      "calculating the sphere 897\n",
      "calculating the sphere 902\n",
      "calculating the sphere 915\n",
      "calculating the sphere 927\n",
      "calculating the sphere 931\n",
      "calculating the sphere 939\n",
      "calculating the sphere 945\n",
      "calculating the sphere 959\n",
      "calculating the sphere 981\n",
      "calculating the sphere 985\n",
      "calculating the sphere 992\n",
      "calculating the sphere 995\n",
      "calculating the sphere 999\n",
      "calculating the sphere 1000\n"
     ]
    }
   ],
   "source": [
    "# extract a 2D section in the mid of the packing\n",
    "xSize=1001;ySize=1001;zSize=1;\n",
    "\n",
    "# Create an array for the calculations\n",
    "matrix = np.zeros((xSize,ySize,zSize))\n",
    "X=np.arange(xSize)*(1/xSize)\n",
    "Y=np.arange(ySize)*(1/ySize)\n",
    "Z=0.5\n",
    "coordinates=np.meshgrid(X,Y,Z)\n",
    "for i in np.arange(nSpheres):\n",
    "    if (centers[i,2]+radii[i]>0.5) and (centers[i,2]-radii[i]<0.5):\n",
    "        #interiors = np.linalg.norm(coordinates-centers[i])<(radii[i])\n",
    "        interiors = (coordinates[0]-centers[i,0])**2+(coordinates[1]-centers[i,1])**2+(coordinates[2]-centers[i,2])**2<radii[i]**2\n",
    "        matrix[interiors]=1\n",
    "        print('calculating the sphere',i)\n",
    "\n",
    "writeVTKDatasetStructure('slice_packing.vtk',xSize,ySize,zSize, 0.0,0.0,0.0, 1/(xSize-1), 1/(ySize-1), 0.01, matrix.reshape(xSize*ySize*zSize) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "if 0:\n",
    "    # write a VTK file with 3D volume file description\n",
    "    xSize=301;ySize=301;zSize=301;\n",
    "\n",
    "    # Create an array for the calculations\n",
    "    matrix = np.zeros((xSize,ySize,zSize))\n",
    "    X=np.arange(xSize)*(1/xSize)\n",
    "    Y=np.arange(ySize)*(1/ySize)\n",
    "    Z=np.arange(zSize)*(1/zSize)\n",
    "    coordinates=np.meshgrid(X,Y,Z)\n",
    "    for i in np.arange(nSpheres):\n",
    "        interiors = np.linalg.norm(coordinates-centers[i])<(radii[i])\n",
    "        #interiors = (coordinates[0]-centers[i,0])**2+(coordinates[1]-centers[i,1])**2+(coordinates[2]-centers[i,2])**2<radii[i]**2\n",
    "        matrix[interiors]=1\n",
    "        print('calculating the sphere',i)\n",
    "\n",
    "    writeVTKDatasetStructure('interior_packing.vtk',xSize,xSize,xSize, 0.0,0.0,0.0, 1/(xSize-1), 1/(ySize-1), 1/(zSize-1), matrix.reshape(101*101*101) )\n",
    "\n",
    "\n",
    "            \n",
    "            \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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