ansible/files/materials/6-Broadcasting (Solutions).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Broadcasting\n",
    "\n",
    "In these exercises, we'll practice using broadcasting to combine arrays of different dimensions.\n",
    "\n",
    "The exercises here will draw on all the lessons we've seen so far. In many ways, numpy's broadcasting system is the glue that makes all the other features of numpy work together in harmony."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "mpl.rc('figure', figsize=(12, 7))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bezier Curves\n",
    "\n",
    "A [Bezier Curve](https://en.wikipedia.org/wiki/B%C3%A9zier_curve) is way to define a two-dimensional curve in terms of a sequence of \"control points\". Intuitively, each control point \"pulls\" the path traced by the curve toward itself.\n",
    "\n",
    "Mathematically, a bezier curve defines a function $B(t)$ from the interval $[0, 1]$ to a two-dimensional point $p$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's an example of a fourth-order bezier curve. You can see that as t moves from 0 to 1, the control points exert different amounts of \"force\", pulling the final point closer toward themselves."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![images/bezier.gif](images/bezier.gif)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise: Linear Bezier Curve\n",
    "\n",
    "The simplest form of bezier curve is a \"first-order\" bezier curve with two control points $p_0$ and $p_1$. A first-order curve simply traces a line from $p_0$ to $p_1$.\n",
    "\n",
    "The formula for first-order bezier curve is:\n",
    "\n",
    "$B(t) = (1 - t)p_0 + tp_1$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implement a function that evaluates a Bezier curve at a single point. \n",
    "\n",
    "Your function should take the following arguments:\n",
    "\n",
    "- `p0`, a length-2 array containing (x, y) coordinates of the first control point.\n",
    "- `p1`, a length-2 array containing (x, y) coordinates of the second control point.\n",
    "- `t`, a scalar value between 0 and 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def evaluate_linear_bezier_curve(p0, p1, t):\n",
    "    return (1 - t) * p0 + t * p1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "p0 = np.array([0, 0])\n",
    "p1 = np.array([2, 1])\n",
    "\n",
    "halfway = evaluate_linear_bezier_curve(p0, p1, 0.5)\n",
    "three_quarters = evaluate_linear_bezier_curve(p0, p1, 0.75)\n",
    "\n",
    "np.testing.assert_almost_equal(halfway, [1.0, 0.5])\n",
    "np.testing.assert_almost_equal(three_quarters, [1.5, 0.75])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implement a function that computes an array of samples from a linear bezier curve. Your function should take the following arguments:\n",
    "\n",
    "- `p0`, a length-2 array containing (x, y) coordinates of the first control point.\n",
    "- `p1`, a length-2 array containing (x, y) coordinates of the second control point.\n",
    "- `ts`, a 1d array of unknown length containing sample values between 0 and 1.\n",
    "\n",
    "Your function should return a `len(t) x 2` array containing (x, y) coordinates of the requested samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_linear_bezier_curve(p0, p1):\n",
    "    ts = np.linspace(0, 1, 50)\n",
    "    samples = compute_linear_bezier_curve(p0, p1, ts)\n",
    "    X = samples[:, 0]\n",
    "    Y = samples[:, 1]\n",
    "    \n",
    "    plt.plot(X, Y)\n",
    "    plt.scatter([p0[0], p1[0]], [p0[1], p1[1]], color='red')\n",
    "\n",
    "def compute_linear_bezier_curve(p0, p1, ts):\n",
    "    ts = ts[:, np.newaxis]\n",
    "    return ts * p0 + (1 - ts) * p1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_linear_bezier_curve(np.array([1, 1]), np.array([2, 3]));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise: Quadratic Bezier Curve\n",
    "\n",
    "The next-simplest form of Bezier Curve is a second-order curve. A second-order Bezier Curve three control points, and can be implemented using the following formula:\n",
    "\n",
    "$b(t) = (1 - t)^2p_0 + 2(1 - t)tp_1 + t^2p_2$\n",
    "\n",
    "Implement a function with the same signature as above, but accept three control points, p0, p1, and p2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_quadratic_bezier_curve(p0, p1, p2):\n",
    "    ts = np.linspace(0, 1, 50)\n",
    "    samples = compute_quadratic_bezier_curve(p0, p1, p2, ts)\n",
    "    X = samples[:, 0]\n",
    "    Y = samples[:, 1]\n",
    "    plt.plot(X, Y)\n",
    "    \n",
    "    points = np.vstack([p0, p1, p2])\n",
    "    plt.scatter(points[:, 0], points[:, 1], color='red')\n",
    "    plt.plot(points[:, 0], points[:, 1], linestyle='--', color='red')\n",
    "    \n",
    "\n",
    "def compute_quadratic_bezier_curve(p0, p1, p2, ts):\n",
    "    ts = ts[:, np.newaxis]\n",
    "    \n",
    "    p0_term = (1 - ts) ** 2 * p0\n",
    "    p1_term = 2 * (1 - ts) * ts * p1\n",
    "    p2_term = (ts ** 2) * p2\n",
    "    \n",
    "    return p0_term + p1_term + p2_term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p0 = np.array([0, 0])\n",
    "p1 = np.array([1, 1])\n",
    "p2 = np.array([2, -2])\n",
    "draw_quadratic_bezier_curve(p0, p1, p2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise: Cubic Bezier Curve\n",
    "\n",
    "A cubic Bezier Curve has four control points, and has the following formula:\n",
    "\n",
    "$b(t) = (1 - t)^3p_0 + 3(1 - t)^2tp_1 + 3(1 - t)t^2p_2 + t^3p_3$\n",
    "\n",
    "Implement an evaluator for a cubic bezier curve following the same pattern as above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_cubic_bezier_curve(p0, p1, p2, p3):\n",
    "    ts = np.linspace(0, 1, 50)\n",
    "    samples = compute_cubic_bezier_curve(p0, p1, p2, p3, ts)\n",
    "    X = samples[:, 0]\n",
    "    Y = samples[:, 1]\n",
    "    plt.plot(X, Y)\n",
    "    \n",
    "    points = np.vstack([p0, p1, p2, p3])\n",
    "    plt.scatter(points[:, 0], points[:, 1], color='red')\n",
    "    plt.plot(points[:, 0], points[:, 1], linestyle='--', color='red')\n",
    "    \n",
    "\n",
    "def compute_cubic_bezier_curve(p0, p1, p2, p3, ts):\n",
    "    ts = ts[:, np.newaxis]\n",
    "    \n",
    "    p0_term = (1 - ts) ** 3 * p0\n",
    "    p1_term = 3 * (1 - ts) ** 2 * ts * p1\n",
    "    p2_term = 3 * (1 - ts) * (ts ** 2) * p2\n",
    "    p3_term = ts ** 3 * p3\n",
    "    \n",
    "    return p0_term + p1_term + p2_term + p3_term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p0 = np.array([0, 0])\n",
    "p1 = np.array([1, 1])\n",
    "p2 = np.array([2, -2])\n",
    "p3 = np.array([3, 3])\n",
    "draw_cubic_bezier_curve(p0, p1, p2, p3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise: Generalized Bezier Curve\n",
    "\n",
    "You may have started to notice a pattern in the coefficients of each control point's contribution to the curve. We're getting [Binomial Coefficients](https://en.wikipedia.org/wiki/Binomial_coefficient)!\n",
    "\n",
    "The general formual for a Bezier curve with $n$ control points is:\n",
    "\n",
    "$b(t) = \\sum_{i=0}^n \\binom{n}{i}(1 - t)^{n - i}t^ip_i$\n",
    "\n",
    "where $\\binom{n}{i}$ is the binomial coefficient of $n$ and $i$.\n",
    "\n",
    "Implement a function that computes samples from a generalized bezier curve. It should take a 2d array of (npoints x 2) and a 1d array of samples, and it should return a (len(t) x 2) array of evaluated samples. \n",
    "\n",
    "(**Hint:** You can use `scipy.special.comb` to evaluate binomial coefficients.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.special import comb\n",
    "\n",
    "def draw_bezier_curve(points):\n",
    "    ts = np.linspace(0, 1, 50)\n",
    "    samples = compute_bezier_curve(points, ts)\n",
    "    X = samples[:, 0]\n",
    "    Y = samples[:, 1]\n",
    "    plt.plot(X, Y)\n",
    "    \n",
    "    plt.scatter(points[:, 0], points[:, 1], color='red')\n",
    "    plt.plot(points[:, 0], points[:, 1], linestyle='--', color='red')\n",
    "    \n",
    "def compute_bezier_curve(points, t):\n",
    "    t = t[:, np.newaxis]\n",
    "    n = len(points) - 1\n",
    "    i = np.arange(len(points))\n",
    "    \n",
    "    # Compute binomial coefficients.\n",
    "    # Examples:\n",
    "    #   In [1]: comb(3, np.arange(4))\n",
    "    #   Out[1]: array([1., 3., 3., 1.])\n",
    "    #   In [2]: comb(4, np.arange(5))\n",
    "    #   Out[2]: array([1., 4., 6., 4., 1.])\n",
    "    #   In [3]: comb(5, np.arange(6))\n",
    "    #   Out[3]: array([ 1.,  5., 10., 10.,  5.,  1.])\n",
    "    binomials = comb(n, i)\n",
    "    \n",
    "    # Multiply by the interpolation weights at each time-step.\n",
    "    # This produces a (nsamples x npoints) array containing the coefficients\n",
    "    # by which to multiply each point at each time.\n",
    "    weights = binomials * (1 - t) ** (n - i) * t ** i\n",
    "    \n",
    "    # At each time-step, we want to multiply all the points by their weights, \n",
    "    # and then sum the contributions from each point. \n",
    "    # That's precisely what a matrix-multiply does!\n",
    "    return weights @ points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_bezier_curve(np.vstack([p0, p1, p2, p3, p3 - [1, 2]]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise: Estimate the Length of a Bezier Curve\n",
    "\n",
    "Write a function that estimates the length of a bezier curve by computing an array of sample points and summing the difference between each successive point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def estimate_curve_length(points, nsamples):\n",
    "    # Generate sample points using the previously-defined function.\n",
    "    samples = compute_bezier_curve(points, np.linspace(0, 1, nsamples))\n",
    "    \n",
    "    # Generate points representing the line segments between samples.\n",
    "    deltas = np.diff(samples, axis=0)\n",
    "    \n",
    "    # Calculate the length of each line segment.\n",
    "    lengths = np.sqrt((deltas ** 2).sum(axis=1))\n",
    "    \n",
    "    # Sum the lengths\n",
    "    return lengths.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.7823170663600765"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "estimate_curve_length([p0, p1, p2, p3, p3], 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.854101966249685\n",
      "4.964603420827521\n",
      "5.033940329994518\n",
      "5.07353336566527\n",
      "5.092520836611209\n",
      "5.104771190900166\n",
      "5.112373676140547\n"
     ]
    }
   ],
   "source": [
    "for i in range(3, 10):\n",
    "    print(estimate_curve_length([p0, p1, p2, p3], i))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}