parametric-curves.ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Parametric equations in plotly"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "Here are some possibilies:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import plotly.plotly as py\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# some parametric eqution\n",
    "def F(t, R=1):\n",
    "    return R*np.cos(t), R*np.sin(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Show parameter on hover"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "t = np.linspace(0, 2*np.pi, 100)\n",
    "x, y = F(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<iframe id=\"igraph\" scrolling=\"no\" style=\"border:none;\"seamless=\"seamless\" src=\"https://plot.ly/~etpinard/3796.embed\" height=\"525\" width=\"100%\"></iframe>"
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      "text/plain": [
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     "execution_count": 4,
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   "source": [
    "trace = dict(\n",
    "    x=x,\n",
    "    y=y,\n",
    "    text=t\n",
    ")\n",
    "\n",
    "layout = dict(\n",
    "    autosize=False,\n",
    "    width=500,\n",
    "    height=500,\n",
    "    hovermode='closest'\n",
    ")\n",
    "\n",
    "fig = dict(data=[trace], layout=layout)\n",
    "\n",
    "py.iplot(fig, filename='parametric-curve')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Delimit parametric curve with condition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def condition(xi, yi):\n",
    "    return xi * yi >= 0  # or some condition in the complex plane\n",
    "\n",
    "def separate_traces_by_condition(condition, x, y):\n",
    "    data = []\n",
    "    state = condition(x[0], y[0])\n",
    "    trace = dict(x=[x[0]], y=[y[0]])\n",
    "    \n",
    "    for xi, yi in zip(x, y)[1:]:\n",
    "        state_at_i = condition(xi, yi)\n",
    "        if state is state_at_i:\n",
    "            trace['x'].append(xi)\n",
    "            trace['y'].append(yi)\n",
    "        else:\n",
    "            data.append(trace)\n",
    "            trace = dict(x=[], y=[])\n",
    "            state = state_at_i\n",
    "\n",
    "    data.append(trace)\n",
    "    return data\n",
    "           \n",
    "t = np.linspace(0, 2*np.pi, 1000)\n",
    "x, y = F(t)\n",
    "data = separate_traces_by_condition(condition, x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
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     "execution_count": 6,
     "metadata": {},
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   ],
   "source": [
    "len(data)  # 4 traces, each with a different color"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
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   "outputs": [
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      "text/html": [
       "<iframe id=\"igraph\" scrolling=\"no\" style=\"border:none;\"seamless=\"seamless\" src=\"https://plot.ly/~etpinard/3797.embed\" height=\"525\" width=\"100%\"></iframe>"
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    "layout = dict(\n",
    "    autosize=False,\n",
    "    width=500,\n",
    "    height=500,\n",
    "    hovermode='closest'\n",
    ")\n",
    "\n",
    "fig = dict(data=data, layout=layout)\n",
    "\n",
    "py.iplot(fig, filename='parametric-curve-2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot points with a colorscale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": [
    "t = np.linspace(0, 2*np.pi, 500)\n",
    "x, y = F(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<iframe id=\"igraph\" scrolling=\"no\" style=\"border:none;\"seamless=\"seamless\" src=\"https://plot.ly/~etpinard/3798.embed\" height=\"525\" width=\"100%\"></iframe>"
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   "source": [
    "trace = dict(\n",
    "    mode='markers',  # line plot can't have a colorscale\n",
    "    x=x,\n",
    "    y=y,\n",
    "    marker=dict(\n",
    "        color=t,\n",
    "        showscale=True\n",
    "            \n",
    "    )\n",
    ")\n",
    "\n",
    "layout = dict(\n",
    "    autosize=False,\n",
    "    width=500,\n",
    "    height=500,\n",
    "    hovermode='closest'\n",
    ")\n",
    "\n",
    "fig = dict(data=[trace], layout=layout)\n",
    "\n",
    "py.iplot(fig, validate=False, filename='parametric-curve-3')\n",
    "\n",
    "# N.B. please enter validate=False as\n",
    "# marker colorscale is not part of our validation system yet"
   ]
  },
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    "<div style=\"float:right; \\\">\n",
    "    <img src=\"http://i.imgur.com/4vwuxdJ.png\" \n",
    " align=right style=\"float:right; margin-left: 5px; margin-top: -10px\" />\n",
    "</div>\n",
    "\n",
    "<h4 style=\"margin-top:60px;\"> Got Questions or Feedback? </h4>\n",
    "\n",
    "About <a href=\"https://plot.ly\" target=\"_blank\">Plotly</a>\n",
    "\n",
    "* email: feedback@plot.ly \n",
    "* tweet: \n",
    "<a href=\"https://twitter.com/plotlygraphs\" target=\"_blank\">@plotlygraphs</a>\n",
    "\n",
    "<h4 style=\"margin-top:30px;\">Notebook styling ideas</h4>\n",
    "\n",
    "Big thanks to\n",
    "\n",
    "* <a href=\"http://nbviewer.ipython.org/github/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/blob/master/Prologue/Prologue.ipynb\" target=\"_blank\">Cam Davidson-Pilon</a>\n",
    "* <a href=\"http://lorenabarba.com/blog/announcing-aeropython/#.U1ULXdX1LJ4.google_plusone_share\" target=\"_blank\">Lorena A. Barba</a>\n",
    "\n",
    "<br>"
   ]
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