Strips-on-sphere.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Strips on sphere ##"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We generate a sphere from 12 strips. The basic strip is parameterized and discretized below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "theta=np.linspace(0, 5*np.pi/36, 30)  #5pi/36=25 degrees\n",
    "phi=np.linspace(-np.pi/2, np.pi/2, 100)\n",
    "theta, phi=np.meshgrid(theta, phi)\n",
    "x=np.cos(theta)*np.cos(phi)\n",
    "y=np.sin(theta)*np.cos(phi)\n",
    "z=np.sin(phi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This strip is rotated about Oz, with integer multiple of $\\pi/6$ radians. Since z-rotation  does not change z values, we define only a planar rotation of `alpha` radians:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def Rot(alpha):\n",
    "    return np.array([[np.cos(alpha), -np.sin(alpha)], [np.sin(alpha), np.cos(alpha)]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead of applying this rotation successively to each point in the basic strip, we make use of the numpy function `einsum` (Einstein summation), and rotate simultaneously   all points with coordinates in  two equally shaped meshgrids (x,y, in our case): "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def rotate_z_mesh(x, y, alpha):\n",
    "    return np.einsum('ji, mni -> jmn', Rot(alpha), np.dstack([x, y]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The colorscale to plot the sphere's strips:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cofee_green=[[0.0,u'#543005'],\n",
    "[0.1,u'#8c510a'],\n",
    "[0.2, u'#bf812d'],\n",
    "[0.3, u'#dfc27d'],\n",
    "[0.4, u'#f6e8c3'],\n",
    "[0.5, u'#f5f5f5'],\n",
    "[0.6, u'#c7eae5'],\n",
    "[0.7, u'#80cdc1'],\n",
    "[0.8, u'#35978f'],\n",
    "[0.9, u'#01665e'],\n",
    "[1.0, u'#003c30']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import plotly.plotly as py\n",
    "import plotly.tools as tls\n",
    "from plotly.graph_objs import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_trace(x,y,z, colsc):# this function creates the trace for each strip on sphere\n",
    "    return Surface(\n",
    "        x=x,\n",
    "        y=y,\n",
    "        z=z,\n",
    "        colorscale=colsc,         \n",
    "        name=''            \n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dt=[make_trace(x,y,z, cofee_green)]#initial strip\n",
    "for k in range(1,12):\n",
    "    rez=rotate_z_mesh(x, y, k*np.pi/6)\n",
    "    dt+=[make_trace(rez[0], rez[1], z, cofee_green)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data=Data(dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The draw time for this plot will be slow for clients without much RAM.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "u'https://plot.ly/~empet/4759'"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "axis = dict(\n",
    "showbackground=True, \n",
    "backgroundcolor='rgb(20, 20, 20)', \n",
    "gridcolor='rgb(75, 75, 75)',      \n",
    "zerolinecolor='rgb(75, 75, 75)'\n",
    "    )\n",
    "\n",
    "layout = Layout(\n",
    "         title='Strips on sphere', \n",
    "         width=800,\n",
    "         height=800,\n",
    "         scene=Scene(  \n",
    "         xaxis=XAxis(axis),\n",
    "         yaxis=YAxis(axis), \n",
    "         zaxis=ZAxis(axis), \n",
    "        )\n",
    "        )\n",
    "        \n",
    "fig = Figure(data=data, layout=layout)\n",
    "py.sign_in('empet', 'my_api_key')\n",
    "py.plot(fig, filename='spherical-strips')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[https://plot.ly/~empet/4759](https://plot.ly/~empet/4759)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       "    /*body {\n",
       "        background-color: #F5F5F5;\n",
       "    }*/\n",
       "    div.cell{\n",
       "        width: 900px;\n",
       "        margin-left: 13% !important;\n",
       "        margin-right: auto;\n",
       "    }\n",
       "    #notebook li { /* More space between bullet points */\n",
       "    margin-top:0.8em;\n",
       "    }\n",
       "\n",
       "    h1 {\n",
       "        font-family: 'Alegreya Sans', sans-serif;\n",
       "    }\n",
       "    .text_cell_render h1 {\n",
       "        font-weight: 200;\n",
       "        font-size: 40pt;\n",
       "        line-height: 100%;\n",
       "        color: rgb(8, 66, 133);\n",
       "        margin-bottom: 0em;\n",
       "        margin-top: 0em;\n",
       "        display: block;\n",
       "    }\n",
       "    h2 {\n",
       "        font-family: 'Fenix', serif;\n",
       "        text-indent:1em;\n",
       "        text-align:center;\n",
       "    }\n",
       "    .text_cell_render h2 {\n",
       "        font-weight: 200;\n",
       "        font-size: 28pt;\n",
       "        line-height: 100%;\n",
       "        color: rgb(8, 66, 133);\n",
       "        margin-bottom: 1.5em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "    }\n",
       "    h3 {\n",
       "        font-family: 'Fenix', serif;\n",
       "        %margin-top:12px;\n",
       "        %margin-bottom: 3px;\n",
       "    }\n",
       "    .text_cell_render h3 {\n",
       "        font-weight: 300;\n",
       "        font-size: 18pt;\n",
       "        line-height: 100%;\n",
       "        color: rgb(8, 66, 133);\n",
       "        margin-bottom: 0.5em;\n",
       "        margin-top: 2em;\n",
       "        display: block;\n",
       "    }\n",
       "    h4 {\n",
       "        font-family: 'Fenix', serif;\n",
       "    }\n",
       "    .text_cell_render h4 {\n",
       "        font-weight: 300;\n",
       "        font-size: 16pt;\n",
       "        color: rgb(8, 66, 133);\n",
       "        margin-bottom: 0.5em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "    }\n",
       "    h5 {\n",
       "        font-family: 'Alegreya Sans', sans-serif;\n",
       "    }\n",
       "    .text_cell_render h5 {\n",
       "        font-weight: 300;\n",
       "        font-style: normal;\n",
       "        font-size: 16pt;\n",
       "        margin-bottom: 0em;\n",
       "        margin-top: 1.5em;\n",
       "        display: block;\n",
       "        }\n",
       "    div.text_cell_render{\n",
       "        font-family: 'Alegreya Sans',Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
       "        line-height: 145%;\n",
       "        font-size: 130%;\n",
       "        width:900px;\n",
       "        margin-left:auto;\n",
       "        margin-right:auto;\n",
       "        %text-align:justify;\n",
       "        %text-justify:inter-word;\n",
       "    }\n",
       "    \n",
       "    \n",
       "    code{\n",
       "      font-size: 78%;\n",
       "    }\n",
       "    .rendered_html code{\n",
       "        background-color: transparent;\n",
       "        white-space: inherit;   \n",
       "    }\n",
       "    .prompt{\n",
       "        display: None;\n",
       "     }\n",
       "    .rendered_html code{\n",
       "    background-color: transparent;\n",
       "    }\n",
       "\n",
       "    blockquote{\n",
       "      display:block;\n",
       "      background: #f3f3f3;\n",
       "      font-family: \"Open sans\",verdana,arial,sans-serif;\n",
       "      width:610px;\n",
       "      padding: 15px 15px 15px 15px;\n",
       "      text-align:justify;\n",
       "      text-justify:inter-word;\n",
       "      }\n",
       "      blockquote p {\n",
       "        margin-bottom: 0;\n",
       "        line-height: 125%;\n",
       "        font-size: 100%;\n",
       "      }\n",
       "   /* element.style {\n",
       "    } */\n",
       "</style>\n",
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\"]\n",
       "                           },\n",
       "                tex2jax: {\n",
       "                    inlineMath: [ [\"$\",\"$\"], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ [\"$$\",\"$$\"], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: \"center\", // Change this to \"center\" to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {\".MathJax_Display\": {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.core.display import HTML\n",
    "def  css_styling():\n",
    "    styles = open(\"./custom.css\", \"r\").read()\n",
    "    return HTML(styles)\n",
    "css_styling()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}