{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "rldycB29g2kd" }, "source": [ "# Problem 2" ] }, { "cell_type": "markdown", "metadata": { "id": "XOffre1ag2ke" }, "source": [ "A photon moving at speed 1 in the x-y plane starts at time $t = 0$ at\n", "$(x, y) = (\\frac{1}{2}, \\frac{1}{10})$ heading due east. Around every integer lattice point\n", "$(i, j)$ in the plane, a circular mirror of radius $ \\frac{1}{3}$ has been erected. How\n", "far from $(0, 0)$ is the photon at $ t = 10 $ ?" ] }, { "cell_type": "markdown", "metadata": { "id": "H3VsMpbcg2ke" }, "source": [ "### Some geometry\n", "Let the position of the photon be $ P = (p_x, p_y) $ with velocity $ \\vec{v} = \\langle v_x, v_y \\rangle $, and suppose it is bouncing off a circle with center $ C = (c_x, c_y) $ with radius $r$.\n", "\n", "We first find the intersection point of the photon and the circle. Since we have that the ray can be represented parametrically as $ r(t) = \\langle p_x + v_x t, p_y + v_y t\\rangle$, we can solve for the time that the ray intersections the circle $t_{\\text{int}}$ as follows:\n", "\n", "$$ \\begin{align*}\n", "(x - c_x)^2 &+ (y - c_y) ^ 2 = r^2 \\\\\n", "&\\implies (p_x + v_x t - c_x)^2 + (p_y + v_y t - c_y) ^ 2 = r^2 \\\\\n", "&\\implies t^2 \\underbrace{(v_x^2 + v_y^2)}_{A} + t \\cdot \\underbrace{ 2 (p_x v_x + p_y v_y - c_x v_x - c_y v_y)}_{B} + \\underbrace{(c_x^2 + c_y^2 - 2 c_x p_x - 2 c_y p_y + p_x^2 + p_y^2 - r^2)}_{C} = 0 \\\\\n", "&\\implies t_{\\text{int}} = \\min\\left(\\frac{-B+(B^2-4AC)^{1/2}}{2A}, \\frac{-B-(B^2-4AC)^{1/2}}{2A}\\right)\n", "\\end{align*}\n", "$$\n", "\n", "Note: if this quadratic has 2 complex roots, then there are no intersection points\n", "\n", "We thus can get the intersection point of the ray and the circular mirror $p_{\\text{int}} = (p_x + v_x t_{\\text{int}}, p_y + v_y t_{\\text{int}}) $\n", "\n", "To get the velocity of the photon after reflection, let $\\overrightarrow{Cp_{\\text{int}}}$ be the vector from the center of the circle to the intersection point. Then, the initial velocity vector can be split up into a component parallel to $\\overrightarrow{Cp_{\\text{int}}}$ and a component perpendicular to $\\overrightarrow{Cp_{\\text{int}}}$ as follows:\n", "\n", "$ \\vec{v} = \\vec{v_{\\parallel}} + \\vec{v_{\\perp}}$\n", "\n", "$ \\vec{v_{\\parallel}} = proj_{\\overrightarrow{Cp_{int}}} \\vec{v} = \\frac{\\vec{v} \\cdot \\overrightarrow{Cp_{int}}}{|\\overrightarrow{Cp_{int}}|^2} \\overrightarrow{Cp_{int}} $\n", "\n", "The reflected vector is thus $ \\vec{v_{\\perp}} - \\vec{v_{\\parallel}} = \\vec{v} - 2 \\frac{\\vec{v} \\cdot \\overrightarrow{Cp_{int}}}{|\\overrightarrow{Cp_{int}}|^2} \\overrightarrow{Cp_{int}} $\n", "\n", "Let's code this (again, using `mpmath` for extended precision):" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "executionInfo": { "elapsed": 508, "status": "ok", "timestamp": 1602316663481, "user": { "displayName": "Husnain Raza", "photoUrl": "", "userId": "16146658556003895350" }, "user_tz": 300 }, "id": "hkHrhfrug2kf" }, "outputs": [], "source": [ "from mpmath import sqrt, mp, mpf\n", "class Vector(list):\n", " def __add__(self, other):\n", " return Vector([self[i]+other[i] for i in range(len(self))])\n", " def __sub__(self, other):\n", " return Vector([self[i]-other[i] for i in range(len(self))])\n", " def __mul__(self,other):\n", " return Vector([self[i]*other for i in range(len(self))])\n", " def __repr__(self):\n", " return f\"({','.join(map(str, self))})\"\n", " def dot(self, other):\n", " return sum([self[i]*other[i] for i in range(len(self))])\n", " def norm(self):\n", " return sqrt(self.dot(self))\n", "def reflect(P, v, C, r):\n", " px, py = P\n", " vx, vy = v\n", " cx, cy = C\n", " a = vx*vx + vy*vy\n", " b = 2*(px*vx+py*vy-cx*vx-cy*vy)\n", " c = cx*cx+cy*cy-2*cx*px-2*cy*py+px*px+py*py-r*r\n", " t1,t2 = (-b+sqrt(b*b-4*a*c))/(2*a), (-b-sqrt(b*b-4*a*c))/(2*a)\n", " potential_t = [t for t in (t1,t2) if t.imag == 0]\n", " if len(potential_t) == 0: return None # there is no intersection\n", " else: t_int = min(potential_t)\n", " p_int = (px+vx*t_int, py+vy*t_int)\n", " px, py = p_int\n", " ray = Vector([cx-px, cy-py]) # ray from center of circle to intersection point\n", " v = Vector(list(v))\n", " v_out = v - ray * (2*(v.dot(ray)/ray.dot(ray)))\n", " return (t_int, Vector(p_int), Vector(v_out))\n", "# Sanity check: \n", "# let P = (5,0), v = (-1,0), C = (0,0), r = 2\n", "assert reflect((5,0),(-1,0),(0,0),2) == (mpf(3), Vector([mpf(2),mpf(0)]), Vector([mpf(1),mpf(0)]))\n", "# Test the case when there is no intersection\n", "assert reflect((2,0),(0,-1),(0,0),1) == None" ] }, { "cell_type": "markdown", "metadata": { "id": "6zfRnokCg2ki" }, "source": [ "Now, once we get a new intersection point and new velocity, we need to find the next circular mirror that the photon will hit. We do this by stepping in the path of the ray until we get a hit. Our step size here will be 1/2 (i.e. each step, we travel a distance of 1/2)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "executionInfo": { "elapsed": 451, "status": "ok", "timestamp": 1602316671300, "user": { "displayName": "Husnain Raza", "photoUrl": "", "userId": "16146658556003895350" }, "user_tz": 300 }, "id": "FLT7tmJAg2kj" }, "outputs": [], "source": [ "from itertools import count\n", "def get_next_hit(time_remaining, P, v):\n", " unit_v = v * (1/sqrt(v.dot(v)))\n", " step_v = v * mpf(\"0.5\")\n", " for i in count(1):\n", " circle_center = list(map(round, P + step_v * i))\n", " reflection = reflect(P, v, circle_center, mpf(\"1/3\"))\n", " if reflection:\n", " t_elapsed, P_int, v_out = reflection\n", " if t_elapsed > 0: return (time_remaining-t_elapsed, P_int, v_out)\n", "def run(prec):\n", " mp.dps = prec\n", " time_remaining = mpf(\"10\")\n", " P = Vector([mpf(\"1/2\"),mpf(\"1/10\")])\n", " v = Vector([1,0])\n", " hits = [(time_remaining,P,v)]\n", " while time_remaining > 0:\n", " hits.append(get_next_hit(time_remaining, P, v))\n", " time_remaining,P,v = hits[-1]\n", " t_final, P_final, v_final = hits[-2]\n", " return (P_final + v_final*t_final).norm()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 12.6 ms, sys: 100 µs, total: 12.7 ms\n", "Wall time: 12.7 ms\n" ] }, { "data": { "text/plain": [ "mpf('0.9952629194433541608903118094267216210294669227341543498032088580729861796228306320991749819479625411445')" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%time run(100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we need about 20 digits of working precision to get an answer with a precision of $ 10^{-10} $" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 840 }, "executionInfo": { "elapsed": 1396, "status": "ok", "timestamp": 1602316675133, "user": { "displayName": "Husnain Raza", "photoUrl": "", "userId": "16146658556003895350" }, "user_tz": 300 }, "id": "pWiUAnq_g2kp", "outputId": "c16ca339-1ea3-4e13-b98b-37c9c4a01a15" }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "ANSWER = float(run(100))\n", "\n", "error = [abs(ANSWER - run(p)) for p in range(1, 30)]\n", "\n", "plt.title(\"Absolute Error vs. Precision used\")\n", "plt.xlabel(\"Precision used (digits)\")\n", "plt.ylabel(\"Error\")\n", "ax = plt.gca()\n", "ax.set_yscale('log')\n", "plt.scatter(range(1,30), error)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see from the plots below, it is very important for us to use high precision through the entire calculation process - otherwise the inaccuracies can compound rapidly." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 545 }, "executionInfo": { "elapsed": 617, "status": "ok", "timestamp": 1602316677764, "user": { "displayName": "Husnain Raza", "photoUrl": "", "userId": "16146658556003895350" }, "user_tz": 300 }, "id": "9Kl5KTb8g2ks", "outputId": "e233650f-e4cd-4615-b444-e956fe880418" }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "from matplotlib import cm\n", "# Generate the hits\n", "def plot(prec):\n", " mp.dps = prec\n", " t = mpf(\"10\")\n", " P = Vector([mpf(\"1/2\"),mpf(\"1/10\")])\n", " v = Vector([1,0])\n", " hits = [(t,P,v)]\n", " while t > 0:\n", " #print(t,P,v)\n", " hits.append(get_next_hit(t, P, v))\n", " t,P,v = hits[-1]\n", " hit_points = [i[1] for i in hits]\n", " fig, ax = plt.subplots()\n", " ax.set_aspect(\"equal\")\n", " centers = [(x,y) for x in [-1,0,1] for y in [-1,0,1]]\n", " for c in centers:\n", " circle = plt.Circle(c, 1./3, fill=False)\n", " ax.add_artist(circle)\n", " plt.plot([i[0] for i in hit_points],[i[1] for i in hit_points], c = \"black\")\n", " plt.scatter([i[0] for i in hit_points],[i[1] for i in hit_points], \n", " c = [cm.winter(i/len(hit_points)) for i in range(len(hit_points))], \n", " s = [30 if i not in [0, len(hit_points)-1] else 120 for i in range(len(hit_points))])\n", " plt.title(\"Running with \" + str(prec) + \" digits of precision\")\n", " plt.show()\n", "plot(2)\n", "plot(20)" ] } ], "metadata": { "colab": { "name": "Problem 2.ipynb", "provenance": [] }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.6" } }, "nbformat": 4, "nbformat_minor": 1 }