mix.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "b1375a04-58de-4bc8-821c-18073fd3cedf",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f39ff2a7-e70d-48b1-a050-08f08ec03459",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Clearing the current figure\n",
    "plt.clf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3f01b373-c60b-4689-879f-5bf65cdbb231",
   "metadata": {},
   "outputs": [],
   "source": [
    "# -------- functionality\n",
    "shw = 1\n",
    "do_prt = 0  # Python plotting: only makes sense when shw > 0\n",
    "bvout = 1\n",
    "bbnet = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5f99f73b-ab04-4715-800c-f1291ce83036",
   "metadata": {},
   "outputs": [],
   "source": [
    "# -------- sizes\n",
    "cfs = 6  # coefficients per patch (total degree quadratic)\n",
    "idx1 = np.arange(1, cfs + 1)  # orientation\n",
    "idx0 = [3, 2, 1, 5, 4, 6]\n",
    "pats = 6  # patches per triangle\n",
    "n = 32  # evaluation density\n",
    "dim = 3  # dimension of range (3-space)\n",
    "tet = 0  # use tetrahedra data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "7ba4ba12-075d-4921-9955-6a34254fc143",
   "metadata": {},
   "outputs": [],
   "source": [
    "# --------- evaluated BB basis functions\n",
    "u0 = np.linspace(0, 1, n)\n",
    "u, v = np.meshgrid(u0, u0)\n",
    "bbb = {1: (1 - u - v) ** 2, 2: 2 * (1 - u - v) * u, 3: u * u, 4: 2 * (1 - u - v) * v, 5: 2 * v * u, 6: v * v}\n",
    "mask = np.ones((n, n))  # suppress half of the 4-sided patch\n",
    "bidx = np.triu_indices(n, k=1)\n",
    "mask[bidx] = np.nan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c79662d9-95f2-4ade-ac1f-81f4e2a1c298",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Valences\n",
    "nn = np.array([3, 4])\n",
    "c0 = np.cos(2 * np.pi / nn)\n",
    "\n",
    "# Rational weights\n",
    "wni = 3 * (1 - c0) / (c0 + 1)\n",
    "wti = 3 / (2 * (c0 + 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "fecf8fa9-7f8b-4b94-abfb-51f338ec21e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# -------- GEOMETRY+CONNECTIVITY:  double simplex\n",
    "# Vertices\n",
    "V = np.array([\n",
    "    np.cos(2 * np.pi * np.array([0, 1, 2]) / 3).tolist() + [0, 0],\n",
    "    np.sin(2 * np.pi * np.array([0, 1, 2]) / 3).tolist() + [0, 0],\n",
    "    [0, 0, 0, -1, 1]\n",
    "])\n",
    "val = np.array([4, 4, 4, 3, 3]) - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "56fbd7ac-687e-47ad-8ea1-79081c29e636",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Neighbors\n",
    "nbr = np.array([\n",
    "    [1, 4, 3, 5, 4, 1],\n",
    "    [2, 2, 2, 2, 3, 3],\n",
    "    [4, 3, 5, 1, 1, 5]\n",
    "]).T\n",
    "\n",
    "if tet == 1:\n",
    "    # -------- tet\n",
    "    V = 3 * np.array([\n",
    "        [-1, 1, 1, -1],\n",
    "        [-1, 1, -1, 1],\n",
    "        [-1, -1, 1, 1]\n",
    "    ])\n",
    "    val = np.array([3, 3, 3, 3]) - 1\n",
    "    nbr = np.array([\n",
    "        [2, 3, 4],\n",
    "        [1, 4, 3],\n",
    "        [4, 1, 2],\n",
    "        [3, 2, 1]\n",
    "    ])\n",
    "\n",
    "nbl = nbr[:, [2, 1, 0]]  # Reorder columns of nbr\n",
    "dim, vts = V.shape  # Get dimensions of V\n",
    "fcs, vfc = nbr.shape  # Get dimensions of nbr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e3c1b135-7ce8-4b4d-b00f-fe3d764dc89c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ---- draw funnel\n",
    "if shw > 0:\n",
    "    clr = ['y', 'c', 'r']  # Colors\n",
    "    fidx = [1, 2, 5]  # Indices for funnel drawing\n",
    "\n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "    for jj in range(3):\n",
    "        ii = fidx[jj] - 1  # 0-based indexing\n",
    "\n",
    "    ax.view_init(elev=-V[0, -1], azim=V[1, -1])  # 0-based indexing\n",
    "    ax.axis('equal')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "e8222df1-504c-425d-90b0-ed2c3c49398d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# --- complete Euclidean part of a single quadratic\n",
    "if bvout == 1:\n",
    "    fp = open('mixW.bv', 'w')\n",
    "for orient in range(1, 3):\n",
    "    if orient == 1:\n",
    "        nbs = nbr\n",
    "        idx = idx1\n",
    "        if bvout == 1:\n",
    "            print(\"group {} odd\".format(orient), file=fp)\n",
    "    else:\n",
    "        nbs = nbl\n",
    "        idx = idx0\n",
    "        if bvout == 1:\n",
    "            print(\"group {} even\".format(orient), file=fp)\n",
    "\n",
    "    fc = [None] * fcs\n",
    "    ctr = np.zeros((V.shape[0], fcs))\n",
    "    dual = [None] * fcs\n",
    "    for ff in range(fcs):\n",
    "        fc[ff] = V[:, nbs[ff, :] - 1]\n",
    "        # ctr[:, ff] = np.dot(fc[ff], np.ones((vfc, 1))) / vfc\n",
    "        ctr[:, ff] = np.mean(fc[ff], axis=0)\n",
    "        dual[ff] = np.zeros((V.shape[0], vfc))\n",
    "        for kk in range(vfc):\n",
    "            dual[ff][:, kk] = (3 * ctr[:, ff] + fc[ff][:, kk]) / 4\n",
    "\n",
    "    # --- project vtx neighbors MISSING(not needed for specific geometry)\n",
    "    for ii in range(vts):\n",
    "        # project duals -- currently left out since valence 3 or 4\n",
    "        pass\n",
    "\n",
    "    for ff in range(fcs):\n",
    "        for kk in range(vfc):  # k = index inside face if rem(pat,2)==1\n",
    "            pat = 2 * kk + orient\n",
    "            km = kk - 1\n",
    "            if km < 0:\n",
    "                km = kk + vfc - 1\n",
    "            kp = kk + 1\n",
    "            if kp >= vfc:\n",
    "                kp = kk - vfc + 1\n",
    "            top = nbs[ff, kk]  # top global vertex index\n",
    "            nxt = nbs[ff, kp]  # bottom left vertex index\n",
    "            prv = nbs[ff, km]  # bottom right vertex index\n",
    "            # kk\n",
    "            # kp km\n",
    "            # nxt prv\n",
    "            ntp = 0\n",
    "            for tt in range(fcs):  # neighbor triangle nxt\n",
    "                for ii in range(vfc):\n",
    "                    ip = ii + 1\n",
    "                    if ip >= vfc:\n",
    "                        ip = 1\n",
    "                    if nbs[tt, ii] == nxt and nbs[tt, ip] == top:\n",
    "                        ntp = tt\n",
    "                        break\n",
    "                if ntp != 0:\n",
    "                    break\n",
    "\n",
    "            ntm = 0\n",
    "            for jj in range(fcs):  # neighbor triangle prv-top edge\n",
    "                for nn in range(vfc):\n",
    "                    np1 = nn + 1\n",
    "                    if np1 >= vfc:\n",
    "                        np1 = 1\n",
    "                    if nbs[jj, nn] == top and nbs[jj, np1] == prv:\n",
    "                        ntm = jj\n",
    "                        break\n",
    "                if ntm != 0:\n",
    "                    break\n",
    "\n",
    "            # v10 v00 ff\n",
    "            # v11 v01\n",
    "            vf0 = dual[ff][:, kk]\n",
    "            vfp = dual[ff][:, kp]\n",
    "            vfm = dual[ff][:, km]\n",
    "            v0p = dual[ntp][:, ip]\n",
    "            v1p = dual[ntp][:, ii]\n",
    "            v0m = dual[ntm][:, nn]\n",
    "            if pat == 1 and ff == 1:\n",
    "                fig = plt.figure()\n",
    "                ax = fig.add_subplot(111, projection='3d')\n",
    "                ax.scatter(vf0[0], vf0[1], vf0[2], color='r', marker='o')\n",
    "                ax.scatter(v0p[0], v0p[1], v0p[2], color='g', marker='*')\n",
    "                ax.scatter(vfp[0], vfp[1], vfp[2], color='b', marker='*')\n",
    "                ax.scatter(v1p[0], v1p[1], v1p[2], color='k', marker='+')\n",
    "                plt.show()\n",
    "\n",
    "            wti_top = wti[val[top - 1] - 2]\n",
    "            wti_bot = wti[val[nxt - 1] - 2]\n",
    "            wni_top = wni[val[top - 1] - 2]\n",
    "            # w_top = 2 * (1 + c0(val(top) - 2)) / 3\n",
    "            # w_bot = 2 * (1 + c0(val(nxt) - 2)) / 3\n",
    "            # w_prv = 2 * (1 + c0(val(prv) - 2)) / 3\n",
    "            w_top = 1\n",
    "            w_bot = 1\n",
    "            w_prv = 1\n",
    "            w1 = np.sqrt(wti_top * wti_bot)\n",
    "            w5 = w_top\n",
    "            w4 = w_top * wti_top\n",
    "            wgt = [w1, w5, (w_top + w_bot + w_prv) / 3, w4, w5, w_top * wni_top]\n",
    "\n",
    "            qE = np.zeros((3, 6)) # Initialize qE as a 3x6 zero matrix: 3 rows for 3D points, 6 columns for the weights\n",
    "            # --- assemble by averaging in coeff_i weight_i\n",
    "            qE[:, 4] = wgt[4] * vf0\n",
    "            qE[:, 1] = wgt[1] * (vf0 + vfp) / 2\n",
    "            midopp = wgt[1] * (v0p + v1p) / 2\n",
    "            qE[:, 3] = wgt[3] * (vf0 + v0p) / 2\n",
    "            qE[:, 0] = wgt[0] * (vf0 + vfp + v0p + v1p) / 4\n",
    "            qE[:, 2] = (w_top * vf0 + w_bot * vfp + w_prv * vfm) / 3\n",
    "\n",
    "            # top is average:  v0p-o + v0m-o = (vf0-o)*2c0\n",
    "            #  v0p+v0m-vf0(2c0) = 2o-2c0o = 2(1-c0)o\n",
    "            cc = c0[val[top - 1] - 2]\n",
    "            tv = (v0p + v0m - 2 * cc * vf0) / (2 * (1 - cc))  # top vertex Euclidian\n",
    "            qE[:, 5] = wgt[5] * tv\n",
    "\n",
    "            if pat == 1 and ff == 1 and kk == 1:\n",
    "                fig = plt.figure()\n",
    "                ax = fig.add_subplot(111, projection='3d')\n",
    "                ax.scatter(v0m[0], v0m[1], v0m[2], color='c', marker='o')\n",
    "                ax.scatter(tv[0], tv[1], tv[2], color='r', marker='+')\n",
    "                plt.show()\n",
    "\n",
    "            # --- assemble\n",
    "            bbase = np.vstack((qE, wgt)).T\n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "02363b15-29cf-453f-a883-b90daa821201",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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