{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Black hole rendering with SageMath\n", "\n", "### Florentin Jaffredo" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction\n", "\n", "This notebook is a step-by-step implementation of a basic rendering engine in curved spacetime. The objective is to obtain a somewhat realistic image of an accretion disk around a black hole.\n", "\n", "The technique consists in launching lightlike geodesics toward the past from a single point (the virtual camera), using the [geodesic integrator](http://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/differentiable/integrated_curve.html) of SageMath. To reduce computation time, the spacetime is assumed be spherical symmetric; this reduces the number of required geodesics to produce an image of $n_x\\times n_y$ pixels from about $O\\left(n_x n_y\\right)$ to $O\\left(\\sqrt{n_x^2+n_y^2}\\right)$.\n", "\n", "This work relies heavily on the [SageManifolds Project](https://sagemanifolds.obspm.fr/). Advanced SageMath notions will also be used throughout this notebook, like Cython compilation and multithreading.\n", "\n", "This notebook requires a version of SageMath at least equal to 9.0:\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 10.5, Release Date: 2024-12-04'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "The code is separated into 9 parts.\n", "\n", "* Declaring the spacetime\n", "* Launching a geodesic\n", "* Launching a lot of geodesics!\n", "* Figuring out where it intersects with the accretion disk\n", "* Adding thickness to the disk\n", "* Using black-body radiation and converting spectra to RGB\n", "* First relativistic effect: Doppler effect\n", "* Second relativistic effect: aberration (forward focalisation)\n", "* Conclusion\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Configuration\n", "\n", "This notebook can be quite ressource hungry to run. For that reason different configurations options are provided. It is recommended to start with the lowest one to check that everything works properly. You can of course adapt the number of CPUs to your needs." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**First configuration:** will run in less than a minute on a 4-core laptop. Produces tiny images with no details (no secondary image)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# n_cpu = 4 # 4 Go Ram minimum\n", "# n_geod = 100\n", "# nx, ny = 180, 90" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Second configuration:** will run in about 5 minutes on a workstation, produces a reasonably sized image:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "n_cpu = 8 # 8 Go Ram minimum\n", "n_geod = 1000\n", "nx, ny = 720, 360" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Third configuration:** will run in 30 minutes on the Google Cloud Compute Engine. Produces a 4K image showing tiny details on the secondary disk images." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# n_cpu = 36 # 144 Go Ram minimum\n", "# n_geod = 30000\n", "# nx, ny = 4000, 2000" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Additional preliminaries: display objects with $ \\LaTeX $ where possible:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Declaring the spacetime\n", "\n", "Let's start slow by declaring the spacetime we'll use for rendering: it is the ***Schwarzschild spacetime***.\n", "\n", "It is important to use a coordinate system that is regular at the horizon. Here we use the *Eddington-Finkelstein coordinates*.\n", "\n", "Let $m$ be the mass of the black hole (that we'll take equal to 2 later). \n", "\n", "We also add a restriction to ensure that nothing touches the central singularity, and we set the metric $g$." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "M = Manifold(4, 'M', structure='Lorentzian')" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle t :\\ \\left( -\\infty, +\\infty \\right) ;\\quad r :\\ \\left( 1 , +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( -\\infty, +\\infty \\right)\\)" ], "text/latex": [ "$\\displaystyle t :\\ \\left( -\\infty, +\\infty \\right) ;\\quad r :\\ \\left( 1 , +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( -\\infty, +\\infty \\right)$" ], "text/plain": [ "t: (-oo, +oo); r: (1, +oo); th: (0, pi); ph: (-oo, +oo)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "C. = M.chart(r't r:(1,+oo) th:(0,pi):\\theta ph:\\phi')\n", "C.coord_range()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "m = var('m')" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\left(\\begin{array}{rrrr}\n", "\\frac{2 \\, m}{r} - 1 & \\frac{2 \\, m}{r} & 0 & 0 \\\\\n", "\\frac{2 \\, m}{r} & \\frac{2 \\, m}{r} + 1 & 0 & 0 \\\\\n", "0 & 0 & r^{2} & 0 \\\\\n", "0 & 0 & 0 & r^{2} \\sin\\left({\\theta}\\right)^{2}\n", "\\end{array}\\right)\\)" ], "text/latex": [ "$\\displaystyle \\left(\\begin{array}{rrrr}\n", "\\frac{2 \\, m}{r} - 1 & \\frac{2 \\, m}{r} & 0 & 0 \\\\\n", "\\frac{2 \\, m}{r} & \\frac{2 \\, m}{r} + 1 & 0 & 0 \\\\\n", "0 & 0 & r^{2} & 0 \\\\\n", "0 & 0 & 0 & r^{2} \\sin\\left({\\theta}\\right)^{2}\n", "\\end{array}\\right)$" ], "text/plain": [ "[ 2*m/r - 1 2*m/r 0 0]\n", "[ 2*m/r 2*m/r + 1 0 0]\n", "[ 0 0 r^2 0]\n", "[ 0 0 0 r^2*sin(th)^2]" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = M.metric()\n", "g[0,0] = -(1 - 2*m/r)\n", "g[0,1] = 2*m/r\n", "g[1,1] = 1 + 2*m/r\n", "g[2,2] = r^2\n", "g[3,3] = (r*sin(th))^2\n", "g[:]" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle g = \\left( \\frac{2 \\, m}{r} - 1 \\right) \\mathrm{d} t\\otimes \\mathrm{d} t + \\frac{2 \\, m}{r} \\mathrm{d} t\\otimes \\mathrm{d} r + \\frac{2 \\, m}{r} \\mathrm{d} r\\otimes \\mathrm{d} t + \\left( \\frac{2 \\, m}{r} + 1 \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + r^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + r^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\\)" ], "text/latex": [ "$\\displaystyle g = \\left( \\frac{2 \\, m}{r} - 1 \\right) \\mathrm{d} t\\otimes \\mathrm{d} t + \\frac{2 \\, m}{r} \\mathrm{d} t\\otimes \\mathrm{d} r + \\frac{2 \\, m}{r} \\mathrm{d} r\\otimes \\mathrm{d} t + \\left( \\frac{2 \\, m}{r} + 1 \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + r^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + r^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$" ], "text/plain": [ "g = (2*m/r - 1) dt⊗dt + 2*m/r dt⊗dr + 2*m/r dr⊗dt + (2*m/r + 1) dr⊗dr + r^2 dth⊗dth + r^2*sin(th)^2 dph⊗dph" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also define a 3-dimensional Euclidean space $E$ to plot some results, using a map $\\phi: M \\rightarrow E$:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\begin{array}{llcl} & M & \\longrightarrow & \\mathbb{E}^{3} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left(x, y, z\\right) = \\left(r \\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), r \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), r \\cos\\left({\\theta}\\right)\\right) \\end{array}\\)" ], "text/latex": [ "$\\displaystyle \\begin{array}{llcl} & M & \\longrightarrow & \\mathbb{E}^{3} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left(x, y, z\\right) = \\left(r \\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), r \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), r \\cos\\left({\\theta}\\right)\\right) \\end{array}$" ], "text/plain": [ "M → E^3\n", " (t, r, th, ph) ↦ (x, y, z) = (r*cos(ph)*sin(th), r*sin(ph)*sin(th), r*cos(th))" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E. = EuclideanSpace()\n", "phi = M.diff_map(E, [r*sin(th)*cos(ph), r*sin(th)*sin(ph), r*cos(th)])\n", "phi.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Launching a geodesic\n", "\n", "[Geodesic integration](http://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/differentiable/integrated_curve.html) was first implemented in SageMath in 2017 and perfected in 2018 to support fast integration and event handling (used to detect the singularity in our case).\n", "\n", "To introduce the method, let's plot an orbit around a black hole.\n", "\n", "To do that, we need to find a starting point $p$ as well as an inital velocity vector $v$. It can be quite troublesome to find a suitable one, but here is a free one:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "p = M((0, 14.98, pi/2, 0))\n", "Tp = M.tangent_space(p)\n", "v = Tp((2, 0, 0.005, 0.05))\n", "v = v / sqrt(-g.at(p)(v, v))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$v$ is defined as a member of the tangent space at $p$. The last line is used to normalize $v$ as a unit timelike vector." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next is the definition of the geodesic. We need to pass a symbolic variable for the proper time (which will not be used). The starting point is deduced from the velocity vector (as the point where the velocity vector is defined)." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "tau = var('tau')\n", "curve = M.integrated_geodesic(g, (tau, 0, 3000), v)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The integration should be very fast. Don't forget to give some numerical value to $m$ here." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "sol = curve.solve(step = 1, method=\"ode_int\", parameters_values={m: 2})\n", "# sol = curve.solve(step = 1, parameters_values={m: 2})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting the solution requires an interpolation. This is automatically done in the next line." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "interp = curve.interpolate()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following cell plots the result using the mapping we provided previously. We also add a grey sphere at $r_s = 2m = 4$ (the event horizon) to give a scale." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P = curve.plot_integrated(mapping=phi, color=\"red\", thickness=2, plot_points=3000)\n", "P += sage.plot.plot3d.shapes.Sphere(4, color='grey')\n", "P" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can see that it look nothing like an ellipse, as we are used to in classical celestial mechanics. At this step, you can try adding an angular momentum to the black hole--in other words going from Schwarzschild to Kerr--by setting a non-zero angular momentum in the definition of the manifold ($J=1$ works fine). When this is the case, the orbits are not even included in a plane. Don't forget to revert back your changes before proceeding to the next part." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Launching a lot of geodesics!\n", "\n", "Of course one geodesic is not enough for us, we'll need at least a few hundred of them.\n", "\n", "Because we don't need to compute the equation again each time, we simply copy the previous declaration of the geodesic while changing the initial point and velocity.\n", "\n", "It will be useful here to introduce the Python module `multiprocessing` and progress bars as widgets:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "import multiprocessing\n", "from ipywidgets import FloatProgress\n", "from IPython.display import display" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It wouldn't be a great idea to set \"1 job = 1 geodesic integration\". Indeed, that would mean copying the geodesic declaration a few hundred times, which would be quite slow. What is done instead is seperating geodesics into batches using the following function:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "def chunks(l, n):\n", " \"\"\"Yield successive n-sized chunks from l.\"\"\"\n", " for i in range(0, len(l), n):\n", " yield l[i:i + n]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The number of batches per CPU in not very important. If set to 1, some CPUs may run faster than other ones and stay idle at the end. If too high, too much time will be spent copying the curve setting. I found 3 to be a good value." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "n_batches_per_cpu = 3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also redefine the previous geodesic to our new needs: fewer steps and the ability to check for chart boundaries when integrating. The $v$ in this case will not be used; it will always be overwritten before starting any integration." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "curve = M.integrated_geodesic(g, (tau, 0, 200), v, across_charts=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When using `multiprocessing`, functions can only accept a single argument. To overcome this limitation, each argument will be a tuple (curve, start index, number of curves to integrate)." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "args = []\n", "start_index = 0\n", "\n", "for chunk in chunks(range(n_geod), n_geod//(n_batches_per_cpu*n_cpu)):\n", " args += [(loads(curve.dumps()), start_index, len(chunk))]\n", " start_index += len(chunk)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The next line prints the list of arguments. We can check that each of the 100 geodesics are correctly set. Our little trick allowed us to only define 13 geodesics (about 3 per core, as we wanted; note, the exact result here will depend on what you used for `n_cpu` at the beginning)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(Integrated geodesic in the 4-dimensional Lorentzian manifold M, 984, 16)\n", "25\n" ] } ], "source": [ "print(args[-1])\n", "print(len(args))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now comes a question: which vector can be used as the starting 4-velocity?\n", "\n", "We need a past-oriented lightlike vector pointing toward the center but with a linearly increasing angle. The 3 space components are already imposed. The time component must then be chosen so that the total vector is lightlike.\n", "\n", "Let $p$ be the initial point and $v$ the initial 4-velociy, with an unknown time coordinate $dt$ ($y$ depends on the angle, it is a known quantity)." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "dt, y, r0 = var('dt, y, r0')" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "p = M((0, r0, pi/2, 0))\n", "Tp = M.tangent_space(p)\n", "v = Tp((dt, -1, 0, y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The norm of $v$ is currently given by:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle r_{0}^{2} y^{2} + \\frac{\\mathit{dt}^{2} {\\left(2 \\, m - r_{0}\\right)}}{r_{0}} - \\frac{4 \\, \\mathit{dt} m}{r_{0}} + \\frac{2 \\, m + r_{0}}{r_{0}}\\)" ], "text/latex": [ "$\\displaystyle r_{0}^{2} y^{2} + \\frac{\\mathit{dt}^{2} {\\left(2 \\, m - r_{0}\\right)}}{r_{0}} - \\frac{4 \\, \\mathit{dt} m}{r_{0}} + \\frac{2 \\, m + r_{0}}{r_{0}}$" ], "text/plain": [ "r0^2*y^2 + dt^2*(2*m - r0)/r0 - 4*dt*m/r0 + (2*m + r0)/r0" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.at(p)(v, v)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We need to find $dt$ so that this expression is equal to 0 (lightlike condition). this is easy:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\left[\\mathit{dt} = -\\frac{\\sqrt{-{\\left(2 \\, m r_{0} - r_{0}^{2}\\right)} y^{2} + 1} r_{0} - 2 \\, m}{2 \\, m - r_{0}}, \\mathit{dt} = \\frac{\\sqrt{-{\\left(2 \\, m r_{0} - r_{0}^{2}\\right)} y^{2} + 1} r_{0} + 2 \\, m}{2 \\, m - r_{0}}\\right]\\)" ], "text/latex": [ "$\\displaystyle \\left[\\mathit{dt} = -\\frac{\\sqrt{-{\\left(2 \\, m r_{0} - r_{0}^{2}\\right)} y^{2} + 1} r_{0} - 2 \\, m}{2 \\, m - r_{0}}, \\mathit{dt} = \\frac{\\sqrt{-{\\left(2 \\, m r_{0} - r_{0}^{2}\\right)} y^{2} + 1} r_{0} + 2 \\, m}{2 \\, m - r_{0}}\\right]$" ], "text/plain": [ "[dt == -(sqrt(-(2*m*r0 - r0^2)*y^2 + 1)*r0 - 2*m)/(2*m - r0), dt == (sqrt(-(2*m*r0 - r0^2)*y^2 + 1)*r0 + 2*m)/(2*m - r0)]" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol = g.at(p)(v, v).solve(dt)\n", "sol" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, there are two solutions: one past-oriented and one future-oriented. In fact, in our case it does not matter, given that the Schwartzschild spacetime is static." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The next cell defines the function that will be called by `multiprocessing`. It starts by unpacking the arguments, setting an empty dictionary as the result, and defining the starting position.\n", "\n", "The initial velocity is then overwritten using the formula above, the integration is performed, and the result is added to the dictionary." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "def calc_some_geodesics(args):\n", " \"\"\"\n", " Compute nb geodesics starting at index n0\n", " \"\"\"\n", " curve, n0, nb = args\n", " res = {}\n", " r = 100\n", " posi = [0, r, pi/2, 0]\n", " p = M(posi)\n", " Tp = M.tangent_space(p)\n", " for i in range(n0, n0+nb):\n", " # starting vector\n", " dy = i*0.006/n_geod\n", " v = Tp([sol[0].rhs()(r0=r, y=dy, m=2).n(), -1, 0, dy])\n", " # overwrite the starting vector\n", " curve._initial_tangent_vector = v\n", " # integration with m=2\n", " curve.solve_across_charts(step=0.2, parameters_values={m:2})\n", " # copy and clear solution\n", " res[i] = (p.coord(), curve._solutions.copy())\n", " curve._solutions.clear()\n", " return res" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`geo` will keep the numerical solutions. I like to see `pool` as a hole in which I can throw some jobs. `multiprocessing` will then magically do them for me using every resource available on the computer." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "geo = {}\n", "\n", "# progress bar display\n", "%display plain\n", "f = FloatProgress(min=0, max=n_geod)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "c4cdaf2577fd4f1a8e0fe90a21f77484", "version_major": 2, "version_minor": 0 }, "text/plain": [ "FloatProgress(value=0.0, max=1000.0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(f)\n", "pool = multiprocessing.Pool(n_cpu)\n", "for i, some_res in enumerate(pool.imap_unordered(calc_some_geodesics, args)): # do and wait\n", " # progress bar update\n", " f.value += len(some_res)\n", " # update result\n", " geo.update(some_res)\n", "\n", "# clean exit\n", "pool.close()\n", "pool.join()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If, for any reason, you don't want to use parallel computing, you can replace the previous cell with this one:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```\n", "display(f)\n", "for arg in args:\n", " some_res = calc_some_geodesics(arg)\n", " f.value += len(some_res)\n", " geo.update(some_res)\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now try to visualize those geodesics.\n", "Next cell will plot 20 of them." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# add the sphere\n", "P = sage.plot.plot3d.shapes.Sphere(4, color='grey')\n", "\n", "# cycle through the solutions\n", "for i in range(0, n_geod, 5*n_geod/100): \n", " # set solution\n", " curve._solutions = geo[i][1]\n", " # do interpolation\n", " interp = curve.interpolate()\n", " # plot the curve\n", " P += curve.plot_integrated(mapping=phi, color=[\"red\"], thickness=2, plot_points=150, \n", " label_axes=False, across_charts=True)\n", "\n", "# show the result \n", "P" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that some fall inside the black hole toward the singularity. That's not an issue because the integration is automaticaly stopped when the geodesic leaves the chart domain defined in part 1." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Intersection with the accretion disk\n", "\n", "Time to transform those simulated light-rays into an image. To do this, we first need to compute the intersection between each geodesic and the accretion disk.\n", "\n", "For this example, the disk spans from $r=8$ to $r=50$, and is tilted by an angle $\\alpha = - \\frac{\\pi}{20}$." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "disk_min = 12\n", "disk_max = 50\n", "alpha = -pi/20" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's plot the disk on top of the last figure.\n", "\n", "(We cheat a little bit here and use a flattened torus.)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "D = sage.plot.plot3d.shapes.Torus((disk_min+disk_max)/2,\n", " (disk_min-disk_max)/2).scale(1,1,0.01).rotateY(-pi/20)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P + D" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The same but tilted on the X-axis by an angle $\\beta=\\frac{\\pi}{3}$. As explained earlier, the final image will be obtained by computing for each pixel : \n", "\n", "* Which geodesic best describes the light-ray\n", "* Which angle $\\beta$ at which the disk should be tilted\n", "* The intersection between the disk and that geodesic\n" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P + D.rotateX(pi/3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The geodesics are formatted in a strange way because of the solver used. The next line makes it easier to use. `geo` is now a list of list of coordinates (and not a dictionary of strange things)." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "geo = [list(geo[i][1].values())[0][0][1].tolist() for i in range(len(geo))]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To detect the intersection between the disk and a geodesic, the only solution is to parse the list of successive coordinates. This is done in the following function.\n", "\n", "For each point of the curve, two rotations are performed (manually for speed purposes) before checking the point coordinates." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "def intersection(curve, alpha, beta):\n", " \"\"\"\n", " Return True if the curve intersect the disk comprised between dmin and dmax\n", " tilted of angles alpha and beta\n", " \"\"\"\n", " n = len(curve)\n", " r, theta, phi = curve[0][2:5]\n", " x, y, z = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta)\n", " x, y, z = x, y*cos(beta)-z*sin(beta), z*cos(beta)+y*sin(beta)\n", " z = z*cos(alpha)+x*sin(alpha)\n", " for i in range(1, n):\n", " # done in 3 lines for speed consideration\n", " r = curve[i][2]\n", " theta = curve[i][3]\n", " phi = curve[i][4]\n", " # conversion to cartesian:\n", " x2, y2, z2 = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta) \n", " # rotation around the X-axis:\n", " y2, z2 = y2*cos(beta)-z2*sin(beta), z2*cos(beta)+y2*sin(beta) \n", " # rotation around the Y-axis:\n", " x2, z2 = x2*cos(alpha)-z2*sin(alpha), z2*cos(alpha)+x2*sin(alpha) \n", " if z!=z2: # needed to prevent a division by zero next line\n", " t = z/(z-z2) # if 0<=t<1 then the curve intersect the disk between the points i and i-1\n", " if t>=0 and t<1 and curve[i][2]>disk_min and curve[i][2]=0 and t<1 and curve[i][2]>dmin and curve[i][2]>> from scipy.misc import bytescale\n", " >>> img = np.array([[ 91.06794177, 3.39058326, 84.4221549 ],\n", " ... [ 73.88003259, 80.91433048, 4.88878881],\n", " ... [ 51.53875334, 34.45808177, 27.5873488 ]])\n", " >>> bytescale(img)\n", " array([[255, 0, 236],\n", " [205, 225, 4],\n", " [140, 90, 70]], dtype=uint8)\n", " >>> bytescale(img, high=200, low=100)\n", " array([[200, 100, 192],\n", " [180, 188, 102],\n", " [155, 135, 128]], dtype=uint8)\n", " >>> bytescale(img, cmin=0, cmax=255)\n", " array([[91, 3, 84],\n", " [74, 81, 5],\n", " [52, 34, 28]], dtype=uint8)\n", " \"\"\"\n", " if data.dtype == np.uint8:\n", " return data\n", "\n", " if high > 255:\n", " raise ValueError(\"`high` should be less than or equal to 255.\")\n", " if low < 0:\n", " raise ValueError(\"`low` should be greater than or equal to 0.\")\n", " if high < low:\n", " raise ValueError(\"`high` should be greater than or equal to `low`.\")\n", "\n", " if cmin is None:\n", " cmin = data.min()\n", " if cmax is None:\n", " cmax = data.max()\n", "\n", " cscale = cmax - cmin\n", " if cscale < 0:\n", " raise ValueError(\"`cmax` should be larger than `cmin`.\")\n", " elif cscale == 0:\n", " cscale = 1\n", "\n", " scale = float(high - low) / cscale\n", " bytedata = (data - cmin) * scale + low\n", " return (bytedata.clip(low, high) + 0.5).astype(np.uint8)\n", "\n", "def toimage(arr, high=255, low=0, cmin=None, cmax=None, pal=None,\n", " mode=None, channel_axis=None):\n", " \"\"\"Takes a numpy array and returns a PIL image.\n", " This function is only available if Python Imaging Library (PIL) is installed.\n", " The mode of the PIL image depends on the array shape and the `pal` and\n", " `mode` keywords.\n", " For 2-D arrays, if `pal` is a valid (N,3) byte-array giving the RGB values\n", " (from 0 to 255) then ``mode='P'``, otherwise ``mode='L'``, unless mode\n", " is given as 'F' or 'I' in which case a float and/or integer array is made.\n", " .. warning::\n", " This function uses `bytescale` under the hood to rescale images to use\n", " the full (0, 255) range if ``mode`` is one of ``None, 'L', 'P', 'l'``.\n", " It will also cast data for 2-D images to ``uint32`` for ``mode=None``\n", " (which is the default).\n", " Notes\n", " -----\n", " For 3-D arrays, the `channel_axis` argument tells which dimension of the\n", " array holds the channel data.\n", " For 3-D arrays if one of the dimensions is 3, the mode is 'RGB'\n", " by default or 'YCbCr' if selected.\n", " The numpy array must be either 2 dimensional or 3 dimensional.\n", " \"\"\"\n", " data = np.asarray(arr)\n", " if np.iscomplexobj(data):\n", " raise ValueError(\"Cannot convert a complex-valued array.\")\n", " shape = list(data.shape)\n", " valid = len(shape) == 2 or ((len(shape) == 3) and\n", " ((3 in shape) or (4 in shape)))\n", " if not valid:\n", " raise ValueError(\"'arr' does not have a suitable array shape for \"\n", " \"any mode.\")\n", " if len(shape) == 2:\n", " shape = (shape[1], shape[0]) # columns show up first\n", " if mode == 'F':\n", " data32 = data.astype(np.float32)\n", " image = Image.frombytes(mode, shape, data32.tobytes())\n", " return image\n", " if mode in [None, 'L', 'P']:\n", " bytedata = bytescale(data, high=high, low=low,\n", " cmin=cmin, cmax=cmax)\n", " image = Image.frombytes('L', shape, bytedata.tobytes())\n", " if pal is not None:\n", " image.putpalette(np.asarray(pal, dtype=np.uint8).tobytes())\n", " # Becomes a mode='P' automagically.\n", " elif mode == 'P': # default gray-scale\n", " pal = (np.arange(0, 256, 1, dtype=np.uint8)[:, np.newaxis] *\n", " np.ones((3,), dtype=np.uint8)[np.newaxis, :])\n", " image.putpalette(np.asarray(pal, dtype=np.uint8).tobytes())\n", " return image\n", " if mode == '1': # high input gives threshold for 1\n", " bytedata = (data > high)\n", " image = Image.frombytes('1', shape, bytedata.tobytes())\n", " return image\n", " if cmin is None:\n", " cmin = np.amin(np.ravel(data))\n", " if cmax is None:\n", " cmax = np.amax(np.ravel(data))\n", " data = (data*1.0 - cmin)*(high - low)/(cmax - cmin) + low\n", " if mode == 'I':\n", " data32 = data.astype(np.uint32)\n", " image = Image.frombytes(mode, shape, data32.tobytes())\n", " else:\n", " raise ValueError(_errstr)\n", " return image\n", "\n", " # if here then 3-d array with a 3 or a 4 in the shape length.\n", " # Check for 3 in datacube shape --- 'RGB' or 'YCbCr'\n", " if channel_axis is None:\n", " if (3 in shape):\n", " ca = np.flatnonzero(np.asarray(shape) == 3)[0]\n", " else:\n", " ca = np.flatnonzero(np.asarray(shape) == 4)\n", " if len(ca):\n", " ca = ca[0]\n", " else:\n", " raise ValueError(\"Could not find channel dimension.\")\n", " else:\n", " ca = channel_axis\n", "\n", " numch = shape[ca]\n", " if numch not in [3, 4]:\n", " raise ValueError(\"Channel axis dimension is not valid.\")\n", "\n", " bytedata = bytescale(data, high=high, low=low, cmin=cmin, cmax=cmax)\n", " if ca == 2:\n", " strdata = bytedata.tobytes()\n", " shape = (shape[1], shape[0])\n", " elif ca == 1:\n", " strdata = np.transpose(bytedata, (0, 2, 1)).tobytes()\n", " shape = (shape[2], shape[0])\n", " elif ca == 0:\n", " strdata = np.transpose(bytedata, (1, 2, 0)).tobytes()\n", " shape = (shape[2], shape[1])\n", " if mode is None:\n", " if numch == 3:\n", " mode = 'RGB'\n", " else:\n", " mode = 'RGBA'\n", "\n", " if mode not in ['RGB', 'RGBA', 'YCbCr', 'CMYK']:\n", " raise ValueError(_errstr)\n", "\n", " if mode in ['RGB', 'YCbCr']:\n", " if numch != 3:\n", " raise ValueError(\"Invalid array shape for mode.\")\n", " if mode in ['RGBA', 'CMYK']:\n", " if numch != 4:\n", " raise ValueError(\"Invalid array shape for mode.\")\n", "\n", " # Here we know data and mode is correct\n", " image = Image.frombytes(mode, shape, strdata)\n", " return image" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With the above definition of `toimage`, we get the actual image from `data`:" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "image/jpeg": 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", "text/plain": [ "" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "img1 = toimage(data)\n", "img1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you have seen the movie *Interstellar*, you will know that this looks a bit like a (monochrome) black hole, a very simple one for sure, but we'll improve it step by step in the following sections." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Adding thickness to the disk\n", "\n", "First we will be adding transpareny and thickness to the disk. For that, let's assume the disk is optically thin. This means light can only be added and never obstructed. What's more, the intensity will be proportional to the total length of emissive medium traversed.\n", "\n", "This length depends on 2 factors: the profile of the disk and the angle $\\theta$ between the disk and the light ray:\n", "\n", "$\\qquad d = \\frac{f(r)}{sin(\\theta)}$\n", "\n", "The computation of the angle $\\theta$ is not trival. The fastest way to obtain it is the perform a change of frame, which will locally (at a single point) give us a Minkowsky metric (orthonormal frame), in which angles are easy to compute.\n", "\n", "To remind you, here is our metric:" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\left(\\begin{array}{rrrr}\n", "\\frac{2 \\, m}{r} - 1 & \\frac{2 \\, m}{r} & 0 & 0 \\\\\n", "\\frac{2 \\, m}{r} & \\frac{2 \\, m}{r} + 1 & 0 & 0 \\\\\n", "0 & 0 & r^{2} & 0 \\\\\n", "0 & 0 & 0 & r^{2} \\sin\\left({\\theta}\\right)^{2}\n", "\\end{array}\\right)\\)" ], "text/latex": [ "$\\displaystyle \\left(\\begin{array}{rrrr}\n", "\\frac{2 \\, m}{r} - 1 & \\frac{2 \\, m}{r} & 0 & 0 \\\\\n", "\\frac{2 \\, m}{r} & \\frac{2 \\, m}{r} + 1 & 0 & 0 \\\\\n", "0 & 0 & r^{2} & 0 \\\\\n", "0 & 0 & 0 & r^{2} \\sin\\left({\\theta}\\right)^{2}\n", "\\end{array}\\right)$" ], "text/plain": [ "[ 2*m/r - 1 2*m/r 0 0]\n", "[ 2*m/r 2*m/r + 1 0 0]\n", "[ 0 0 r^2 0]\n", "[ 0 0 0 r^2*sin(th)^2]" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%display latex\n", "g[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or for a point of the disk:" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\left(\\begin{array}{rrrr}\n", "\\frac{2 \\, m - r_{0}}{r_{0}} & \\frac{2 \\, m}{r_{0}} & 0 & 0 \\\\\n", "\\frac{2 \\, m}{r_{0}} & \\frac{2 \\, m + r_{0}}{r_{0}} & 0 & 0 \\\\\n", "0 & 0 & r_{0}^{2} & 0 \\\\\n", "0 & 0 & 0 & r_{0}^{2}\n", "\\end{array}\\right)\\)" ], "text/latex": [ "$\\displaystyle \\left(\\begin{array}{rrrr}\n", "\\frac{2 \\, m - r_{0}}{r_{0}} & \\frac{2 \\, m}{r_{0}} & 0 & 0 \\\\\n", "\\frac{2 \\, m}{r_{0}} & \\frac{2 \\, m + r_{0}}{r_{0}} & 0 & 0 \\\\\n", "0 & 0 & r_{0}^{2} & 0 \\\\\n", "0 & 0 & 0 & r_{0}^{2}\n", "\\end{array}\\right)$" ], "text/plain": [ "[(2*m - r_0)/r_0 2*m/r_0 0 0]\n", "[ 2*m/r_0 (2*m + r_0)/r_0 0 0]\n", "[ 0 0 r_0^2 0]\n", "[ 0 0 0 r_0^2]" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r0, phi = var('r_0, phi')\n", "p = M((0, r0, pi/2, phi))\n", "g.at(p)[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are not that far off. Some rescaling and mixing the first two lines should do the trick." ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [], "source": [ "# default frame\n", "fr = C.frame()\n", "\n", "# create an automorphism field\n", "aut = M.automorphism_field()\n", "\n", "# some symbolic variables\n", "a, b, c = var('a, b, c')\n", "\n", "# let's try with the simplest matrix possible\n", "aut.add_comp()[:] = [[a, 0, 0, 0], [b, c, 0, 0], [0, 0, 1/r0, 0], \n", " [0, 0, 0, 1/r0]] # only b is off-diagonal\n", "fr2 = fr.new_frame(aut, 'f2')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this new frame, the metric at $p$ looks like this:" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\left(\\begin{array}{rrrr}\n", "\\frac{b^{2} {\\left(2 \\, m + r_{0}\\right)}}{r_{0}} + \\frac{a^{2} {\\left(2 \\, m - r_{0}\\right)}}{r_{0}} + \\frac{4 \\, a b m}{r_{0}} & \\frac{b c {\\left(2 \\, m + r_{0}\\right)}}{r_{0}} + \\frac{2 \\, a c m}{r_{0}} & 0 & 0 \\\\\n", "\\frac{b c {\\left(2 \\, m + r_{0}\\right)}}{r_{0}} + \\frac{2 \\, a c m}{r_{0}} & \\frac{c^{2} {\\left(2 \\, m + r_{0}\\right)}}{r_{0}} & 0 & 0 \\\\\n", "0 & 0 & 1 & 0 \\\\\n", "0 & 0 & 0 & 1\n", "\\end{array}\\right)\\)" ], "text/latex": [ "$\\displaystyle \\left(\\begin{array}{rrrr}\n", "\\frac{b^{2} {\\left(2 \\, m + r_{0}\\right)}}{r_{0}} + \\frac{a^{2} {\\left(2 \\, m - r_{0}\\right)}}{r_{0}} + \\frac{4 \\, a b m}{r_{0}} & \\frac{b c {\\left(2 \\, m + r_{0}\\right)}}{r_{0}} + \\frac{2 \\, a c m}{r_{0}} & 0 & 0 \\\\\n", "\\frac{b c {\\left(2 \\, m + r_{0}\\right)}}{r_{0}} + \\frac{2 \\, a c m}{r_{0}} & \\frac{c^{2} {\\left(2 \\, m + r_{0}\\right)}}{r_{0}} & 0 & 0 \\\\\n", "0 & 0 & 1 & 0 \\\\\n", "0 & 0 & 0 & 1\n", "\\end{array}\\right)$" ], "text/plain": [ "[b^2*(2*m + r_0)/r_0 + a^2*(2*m - r_0)/r_0 + 4*a*b*m/r_0 b*c*(2*m + r_0)/r_0 + 2*a*c*m/r_0 0 0]\n", "[ b*c*(2*m + r_0)/r_0 + 2*a*c*m/r_0 c^2*(2*m + r_0)/r_0 0 0]\n", "[ 0 0 1 0]\n", "[ 0 0 0 1]" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.at(p)[fr2.at(p), :]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This lets us find the values of $ a $, $ b $ and $ c $:" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [], "source": [ "c = sqrt(r/(r+2*m))\n", "a = sqrt(((r+2*m)/(r)))\n", "b = -2*a*m/(2*m+r)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's check:" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [], "source": [ "aut2 = M.automorphism_field() # new automorphism field\n", "aut2.add_comp()[:] = [[a, 0, 0, 0], [b, c, 0, 0], [0, 0, 1/r, 0], [0, 0, 0, 1/(r*sin(th))]]\n", "fr3 = fr.new_frame(aut2, 'f3')" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\left(\\begin{array}{rrrr}\n", "-1 & 0 & 0 & 0 \\\\\n", "0 & 1 & 0 & 0 \\\\\n", "0 & 0 & 1 & 0 \\\\\n", "0 & 0 & 0 & 1\n", "\\end{array}\\right)\\)" ], "text/latex": [ "$\\displaystyle \\left(\\begin{array}{rrrr}\n", "-1 & 0 & 0 & 0 \\\\\n", "0 & 1 & 0 & 0 \\\\\n", "0 & 0 & 1 & 0 \\\\\n", "0 & 0 & 0 & 1\n", "\\end{array}\\right)$" ], "text/plain": [ "[-1 0 0 0]\n", "[ 0 1 0 0]\n", "[ 0 0 1 0]\n", "[ 0 0 0 1]" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[fr3, :]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Success!\n", "\n", "We now have an orthonormal frame everywhere (this is only possible because this frame doesn't correspond to a system of coordinates; otherwise the spacetime would be flat).\n", "\n", "Don't forget that vectors are contravariant tensors, so the components of the 4-velocity will be transformed by this matrix:" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\left(\\begin{array}{rrrr}\n", "\\frac{\\sqrt{r}}{\\sqrt{2 \\, m + r}} & 0 & 0 & 0 \\\\\n", "\\frac{2 \\, m}{\\sqrt{2 \\, m + r} \\sqrt{r}} & \\frac{\\sqrt{2 \\, m + r}}{\\sqrt{r}} & 0 & 0 \\\\\n", "0 & 0 & r & 0 \\\\\n", "0 & 0 & 0 & r \\sin\\left({\\theta}\\right)\n", "\\end{array}\\right)\\)" ], "text/latex": [ "$\\displaystyle \\left(\\begin{array}{rrrr}\n", "\\frac{\\sqrt{r}}{\\sqrt{2 \\, m + r}} & 0 & 0 & 0 \\\\\n", "\\frac{2 \\, m}{\\sqrt{2 \\, m + r} \\sqrt{r}} & \\frac{\\sqrt{2 \\, m + r}}{\\sqrt{r}} & 0 & 0 \\\\\n", "0 & 0 & r & 0 \\\\\n", "0 & 0 & 0 & r \\sin\\left({\\theta}\\right)\n", "\\end{array}\\right)$" ], "text/plain": [ "[ sqrt(r)/sqrt(2*m + r) 0 0 0]\n", "[2*m/(sqrt(2*m + r)*sqrt(r)) sqrt(2*m + r)/sqrt(r) 0 0]\n", "[ 0 0 r 0]\n", "[ 0 0 0 r*sin(th)]" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "aut2.inverse()[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The angle $\\theta$ can now be computed using: \n", "$$\\theta = \\arctan\\left(\\frac{\\overrightarrow{v}_{\\bot}}{\\overrightarrow{v}_{\\parallel}}\\right)$$ \n", "Because this formula is using 3-vectors, it was indeed important to have been in an orthonormal frame.\n", "\n", "We also need to perform rotation of the angles $\\alpha$ and $\\beta$ for the 4-velocity. In the next cell is a Cython version optimized for speed." ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [], "source": [ "%%cython\n", "from libc.math cimport cos, sin, sqrt\n", "\n", "cpdef tuple spherical_to_xyz(float dr, float dtheta, float dphi, float r, \n", " float theta, float phi, float alpha, float beta):\n", " \"\"\"\n", " Convert spherical coordinates to cartesian and apply the \n", " two rotations at the same time.\n", " \"\"\"\n", " cdef float dx, dy, dz\n", " cdef float ca, cb, ct, cp\n", " cdef float sa, sb, st, sp\n", " \n", " ca = cos(alpha); sa = sin(alpha)\n", " cb = cos(beta); sb = sin(beta)\n", " ct = cos(theta); st = sin(theta)\n", " cp = cos(phi); sp = sin(phi)\n", " \n", " dx = ((-cb*ct*sa - (sa*sb*sp - ca*cp)*st)*dr + \n", " (r*cb*sa*st - (sa*sb*sp - ca*cp)*r*ct)*dtheta +\n", " (-(cp*sa*sb + ca*sp)*r*st)*dphi)\n", " \n", " dy = ((cb*sp*st - sb*ct)*dr +\n", " (r*ct*cb*sp + r*sb*st)*dtheta +\n", " (r*cp*cb*st)*dphi)\n", " \n", " dz = ((ca*cb*ct + (ca*sb*sp + cp*sa)*st)*dr +\n", " (-r*ca*cb*st+(ca*sb*sp + cp*sa)*r*ct)*dtheta +\n", " ((ca*cp*sb - sa*sp)*r*st)*dphi)\n", " \n", " return (dx, dy, dz)\n", "\n", "\n", "cpdef tuple xyz_to_spherical(float dx, float dy, float dz, float x, \n", " float y, float z):\n", " \"\"\"\n", " Convert cartesian back to spherical\n", " \"\"\"\n", " cdef r, dr, dth, dph\n", " r = sqrt(x**2+y**2+z**2)\n", " dr = (x*dx+y*dy*z*dz)/r\n", " dth = ((x*z*dx+y*z*dy)/r**2/sqrt(x**2+y**2)-sqrt(x**2+y**2)*dz)/r**2\n", " dph = -y/(x**2+y**2)*dx+x/(x**2+y**2)*dy\n", " return (dr, dth, dph)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These formulas were obtained automatically by creating another chart and asking for the change of frames. Example:" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ -cos(beta)*cos(theta)*sin(alpha) - (sin(alpha)*sin(beta)*sin(phi) - cos(alpha)*cos(phi))*sin(theta) r*cos(beta)*sin(alpha)*sin(theta) - (sin(alpha)*sin(beta)*sin(phi) - cos(alpha)*cos(phi))*r*cos(theta) -(cos(phi)*sin(alpha)*sin(beta) + cos(alpha)*sin(phi))*r*sin(theta)]\n", "[ cos(beta)*sin(phi)*sin(theta) - cos(theta)*sin(beta) r*cos(beta)*cos(theta)*sin(phi) + r*sin(beta)*sin(theta) r*cos(beta)*cos(phi)*sin(theta)]\n", "[ cos(alpha)*cos(beta)*cos(theta) + (cos(alpha)*sin(beta)*sin(phi) + cos(phi)*sin(alpha))*sin(theta) -r*cos(alpha)*cos(beta)*sin(theta) + (cos(alpha)*sin(beta)*sin(phi) + cos(phi)*sin(alpha))*r*cos(theta) (cos(alpha)*cos(phi)*sin(beta) - sin(alpha)*sin(phi))*r*sin(theta)]\n" ] } ], "source": [ "def print_formulas(): # enclosed in a function to prevent altering the namespace\n", " alpha, beta = var('alpha, beta')\n", " spher. = E.chart()\n", " x, y, z = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta) # normal Spherical->Cartesian transformation\n", " y, z = y*cos(beta)-z*sin(beta), z*cos(beta)+y*sin(beta) # first rotation\n", " x, z = x*cos(alpha)-z*sin(alpha), z*cos(alpha)+x*sin(alpha) # second rotation\n", " spher.transition_map(E.default_chart(), [x, y, z])\n", " print(list(E.changes_of_frame().values())[0][spher.frame(),:, spher])\n", "\n", "print_formulas()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The thickness of the disk will follow this profile, obtained from my high level understanding of black holes mechanics (i.e. it's mostly random, but looks nice)" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [], "source": [ "%%cython\n", "from libc.math cimport exp, erf\n", "\n", "cpdef float profile(float x, float disk_min, float disk_max):\n", " cdef float y \n", " # we really don't want negative values\n", " if xdisk_max:\n", " return 0\n", " y = (exp(-(disk_min-20-x)**2/400)*(x-disk_min)**2*(disk_max-x)**2/10000 +\n", " exp(-(32-x)**2/70)/2*(x-disk_min)**2*(disk_max-x)**2/150000)\n", " return max(y, 0)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "image/png": 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jhu00saVJEyk314zOXXqp9OGHthMBQPRVaFKEz+cr82fHcY567LD169fr7rvv1mOPPaa8vDx9+OGH2rx5s0aNGlXu+ycmJiopKanMDYglM2eanQ5uv912kth0xhnmlOull0r9+pmFiAEgliWE8+T69euratWqR43G7dix46hRu8MyMzPVs2dPPfjgg5Kk9u3bq1atWurVq5f+8Ic/qHHjxhWMDnjXK69IV1whcTVB9NSsKc2ebRYivvFG6d13pf79bacCgOgIa4SuevXqSk1NVU5OTpnHc3Jy1KNHj2O+Zu/evapSpeynqVq1qiQzsgfEm1WrzKK4v/617SSxLyFBevNNacAAsxPH3/9uOxEAREfYp1zHjBmjV155RVOnTtWGDRt03333aevWraWnUMeOHauMjIzS5/fr10+zZs3SlClTtGnTJn3++ee6++67dcEFF6hJkyaR+0oAj3jlFalRI7OYMKIvIUGaMUO6+mrpV78yixEDQKwJ65SrJA0aNEi7du3SuHHjtH37drVr107z5s1TixYtJEnbt28vsybd8OHDVVRUpEmTJun+++9XnTp1dOmll+qPf/xj5L4KwCP27ZPeeksaNcosiovKUa2a9Pbb0vXXm9OuH38s9expOxUARE7Y69DZEAqF5Pf7WYcOnjdzpjRkiFmD7txzbaeJP8XF0i9/Ka1dK33xhdSqle1EABAZ7OUKVKLp06Xu3SlztiQmmokSDRpIfftK//637UQAEBkUOqCS/PvfZk20oUNtJ4lvZ5whzZtn1gK85hpzGhwAvI5CB1SSv/xF8vmkgQNtJ0HLltLf/mZmHN98s1RSYjsRAJwaCh1QSaZPN9dvNWhgOwkkKS3NXNM4a5b0f8tkAoBnUeiASvCvf5mL8Dnd6i79+0vPPSc9+6z0wgu20wBAxYW9bAmA8M2YIdWqZa7Zgrv85jfSl19K99wjdelibgDgNSxbAkSZ45iN4i+4QJo2zXYaHEtxsdSrl5m4snKlmTgBAF7CKVcgytauNSNAN95oOwnKk5hoJq0Eg9Lw4aaEA4CXUOiAKJszRzr9dOmyy2wnwfGcdZYZQZ07Vxo/3nYaAAgPhQ6IsjlzpCuvNKNAcLerr5Z++1vp4Yelzz+3nQYATp6rC11WVpZSUlKUlpZmOwpQIVu2mGuyBgywnQQn68knpR49pEGD2EkCgHcwKQKIookTpQcekHbulPjW9Y5t26SOHaVLLpHeecd2GgA4MVeP0AFeN2eOuXaOMuctTZtKWVnSu+9S6AB4A4UOiJJdu6TcXE63etUNN0jXXSeNHs2pVwDuR6EDouRvfzN7hPbvbzsJKsLnM6N0JSVm8WEAcDMKHRAlc+ZI3bpJjRrZToKKSk6Wnn9eys6W3nvPdhoAKB+FDoiCvXul+fM53RoLbrzR/H+8804zuQUA3IhCB0TBggXSvn3StdfaToJT5fNJU6ZIBw6Y/V4BwI0odEAUzJkjpaRIrVrZToJIaNTInHqdMcP8vwUAt6HQARF28KD0/vucbo01Q4ZI11wj3XGHFArZTgMAZVHogAj77DPpP//hdGusOTzrNRSSfv9722kAoCwKHRBhc+eahWlTU20nQaSdeab0P/8jPfectG6d7TQA8F8UOiDCFiyQrrjCjOgg9owZI7VsKd19t+T+jRMBxAsKHRBBBQXS+vXSL39pOwmiJTHR7NH7ySdmazAAcAMKHRBBOTlmZO6yy2wnQTT17WsmSNx/v7Rnj+00AEChAyJq/nwpLU2qW9d2EkTbn/8sff+9uQcA2yh0QIQcOiR99BGnW+PF2Web3SOeeYYdJADY5+pCl5WVpZSUFKWlpdmOApzQypVmuZL0dNtJUFkeecTcZ2bazQEAPsdx/zytUCgkv9+vYDCopKQk23GAY/rDH8xoza5dUrVqttOgsowbJz35pPTVV1Lz5rbTAIhXrh6hA7xkwQIzGYIyF1/GjJHq1JGeeMJ2EgDxjEIHREAoJH3xBadb41Ht2tLvfie98YZZsgYAbKDQARHw6admD1cKXXy67TapRYv/XlMHAJWNQgdEwIIF0jnnmBviT/Xq0v/+r/TXv5qRWgCobBQ6IAIWLGB0Lt4NHiy1by89/DBbggGofBQ64BRt2iR9/TWFLt5VqWKWL8nNlT780HYaAPGGQgecogULpKpVpUsvtZ0EtvXtK/XqJY0dK5WU2E4DIJ5Q6IBT9NFHUteuEkskwueTnn5aWrVKevdd22kAxBMKHXAKSkqkRYsYncN/9egh9ekjPfUU19IBqDwUOuAUrFtn9vG85BLbSeAmjz5qRun+/nfbSQDECwodcAoWLjRLVnTvbjsJ3OSii6SePc2WYIzSAagMFDrgFCxcaK6fq1nTdhK4ic9nRumWLjWLTgNAtFHogAoqKTGFrndv20ngRldcIXXubEbpACDaKHRABa1dK/3nP1w/h2Pz+cxWYJ98YkbqACCaKHRABS1cKCUmcv0cynfttVKbNozSAYg+Ch1QQZ9+KnXrJtWoYTsJ3KpKFbPI8N/+Zma9AkC0uLrQZWVlKSUlRWlpabajAGUcXn+O6+dwIoMHSy1aSOPH204CIJb5HMf9k+pDoZD8fr+CwaCSWI4fLrBqldSxoxml4xo6nMizz0oPPyx9843UpIntNABikatH6AC3WrxYqlbNLFkCnMiIEeZ6y6ws20kAxCoKHVABn38upaZKp51mOwm8wO+XRo6UXnhB2rvXdhoAsYhCB1TA4sXShRfaTgEvuftu6ccfpWnTbCcBEIsodECYtm6VCgrM1k7AyWrZ0ixjMmGCmVQDAJFEoQPC9Pnn5p5Ch3Ddd5/05ZfSBx/YTgIg1lDogDB9/rnUurXUoIHtJPCaHj2kCy6Q/vxn20kAxBoKHRAmrp9DRfl80pgx0scfs9AwgMii0AFhCAalNWsodKi4666TmjUz19IBQKRQ6IAwLF1qLmjn+jlUVEKCmfE6fbpUWGg7DYBYQaEDwvD55+bauVatbCeBl40caRamfvll20kAxAoKHRCGxYvN6JzPZzsJvKxOHWnoUOnFF6WDB22nARALKlToJk+erJYtW6pGjRpKTU3VZ599dtznFxcX69FHH1WLFi2UmJioc845R1OnTq1QYMCWAwekZcu4fg6Rceed0rZt0vvv204CIBYkhPuC7Oxs3XvvvZo8ebJ69uypF198UX379tX69evVvHnzY75m4MCB+v777/Xqq6/q3HPP1Y4dO3SQX0vhMYGA2baJ6+cQCR07St26SVOmmAWHAeBU+BzHccJ5QdeuXdW5c2dNmTKl9LE2bdpowIAByszMPOr5H374oW688UZt2rRJdevWrVDIUCgkv9+vYDCopKSkCr0HcKomTJDGjjUzXatXt50GseDNN6WMDGnjRq7LBHBqwjrlun//fuXl5Sk9Pb3M4+np6VqyZMkxXzN37lx16dJFzzzzjJo2barWrVvrgQce0L59+8r9PMXFxQqFQmVugG2LF5tFYSlziJQbbpDq1ZNeeMF2EgBeF1ah27lzpw4dOqTk5OQyjycnJ6uwnPn3mzZt0uLFi7V27VrNnj1bEyZM0LvvvqvRo0eX+3kyMzPl9/tLb82aNQsnJhBxjmNmuHL9HCKpRg3p1lul114zp/MBoKIqNCnCd8QUP8dxjnrssJKSEvl8Pk2fPl0XXHCBrrzySj377LN6/fXXyx2lGzt2rILBYOmtoKCgIjGBiNm0yawZxvVziLTbb5d+/FHKzradBICXhVXo6tevr6pVqx41Grdjx46jRu0Oa9y4sZo2bSq/31/6WJs2beQ4jr799ttjviYxMVFJSUllboBNh68o6N7dbg7EnnPOka64wkyOAICKCqvQVa9eXampqcrJySnzeE5Ojnr06HHM1/Ts2VPfffeddu/eXfrYxo0bVaVKFZ155pkViAxUvmXLpPPOk844w3YSxKI77pCWLzc3AKiIsE+5jhkzRq+88oqmTp2qDRs26L777tPWrVs1atQoSeZ0aUZGRunzhwwZonr16umWW27R+vXrlZubqwcffFC33nqrTjvttMh9JUAULVtmlpgAouHKK6XmzZkcAaDiwi50gwYN0oQJEzRu3Dh17NhRubm5mjdvnlq0aCFJ2r59u7Zu3Vr6/Nq1aysnJ0c//vijunTpoqFDh6pfv36aOHFi5L4KIIr27TNr0HXtajsJYlXVqtKIEeY6uqIi22kAeFHY69DZwDp0sGnJEjMZIi9P6tzZdhrEqq1bpbPOMvu7jhhhOw0Ar2EvV+AEli0zy0ucf77tJIhlzZtL6enSq6/aTgLAiyh0wAksWyalpkrVqtlOglg3YoT0xRfShg22kwDwGgodcALLlnH9HCrHNdeYnSMYpQMQLgodcBzffy998w2FDpUjMdHs7frGG9L+/bbTAPASCh1wHMuWmXsKHSrLiBHSzp3S++/bTgLASyh0wHEsWyY1amQuWAcqQ9u25hcITrsCCAeFDjiOw9fPlbNVMRAVI0ZI8+dL5eyOCABHodAB5SgpMVsxcboVlW3QILNUzuuv204CwCsodEA5/vlPKRSi0KHyJSVJAwdKU6eaXywA4EQodEA5li0zp1q7dLGdBPFoxAhp82bp009tJwHgBa4udFlZWUpJSVFaWprtKIhDS5dKKSlmtASobD17Suedx+QIACeHvVyBcnTsaHaI4B9U2PKnP0m/+520fbt0xhm20wBwM1eP0AG27N0rrV0rXXCB7SSIZxkZ0qFD0vTptpMAcDsKHXAMgYD5h5Sz/bApOVm68kpp2jTbSQC4HYUOOIbly802TOefbzsJ4l1Ghvl+/Oc/bScB4GYUOuAYli8319BVq2Y7CeLd1VdLdepIb75pOwkAN6PQAcewYgWnW+EOiYlmoeE332RNOgDlo9ABRwgGpS+/pNDBPW6+WSookBYtsp0EgFtR6IAj5OWZewod3KJHD+nsszntCqB8FDrgCCtWSLVrm0VdATfw+czkiHfeMUvqAMCRKHTAEfLypE6dpCr87YCL3HSTtHu39Ne/2k4CwI34Jws4wsqVZocIwE3OOcdsB8aadACOhUIH/EwwKH39tdS5s+0kwNEyMqQFC8xWYADwcxQ64GdWrjT3jNDBjW64QUpIkGbOtJ0EgNtQ6ICfWblSqlmTCRFwpzPOkK65htOuAI5GoQN+Ji/P7BBRtartJMCx3XyztGqVtHq17SQA3IRCB/xMXh6nW+FuV1wh1a/PmnQAyqLQAf8nFJI2bqTQwd2qV5cGD5amT5cOHbKdBoBbuLrQZWVlKSUlRWks2Y9KEAiYe2a4wu1uvtnMdP34Y9tJALiFz3Ecx3aIEwmFQvL7/QoGg0pKSrIdBzHqz3+WHnlEKioyMwkBt3IcKSXFjCa/9ZbtNADcwNUjdEBlWrlS6tCBMgf38/nMKN2sWeYXEACg0AH/hwkR8JKbbpL27ZPee892EgBuQKEDZPbI/Oc/KXTwjubNpYsvlmbMsJ0EgBtQ6ACZdb0chwkR8JahQ83EiMJC20kA2EahA2ROtyYmSm3b2k4CnLzrrjOLYP/lL7aTALCNQgfITIho316qVs12EuDk1a0r9e1r1qQDEN8odIDMCB2nW+FFQ4ZI//iH9PXXtpMAsIlCh7i3d6+0fj0TIuBN/fpJtWtLM2faTgLAJgod4t7q1VJJCSN08KaaNaVrrzWnXd2/TDyAaKHQIe7l5Zlr59q1s50EqJghQ6Qvv5Ty820nAWALhQ5xLy9POv98M8sV8KLLL5caNGBNOiCeUegQ91au5HQrvC0hQRo0yFxHd+iQ7TQAbKDQIa799JO0bh0TIuB9Q4ZI330nffaZ7SQAbKDQIa6tXSsdPCh16mQ7CXBqunWTzjqL065AvKLQIa4FAlKVKuYaOsDLfD4zSvfOO1Jxse00ACqbqwtdVlaWUlJSlJaWZjsKYlQgIJ13nln6AfC6oUOlH3+UPvzQdhIAlc3nOO5fuSgUCsnv9ysYDCopKcl2HMSQXr2kZs04TYXY0bGj+SUlO9t2EgCVydUjdEA0lZRIq1ZJHTrYTgJEzpAh0ty5UlGR7SQAKhOFDnFr82bzj17HjraTAJFz441m9vbs2baTAKhMFDrErUDA3FPoEEuaN5cuuojLCIB4Q6FD3AoEpEaNpORk20mAyBoyRProI+n7720nAVBZKHSIW4EAo3OITddfb5Yxeecd20kAVBYKHeIWhQ6xql496YorpOnTbScBUFkodIhLu3ZJ335LoUPsGjpUWrpU2rTJdhIAlYFCh7i0apW5Z8kSxKp+/aRataSZM20nAVAZKHSIS4GAdNppUqtWtpMA0VGrljRggDnt6v7l4wGcKgod4lIgILVvL1WtajsJED1Dh0obNkirV9tOAiDaKHSIS0yIQDy4/HKpfn0mRwDxgEKHuPPTT2bUgkKHWFetmjRwoLmOrqTEdhoA0VShQjd58mS1bNlSNWrUUGpqqj777LOTet3nn3+uhIQEdeRfUli0fr108CCFDvFhyBAzo3vxYttJAERT2IUuOztb9957rx599FHl5+erV69e6tu3r7Zu3Xrc1wWDQWVkZOiyyy6rcFggElatMouunn++7SRA9PXoIZ11FqddgVgXdqF79tlnNWLECI0cOVJt2rTRhAkT1KxZM02ZMuW4r7v99ts1ZMgQde/e/YSfo7i4WKFQqMwNiJRAwMxurVXLdhIg+nw+afBgs2vE/v220wCIlrAK3f79+5WXl6f09PQyj6enp2vJkiXlvu61117Tv/71Lz3++OMn9XkyMzPl9/tLb82aNQsnJnBcTIhAvBk6VPrhB+mDD2wnARAtYRW6nTt36tChQ0o+Yjfz5ORkFRYWHvM1X331lR5++GFNnz5dCQkJJ/V5xo4dq2AwWHorKCgIJyZQLseh0CH+tG1rFtHmtCsQu06uYR3B5/OV+bPjOEc9JkmHDh3SkCFD9Pvf/16tW7c+6fdPTExUYmJiRaIBx/XNN1IoRKFD/Bk6VHrsMfP9n5RkOw2ASAtrhK5+/fqqWrXqUaNxO3bsOGrUTpKKioq0YsUK3XXXXUpISFBCQoLGjRunVatWKSEhQZ988smppQfCFAiYewod4s3gwVJxsTRrlu0kAKIhrEJXvXp1paamKicnp8zjOTk56tGjx1HPT0pK0po1axQIBEpvo0aN0nnnnadAIKCuXbueWnogTKtWSQ0bSo0a2U4CVK4zz5QuvpjTrkCsCvuU65gxY3TzzTerS5cu6t69u1566SVt3bpVo0aNkmSuf9u2bZumTZumKlWqqF27dmVe37BhQ9WoUeOox4HKcPj6uWNcIQDEvJtukn79a+m776QmTWynARBJYS9bMmjQIE2YMEHjxo1Tx44dlZubq3nz5qlFixaSpO3bt59wTTrAlkDAXBwOxKPrrjO7R7z9tu0kACLN5ziOYzvEiYRCIfn9fgWDQSVxNS8q6IcfpLp1zSmnIUNspwHsuO46MzkoL892EgCRxF6uiBurVpl7JkQgng0dKq1cKf3zn7aTAIgkCh3iRiAg1aghhbGCDhBzrrxS8vuZHAHEGgod4kYgYPZvPcn1rYGYVKOGdP310owZZqFtALGBQoe4sWoVp1sByZx23bRJWrrUdhIAkUKhQ1zYv19at45CB0hmPbqmTTntCsQSCh3iwoYN0oEDLFkCSFKVKmbniOxs8/cCgPdR6BAXDm/51b691RiAawwdKu3cKR2x8Q8Aj6LQIS4EAtK550qnn247CeAOHTpIKSnSW2/ZTgIgEih0iAuHt/wCYPh8Ziuwv/5V2r3bdhoAp4pCh5jnOBQ64FiGDJH27pXmzLGdBMCpcnWhy8rKUkpKitLS0mxHgYcVFEg//kihA47UooV04YXMdgViAXu5IubNnSv17y99+61ZqgHAf73wgnTXXdJ330kNG9pOA6CiXD1CB0RCICDVqyc1aWI7CeA+N9xgrqfLzradBMCpoNAh5h2+fs7ns50EcJ969aS+fTntCngdhQ4xjwkRwPENHSotWyZ9/bXtJAAqikKHmBYMSps3U+iA4+nXT6pdW5oxw3YSABVFoUNMW73a3FPogPLVrCldd5305ptmmR8A3kOhQ0wLBKTEROm882wnAdwtI8Occv3iC9tJAFQEhQ4xLRCQ2rWTqlWznQRwt0sukZo3l954w3YSABVBoUNMCwTMnpUAjq9KFenmm6W335b27bOdBkC4KHSIWQcOSGvXcv0ccLKGDZNCIbO/KwBvodAhZv3zn9L+/RQ64GS1aiX16MFpV8CLKHSIWYGAuW/f3moMwFOGDZMWLDBbgQHwDgodYtaqVdLZZ0t+v+0kgHcMHGgmEbFzBOAtFDrELHaIAMJXp440YIA57cqadIB3UOgQkxyHQgdU1LBh0rp1Ul6e7SQAThaFDjFp2zZp1y6WLAEqok8fqXFjJkcAXuLqQpeVlaWUlBSlpaXZjgKPOTwhghE6IHwJCdJNN0kzZ5qZ4gDcz9WFbvTo0Vq/fr2WL19uOwo8JhCQzjhDatbMdhLAm4YNM6Pcf/+77SQAToarCx1QUYevn/P5bCcBvKltWyk1ldOugFdQ6BCTVq3idCtwqoYNMyN0//637SQAToRCh5hTVCR9/TWFDjhVgwebUW7WpAPcj0KHmLN6tbmn0AGnpn596ZprpFdeYU06wO0odIg5gYBZ6f4Xv7CdBPC+224za9ItXWo7CYDjodAh5gQC5oLu6tVtJwG87/LLpbPOkl5+2XYSAMdDoUPMYYcIIHKqVJFGjJCys6VQyHYaAOWh0CGmHDworVlDoQMi6ZZbpJ9+kmbMsJ0EQHkodIgpGzdKxcUUOiCSmjaVrrqK066Am1HoEFMOb/nFHq5AZP3619LKleYGwH0odIgpgYC5gLtOHctBgBjTt68ZqWOUDnAnCh1iSn4+p1uBaEhIkG691SwyvHu37TQAjkShQ8xwHFPoOnWynQSITSNGmDL3l7/YTgLgSBQ6xIxvv5V27aLQAdHSooWUns5pV8CNKHSIGfn55p5CB0TPr39tdo1Yu9Z2EgA/5+pCl5WVpZSUFKWlpdmOAg/Izzd7TzZtajsJELv69ZMaNmSUDnAbn+O4f8vlUCgkv9+vYDCopKQk23HgUv37S/v2SQsW2E4CxLaHHjKF7rvvpBo1bKcBILl8hA4IBxMigMoxcqT0ww/Se+/ZTgLgMAodYsKuXVJBAYUOqAytWkm9e0svvWQ7CYDDKHSICUyIACrX7bdLublMjgDcgkKHmJCfL9WqZUYOAETftddKjRpJkyfbTgJAotAhRuTnm/1bq/AdDVSK6tXNKN20aVIwaDsNAP75Q0xgQgRQ+W67TSouNqUOgF0UOnjenj3Sl19S6IDK1qSJ9KtfSVlZZus9APZQ6OB5q1ebf0wodEDlGz3a/EL18ce2kwDxjUIHz8vPlxISpLZtbScB4k+vXtL550uTJtlOAsQ3Ch08Lz/flLnERNtJgPjj80l33SW9/760aZPtNED8otDB85gQAdh1001SnTrS88/bTgLELwodPO3AAWnNGgodYFPNmmYJk1dflUIh22mA+FShQjd58mS1bNlSNWrUUGpqqj777LNynztr1iz16dNHDRo0UFJSkrp376758+dXODDwcxs2SPv3U+gA20aPlvbtk6ZOtZ0EiE9hF7rs7Gzde++9evTRR5Wfn69evXqpb9++2rp16zGfn5ubqz59+mjevHnKy8tT79691a9fP+Uf3qsJOAWHv406dLCbA4h3TZtKgwZJEydKhw7ZTgPEH5/jhLd6UNeuXdW5c2dNmTKl9LE2bdpowIAByszMPKn3aNu2rQYNGqTHHnvspJ4fCoXk9/sVDAaVlJQUTlzEuHvvlebNkzZutJ0EQF6e1KWLNGuW2RoMQOUJa4Ru//79ysvLU3p6epnH09PTtWTJkpN6j5KSEhUVFalu3brlPqe4uFihUKjMDTiWvDxOtwJukZoqXXih9OyztpMA8SesQrdz504dOnRIycnJZR5PTk5WYWHhSb3H+PHjtWfPHg0cOLDc52RmZsrv95femjVrFk5MxIlDh8wp1y5dbCcBcNgDD0iLF0sn+Ts+gAip0KQIn89X5s+O4xz12LHMnDlTTzzxhLKzs9WwYcNynzd27FgFg8HSW0FBQUViIsZ9+aXZ9otCB7hHv35SmzbSH/9oOwkQXxLCeXL9+vVVtWrVo0bjduzYcdSo3ZGys7M1YsQIvfPOO7r88suP+9zExEQlskosTiAvz9x37mw3B4D/qlJFeughafhwad06dnABKktYI3TVq1dXamqqcnJyyjyek5OjHj16lPu6mTNnavjw4ZoxY4auuuqqiiUFjrBihXTuuZLfbzsJgJ8bPFhq1oxROqAyhX3KdcyYMXrllVc0depUbdiwQffdd5+2bt2qUaNGSTKnSzMyMkqfP3PmTGVkZGj8+PHq1q2bCgsLVVhYqGAwGLmvAnHp8Iw6AO5Svbp0//3SjBnSli220wDxIexCN2jQIE2YMEHjxo1Tx44dlZubq3nz5qlFixaSpO3bt5dZk+7FF1/UwYMHNXr0aDVu3Lj0ds8990Tuq0DcOTwhIjXVdhIAxzJypNkObPx420mA+BD2OnQ2sA4djrRundSunfTpp9Ill9hOA+BYxo2Tnn7ajNI1aGA7DRDb2MsVnnR4QgRr0AHuNXq0mSQxcaLtJEDso9DBk1askFq3ZkIE4Gb16km33SZNmiQVFdlOA8Q2Ch08KS+P6+cALxgzxqwX+bPdIgFEAYUOnnPwIDtEAF5x5pnSLbdIf/qTKXYAooNCB8/ZsEHat48ROsArHnlECgalrCzbSYDYRaGD5yxbZi60ptAB3tCihXTrrWaUbvdu22mA2EShg+csW2aWLKld23YSACeLUToguih08Jxly6SuXW2nABCO5s2lX//abAf2ww+20wCxh0IHTykqktaupdABXvTYY9L+/VJmpu0kQOyh0MFTVqyQHEfq1s12EgDhSk6WHnzQLDT8sx0iAUSAqwtdVlaWUlJSlJaWZjsKXGLZMun006Vf/MJ2EgAVcf/9Zo/X3/3OdhIgtrCXKzxlwAAzS+6jj2wnAVBRU6aYbcHy86UOHWynAWKDq0fogJ9zHCZEALFg5EipVSvpoYdsJwFiB4UOnlFQIBUWUugAr6tWzUyMmD+f0XYgUih08IylS809hQ7wvmuvlbp3l377W6mkxHYawPsodPCMZcuks84yM+UAeJvPZ3aOyM+X3n7bdhrA+yh08AyunwNiS8+eUv/+ZheJfftspwG8jUIHTzhwQMrLY/05INY884z03XdmBwkAFUehgyesXi399BMjdECsad3aLDb89NPS11/bTgN4F4UOnrBsmZkZ16mT7SQAIu3RR6VGjaTf/MYsTwQgfBQ6eMLSpVLHjlKNGraTAIi0mjXNdmAffijNnm07DeBNFDp4AhMigNh2zTXS1VdL995rdoMBEB4KHVzv3/+WNm40a1YBiF0TJ5q/7+PG2U4CeA+FDq732WfmvlcvuzkARFfLltJjj0njx0v/+IftNIC3UOjgerm55gd9s2a2kwCItgcfNJOfhg83M9sBnBwKHVwvN1e66CLbKQBUhoQE6Y03pH/9S3riCdtpAO+g0MHVgkEpEJAuvth2EgCVpW1bU+b+9CczIQrAiVHo4GqLF5t1qRihA+LLgw9KqamcegVOlqsLXVZWllJSUpSWlmY7CizJzZWaNJHOPtt2EgCVKSFBev11afNm6aGHbKcB3M/nOO5flzsUCsnv9ysYDCopKcl2HFSi7t2ls86SZs60nQSADZMmmR0k5s6V+vWznQZwL1eP0CG+7dkjrVjB9XNAPBs92iw6fMst0rZtttMA7kWhg2t98YV08CDXzwHxzOeTpk412/4NHSodOGA7EeBOFDq4Vm6uVL++1KaN7SQAbKpXz1x28fnn0v33204DuBOFDq6Vm2t2h/D5bCcBYFuvXtLzz5vbq6/aTgO4D4UOrrRvn7R0KadbAfzXqFHmdscd0pIlttMA7kKhgyvl5krFxVKfPraTAHCT556TunWTfvUrqaDAdhrAPSh0cKX586Uzz5RSUmwnAeAm1atL774rJSZK115rRvMBUOjgUh9+KF1xBdfPAThaw4bSnDnS+vVSRoZ06JDtRIB9FDq4zpYt0oYNptABwLF06iTNmCHNmiXddZfZIhCIZxQ6uM78+VLVqtJll9lOAsDNBgyQXnpJeuEF6fHHbacB7EqwHQA40vz55qLnOnVsJwHgdiNGSDt3Sg8/bEbpxo3jUg3EJwodXOXAAemjj6QHH7SdBIBXPPSQVKWK9NvfSrt3S88+S6lD/KHQwVWWLpVCIa6fAxCeBx+UatUye7/u2SNNmWIu3QDiBYUOrvLhh2a7r86dbScB4DV33mlK3a23mlL3+utStWq2UwGVg0IH13Ac6Z13pKuvNqdPACBcw4aZUjd4sCl12dlmzTog1rn6n82srCylpKQoLS3NdhRUgrw86auvpKFDbScB4GXXX2/WqfvwQzNbvrDQdiIg+nyO4/7Ve0KhkPx+v4LBoJKSkmzHQZTcd580c6a0bRvXvgA4dUuXmi3CqlQx69VdcIHtRED0uHqEDvHj0CHp7belG2+kzAGIjG7dpBUrpObNpV69pKlTWYAYsYtCB1dYuNCcFhkyxHYSALGkSRPp00/NtXUjRkgDB0q7dtlOBUQehQ6uMGOGdM45EpdLAoi0xESzo0R2tvTxx9L555vr64BYQqGDdT/9JL33nhmdYzFQANEycKC0dq3Uvr3Ut690221mlwkgFlDoYN28eVIwyOlWANHXpIn0wQfS5MnSX/4itW4tTZokHTxoOxlwaih0sG7GDLOQ8C9+YTsJgHjg80l33CFt3GiWOLn7bqlTJ7PtIJMm4FUUOli1a5f0t78xOgeg8jVsaK6tW75cSkqS+vSRunY1C5wzYgevodDBqqeeMlvzZGTYTgIgXqWmSosXm8s/atc219q1bi1lZUl799pOB5wcCh2s2bLFXLvy299KDRrYTgMgnvl8ZqLEJ5+Yteu6djWnYps3lx57zCx4DrgZO0XAmuHDzdIBX39tfisGADf55hvpz3+WXnlF2rdPuvRSszVh//5S3bq20wFlMUIHK9askaZNM7/5UuYAuNFZZ0nPPSd9950pdSUlZnHihg3NHrETJkjr1jGRAu7ACB2s6NdP2rDB3KpVs50GAE7O9u3SX/8qzZ5tdrjZv19q3Fjq3dssjJ6aambM8osqKhuFDpWqpER68UXpzjvN3q2DBtlOBAAVs3evmUzx0UfSZ59JgYBZKN3nM8swpaZKXbpIKSnS2Web6/H4BRbRQqFDpdmwQbr9dvODb+RIU+yqcNIfQIw4eFBav95MqsjLM/erVknFxebjVauaUnf22ebWuLGZENawobkd/u+6dc1zgXAk2PrEjuOoqKjomB8rLi5W8eG/AZJmzNgnSZo4MaQaNSolHiJsyxbphRfMD7O5c6WLL5Z277adCgAi66yzzO36682fDx6UCgrMBIvNm/97/49/SDt2SP/+97HXvKtdW6pZ87/3tWr991azptmfNiHBjPhVrWr++1i3qlXLbql45PaKx/tYec870XNxYq1amdP0J+v000+X7wQH3doI3eFRNwAAAJTvZM5QWit04YzQbd++XRdccIHWr1+vpk2bnvLnTktL0/Lly0/5fSL5Xm7MFAqF1KxZMxUUFETkVLcbv8ZIvhfH3dvvxXG3916RPPZu/Prc+l5u/Z5347GK5HtV5LifzAidtVOuPp8v7G+g008/PSLfdFWrVo3YtXiRei83ZjosKSkppr9GN/4/lDjutt6L427nvaTIHHu3fn1ufS/Jfd/zbj1Wbj3uh8XlJemjR4923Xu5MVOkufVrdOP/w0hy47Fy83tFilu/Pre+V6S49etz63tFkht/lrr1vaLBE7Ncv/3229LhyTPPPNN2nLjB7GI7OO52cNzt4djbwXG3I1rH3RMjdImJiWXuUTkSExP1+OOPc9wrGcfdDo67PRx7OzjudkTruHtihI7fIgAAAMrniRE6AAAAlI9CBwAA4HEUOgAAAI/zxDV0hxchPpmF9QAAAOKNJwodAAAAyscpVyg3N1f9+vVTkyZN5PP5NGfOnDIfdxxHTzzxhJo0aaLTTjtNl1xyidatW2cnbIzIzMxUWlqaTj/9dDVs2FADBgzQl19+WeY5HPfomDJlitq3b1+6Snv37t31wQcflH6c4x59mZmZ8vl8uvfee0sf47hHxxNPPCGfz1fm1qhRo9KPc9yjZ9u2bbrppptUr1491axZUx07dlReXl7pxyN97Cl00J49e9ShQwdNmjTpmB9/5pln9Oyzz2rSpElavny5GjVqpD59+pS7Fy9ObNGiRRo9erSWLl2qnJwcHTx4UOnp6dqzZ0/pczju0XHmmWfq6aef1ooVK7RixQpdeuml6t+/f+kPUo57dC1fvlwvvfSS2rdvX+Zxjnv0tG3bVtu3by+9rVmzpvRjHPfo+OGHH9SzZ09Vq1ZNH3zwgdavX6/x48erTp06pc+J+LF3gJ+R5MyePbv0zyUlJU6jRo2cp59+uvSxn376yfH7/c4LL7xgIWFs2rFjhyPJWbRokeM4HPfKdsYZZzivvPIKxz3KioqKnFatWjk5OTnOxRdf7Nxzzz2O4/D9Hk2PP/6406FDh2N+jOMePQ899JBz4YUXlvvxaBx7RuhwXJs3b1ZhYaHS09NLH0tMTNTFF1+sJUuWWEwWW4LBoCSpbt26kjjuleXQoUN6++23tWfPHnXv3p3jHmWjR4/WVVddpcsvv7zM4xz36Prqq6/UpEkTtWzZUjfeeKM2bdokieMeTXPnzlWXLl10ww03qGHDhurUqZNefvnl0o9H49hT6HBchYWFkqTk5OQyjycnJ5d+DKfGcRyNGTNGF154odq1ayeJ4x5ta9asUe3atZWYmKhRo0Zp9uzZSklJ4bhH0dtvv62VK1cqMzPzqI9x3KOna9eumjZtmubPn6+XX35ZhYWF6tGjh3bt2sVxj6JNmzZpypQpatWqlebPn69Ro0bp7rvv1rRp0yRF53s+4dQiI14cuVyM4zgsIRMhd911l1avXq3Fixcf9TGOe3Scd955CgQC+vHHH/Xee+9p2LBhWrRoUenHOe6RVVBQoHvuuUcLFixQjRo1yn0exz3y+vbtW/rf559/vrp3765zzjlHb7zxhrp16yaJ4x4NJSUl6tKli5566ilJUqdOnbRu3TpNmTJFGRkZpc+L5LFnhA7HdXg21JG/MezYseOo3ywQvt/85jeaO3euPv30U5155pmlj3Pco6t69eo699xz1aVLF2VmZqpDhw567rnnOO5RkpeXpx07dig1NVUJCQlKSEjQokWLNHHiRCUkJJQeW4579NWqVUvnn3++vvrqK77fo6hx48ZKSUkp81ibNm20detWSdH5GU+hw3G1bNlSjRo1Uk5OTulj+/fv16JFi9SjRw+LybzNcRzdddddmjVrlj755BO1bNmyzMc57pXLcRwVFxdz3KPksssu05o1axQIBEpvXbp00dChQxUIBHT22Wdz3CtJcXGxNmzYoMaNG/P9HkU9e/Y8aimqjRs3qkWLFpKi9DO+QlMpEFOKioqc/Px8Jz8/35HkPPvss05+fr6zZcsWx3Ec5+mnn3b8fr8za9YsZ82aNc7gwYOdxo0bO6FQyHJy77rjjjscv9/vLFy40Nm+fXvpbe/evaXP4bhHx9ixY53c3Fxn8+bNzurVq51HHnnEqVKlirNgwQLHcTjuleXns1wdh+MeLffff7+zcOFCZ9OmTc7SpUudq6++2jn99NOdb775xnEcjnu0/OMf/3ASEhKcJ5980vnqq6+c6dOnOzVr1nTeeuut0udE+thT6OB8+umnjqSjbsOGDXMcx0yvfvzxx51GjRo5iYmJzkUXXeSsWbPGbmiPO9bxluS89tprpc/huEfHrbfe6rRo0cKpXr2606BBA+eyyy4rLXOOw3GvLEcWOo57dAwaNMhp3LixU61aNadJkybOr371K2fdunWlH+e4R8/777/vtGvXzklMTHR+8YtfOC+99FKZj0f62LP1FwAAgMdxDR0AAIDHUegAAAA8jkIHAADgcRQ6AAAAj6PQAQAAeByFDgAAwOModAAAAB5HoQMAAPA4Ch0AAIDHUegAAAA8jkIHAADgcf8fdwhadME3k4YAAAAASUVORK5CYII=", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(lambda x, d1=disk_min, d2=disk_max: profile(x, d1, d2), \n", " xmin=0, xmax=60, ymin=0, ymax=1.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now rewrite the function `intersection` taking everything into account. This time it directly returns an RGB value." ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [], "source": [ "%%cython\n", "from libc.math cimport cos, sin, acos, sqrt, abs, atan2\n", "cimport cython\n", "from __main__ import profile\n", "from __main__ import xyz_to_spherical\n", "from __main__ import spherical_to_xyz\n", "\n", "@cython.boundscheck(False)\n", "@cython.wraparound(False)\n", "cpdef tuple intersection(list curve, float m, float alpha, float beta, \n", " float dmin, float dmax):\n", " cdef float x, y, z\n", " cdef float x2, y2, z2\n", " cdef float r, theta, phi\n", " cdef int n, i\n", " cdef float t\n", " cdef float sinalpha, cosalpha\n", " cdef float sinbeta, cosbeta\n", " cdef float R, G, B\n", " cdef float dr, dtheta, dphi\n", " cdef float dx, dy, dz\n", " cdef float th\n", " R, G, B = 0., 0., 0. # return values\n", " sinalpha = sin(alpha)\n", " cosalpha = cos(alpha)\n", " sinbeta = sin(beta)\n", " cosbeta = cos(beta)\n", " n = len(curve)\n", " r, theta, phi = curve[0][2:5]\n", " x, y, z = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta)\n", " x, y, z = x, y*cos(beta)-z*sin(beta), z*cos(beta)+y*sin(beta)\n", " z = z*cos(alpha)+x*sin(alpha)\n", " for i in range(1, n): \n", " r = curve[i][2]\n", " theta = curve[i][3]\n", " phi = curve[i][4]\n", " # rotations\n", " x2, y2, z2 = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta)\n", " y2, z2 = y2*cosbeta-z2*sinbeta, z2*cosbeta+y2*sinbeta\n", " x2, z2 = x2*cosalpha-z2*sinalpha, z2*cosalpha+x2*sinalpha\n", " if z!=z2:\n", " t = z/(z-z2)\n", " if t>=0 and t<1 and curve[i][2]>dmin and curve[i][2]= 255:\n", " R = 255\n", " return R, G, B" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also have to rewrite `render_row` to accept an RGB value." ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [], "source": [ "def render_row(x):\n", " \"\"\"\n", " Render a single row of the image\n", " \"\"\"\n", " res = np.zeros((ny,3)) # result row in RGB format\n", " for y in range(ny):\n", " beta = atan2(y-ny/2,x) # beta angle \n", " r = sqrt(x**2+(y-ny/2)**2) # pixel distance to the center of the image\n", " ind_geo = int(r/400*n_geod*720/nx) # index of the geodesic to use. values are obtained by trial and error.\n", " if ind_geo" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%display plain\n", "data = np.zeros( (ny, nx, 3), dtype=float )\n", "render()\n", "img2 = toimage(data)\n", "img2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Much more beautiful! \n", "\n", "But enough of red black holes, let's add real spectra into the mix." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Black body spectrum\n", "\n", "It's quite easy to associate a spectrum to each light ray, but it's also important to be able to convert it back to displayable colors.\n", "\n", "This part shows how to do that, using the CIE standard XYZ function. This function should contain all information about a spectrum that is relevant to the human eye. They can then be converted to RGB for example. What's more, these functions are simply obtained by integrating the spectrum against a function. They are then linearly dependant on the spectrum.\n", "\n", "To compute the XYZ functions, we first need the function that defines them. I got mine from here: \n", "http://www.cvrl.org/database/data/cmfs/ciexyzjv.csv\n", "\n", "But because we are planning to add the Doppler effect, I added a lot of zeros at the beginning and the end to evntually encompass more wavelengths (I went from 5 to 3000 nm, instead of 380-780 for visible light)." ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [], "source": [ "from six.moves.urllib.request import urlretrieve # valid for both Python 2 and Python 3\n", "urlretrieve(\"http://www.cvrl.org/database/data/cmfs/ciexyzjv.csv\", \n", " \"ciexyzjv.csv\")\n", "ciexyz = np.genfromtxt(\"ciexyzjv.csv\", delimiter=\",\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is what they look like. Y can be seen as the luminosity of a normalized spectrum (e.g. for the same light intensity, green will appear much brighter to the human eye than purple). The other two don't really have an interpretation." ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "plt.plot(ciexyz[:,0],ciexyz[:,3], label='Z')\n", "plt.plot(ciexyz[:,0],ciexyz[:,2], label='Y')\n", "plt.plot(ciexyz[:,0],ciexyz[:,1], label='X')\n", "plt.legend(loc='best')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we need to compute the black body spectrum for a given temperature, using Planck's law. \n", "I already include the Doppler effect in the formula." ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [], "source": [ "%%cython\n", "from libc.math cimport exp\n", "\n", "cpdef float blackbody(float nu, float T, float doppler):\n", " \"\"\"\n", " Spectral power emmited at frequency nu by a black-body at \n", " temperature T per square meter par steradian\n", " \"\"\"\n", " cdef float h = 6.62e-34\n", " cdef float k = 1.38e-23\n", " cdef float c = 3e8\n", " cdef float h_sur_k = 4.79710144927536e-11\n", " return (2*h)*nu/c*nu/c*nu/(exp(h_sur_k*nu/doppler/T)-1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In fact there is a small trick in the previous cell. Because of the exponent in the constants, it's fairly easy to overflow. That's why the $\\nu^3/c^2$ is written this way.\n", "\n", "Let's try at 10,000 K:" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "verbose 0 (3954: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 171 points.\n", "verbose 0 (3954: plot.py, generate_plot_points) Last error message: 'Unable to compute f(3000.0)'\n" ] }, { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(spline([(l, blackbody(3e8/(l/1e9), 10000, 1)) for l in ciexyz[:,0]]), \n", " xmin=5, xmax=3000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once again, we'll use Cython to convert a temperature into XYZ. Because XYZ depends linearly on the intensity, and not RGB, the conversion will be done in post-processing. Everything is redeclared in Cython for optimization (hence all the type declarations). Even the XYZ arrays are reloaded in this Cython environment." ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [], "source": [ "%%cython\n", "from __main__ import blackbody\n", "from libc.math cimport exp\n", "import numpy as np\n", "cimport numpy as np\n", "cimport cython\n", "\n", "DTYPE = float\n", "ctypedef np.float_t DTYPE_t\n", "\n", "cdef np.float_t[:] cielamb\n", "cdef np.float_t[:] ciex\n", "cdef np.float_t[:] ciey\n", "cdef np.float_t[:] ciez\n", "\n", "def init_arrays():\n", " global cielamb, ciex, ciey, ciez\n", " cdef np.ndarray[np.float_t, ndim=2] ciexyz = np.genfromtxt('ciexyzjv.csv', delimiter=\",\") \n", " cielamb = ciexyz[:, 0]\n", " ciex = ciexyz[:, 1]\n", " ciey = ciexyz[:, 2]\n", " ciez = ciexyz[:, 3]\n", " \n", "init_arrays()\n", "\n", "cpdef tuple temp_to_XYZ(float T, float doppler):\n", " cdef int nl = len(cielamb)\n", " cdef np.ndarray[np.float_t, ndim=1] sp = np.zeros(nl)\n", " cdef int i\n", " cdef float x, y, z\n", " for i in range(nl):\n", " sp[i] = blackbody(3e8/(cielamb[i]/1e9), T, doppler)\n", " x = np.dot(sp, ciex)\n", " y = np.dot(sp, ciey)\n", " z = np.dot(sp, ciez)\n", " return (x, y, z)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's convert it to RGB, using one of the many formulas, just to see how it looks:" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [], "source": [ "def xyz_to_rgb(*args):\n", " # constants\n", " fact = 3e-8 # arbitrary\n", " gamma = 1/2.2\n", " mat = [[3.24047, -1.53715, -0.498835],\n", " [-0.96256, 1.8752, 0.041556],\n", " [0.055648, -0.204043, 1.057311]]\n", " # conversion\n", " r, g, b = np.dot(mat, np.transpose(args)/fact).tolist()\n", " # gamma correction and clipping\n", " r = min(1,max(0, r)**gamma)\n", " g = min(1,max(0, g)**gamma)\n", " b = min(1,max(0, b)**gamma)\n", " return r, g, b" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from matplotlib.patches import Rectangle\n", "axes = plt.gca()\n", "axes.set_xlim([1000, 6000])\n", "for T in range(1000, 6000, 200):\n", " # plot a rectangle at a color obtained from the temperature\n", " axes.add_patch(Rectangle((T, 0), 200, 1, facecolor=xyz_to_rgb(*temp_to_XYZ(T, 1))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With this formula, it becomes bright very quickly. Adjusting the $\\gamma$ correction could help.\n", "\n", "We can now add it to our black hole ray tracer:" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [], "source": [ "%%cython\n", "from libc.math cimport cos, sin, acos, sqrt, abs, atan2\n", "cimport cython\n", "from __main__ import profile\n", "from __main__ import xyz_to_spherical\n", "from __main__ import spherical_to_xyz\n", "from __main__ import temp_to_XYZ\n", "\n", "@cython.boundscheck(False)\n", "@cython.wraparound(False)\n", "cpdef tuple intersection(list curve, float m, float alpha, float beta, \n", " float dmin, float dmax):\n", " cdef float x, y, z\n", " cdef float x2, y2, z2\n", " cdef float r, theta, phi\n", " cdef int n, i\n", " cdef float t\n", " cdef float sinalpha, cosalpha\n", " cdef float sinbeta, cosbeta\n", " cdef float X, Y, Z\n", " cdef float X0, Y0, Z0\n", " cdef float dr, dtheta, dphi\n", " cdef float dx, dy, dz\n", " cdef float th, doppler, factor,\n", " X, Y, Z = 0., 0., 0. # return values\n", " # 20 percent speed gain\n", " sinalpha = sin(alpha)\n", " cosalpha = cos(alpha)\n", " sinbeta = sin(beta)\n", " cosbeta = cos(beta)\n", " n = len(curve)\n", " r, theta, phi = curve[0][2:5]\n", " # rotations\n", " x, y, z = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta)\n", " x, y, z = x, y*cos(beta)-z*sin(beta), z*cos(beta)+y*sin(beta)\n", " z = z*cos(alpha)+x*sin(alpha)\n", " for i in range(1, n): \n", " r = curve[i][2]\n", " theta = curve[i][3]\n", " phi = curve[i][4]\n", " # rotations\n", " x2, y2, z2 = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta)\n", " y2, z2 = y2*cosbeta-z2*sinbeta, z2*cosbeta+y2*sinbeta\n", " x2, z2 = x2*cosalpha-z2*sinalpha, z2*cosalpha+x2*sinalpha\n", " if z!=z2:\n", " t = z/(z-z2)\n", " if t>=0 and t<1 and curve[i][2]>dmin and curve[i][2]" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "img3 = toimage(data_rgb)\n", "img3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## First relativistic effect: Doppler effect\n", "\n", "Everything has been so far done in such a way as to make this part easy. All we have to do is evalute the Doppler factor.\n", "\n", "To compute the Doppler effect due to the rotation of the disk, we need to consider the interaction between to disk and the light ray in the orthonormal frame again. The goal is to use the general formula:\n", "\n", "$$f_0 = \\frac{f_s}{\\gamma \\left(1+\\beta \\cos(\\theta)\\right)}$$\n", "\n", "To do that, we need to estimate $\\beta$ and $\\theta$. \n", "Let's first look at the equation of motion of a single particle, and impose circular motion: $dr=0$ and $\\theta=\\pi/2$" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [], "source": [ "eqs = curve._equations_rhs[C]" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [], "source": [ "dt, dr, dth, dph = curve._velocities" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The 4 equations become (note: for technical reasons the equations below display $ dt $ as $ Dt $ and $ d\\phi $ as $ Dph $; we could fix that but this is just an intermediate result so we don't bother):" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\frac{2 \\, {\\left(\\mathit{Dph}^{2} m r^{3} - \\mathit{Dt}^{2} m^{2}\\right)}}{r^{3}}\\)" ], "text/latex": [ "$\\displaystyle \\frac{2 \\, {\\left(\\mathit{Dph}^{2} m r^{3} - \\mathit{Dt}^{2} m^{2}\\right)}}{r^{3}}$" ], "text/plain": [ "2*(Dph^2*m*r^3 - Dt^2*m^2)/r^3" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%display latex\n", "# d^2t/dtau^2 = \n", "eqs[0].subs({th: pi/2, dr: 0, dth: 0})" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle -\\frac{2 \\, \\mathit{Dph}^{2} m r^{3} - \\mathit{Dph}^{2} r^{4} - 2 \\, \\mathit{Dt}^{2} m^{2} + \\mathit{Dt}^{2} m r}{r^{3}}\\)" ], "text/latex": [ "$\\displaystyle -\\frac{2 \\, \\mathit{Dph}^{2} m r^{3} - \\mathit{Dph}^{2} r^{4} - 2 \\, \\mathit{Dt}^{2} m^{2} + \\mathit{Dt}^{2} m r}{r^{3}}$" ], "text/plain": [ "-(2*Dph^2*m*r^3 - Dph^2*r^4 - 2*Dt^2*m^2 + Dt^2*m*r)/r^3" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# d^2r/dtau^2 = \n", "eqs[1].subs({th: pi/2, dr: 0, dth: 0})" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle 0\\)" ], "text/latex": [ "$\\displaystyle 0$" ], "text/plain": [ "0" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# d^2th/dtau^2 = \n", "eqs[2].subs({th: pi/2, dr: 0, dth: 0})" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle 0\\)" ], "text/latex": [ "$\\displaystyle 0$" ], "text/plain": [ "0" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# d^2ph/dtau^2 = \n", "eqs[3].subs({th: pi/2, dr: 0, dth: 0})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In particular $d\\phi$ is constant. We also solve the second equation for $dt$\n", "(the sign depends on the directions of the rotations):" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\left[\\mathit{Dt} = -\\mathit{Dph} r \\sqrt{\\frac{r}{m}}, \\mathit{Dt} = \\mathit{Dph} r \\sqrt{\\frac{r}{m}}\\right]\\)" ], "text/latex": [ "$\\displaystyle \\left[\\mathit{Dt} = -\\mathit{Dph} r \\sqrt{\\frac{r}{m}}, \\mathit{Dt} = \\mathit{Dph} r \\sqrt{\\frac{r}{m}}\\right]$" ], "text/plain": [ "[Dt == -Dph*r*sqrt(r/m), Dt == Dph*r*sqrt(r/m)]" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eqs[1].subs({th: pi/2, dr: 0, dth: 0}).solve(dt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And so by reinjecting in the first equation $dt$ is constant, and so is $d\\phi$, like in Newtonian gravity. \n", "Their values are obtained from the normalization condition." ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [], "source": [ "p = M((0, r, pi/2, 0))\n", "Tp = M.tangent_space(p)\n", "v = Tp((r*sqrt(r/m)*dph, 0, 0, dph))" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\mathit{Dph}^{2} r^{2} + \\frac{\\mathit{Dph}^{2} {\\left(2 \\, m - r\\right)} r^{2}}{m}\\)" ], "text/latex": [ "$\\displaystyle \\mathit{Dph}^{2} r^{2} + \\frac{\\mathit{Dph}^{2} {\\left(2 \\, m - r\\right)} r^{2}}{m}$" ], "text/plain": [ "Dph^2*r^2 + Dph^2*(2*m - r)*r^2/m" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.at(p)(v,v)" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\left[\\mathit{Dph} = -\\frac{\\sqrt{-\\frac{m}{3 \\, m - r}}}{r}, \\mathit{Dph} = \\frac{\\sqrt{-\\frac{m}{3 \\, m - r}}}{r}\\right]\\)" ], "text/latex": [ "$\\displaystyle \\left[\\mathit{Dph} = -\\frac{\\sqrt{-\\frac{m}{3 \\, m - r}}}{r}, \\mathit{Dph} = \\frac{\\sqrt{-\\frac{m}{3 \\, m - r}}}{r}\\right]$" ], "text/plain": [ "[Dph == -sqrt(-m/(3*m - r))/r, Dph == sqrt(-m/(3*m - r))/r]" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(g.at(p)(v,v)==-1).solve(dph)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see, the smallest circular orbit can only by at $r=3m$, with:\n", "
\n", "
\n", "\n", "$$ d\\phi = \\pm \\frac{1}{r} \\sqrt{\\frac{m}{r-3m}} \\qquad dt =\\frac{1}{\\sqrt{r}\\sqrt{r-3m}} $$\n", "\n", "We can see that:\n", "\n", "If we switch to the orthonormal frame (just multiply $d\\phi$ by $r$, as seen in the change of frame), we can see that:\n", "\n", "$$\\beta = \\frac{v}{c} = \\sqrt{\\frac{m}{r-3m}}$$\n", "\n", "To find $\\theta$, we use the formula:\n", "\n", "$$\\theta = \\arccos\\left(\\frac{\\overrightarrow{v_1}\\cdot \\overrightarrow{v_2}}{||\\overrightarrow{v_1}||\\cdot||\\overrightarrow{v_2}||}\\right)$$\n", "\n", "Finally, the gravitational redshift is easier. It is simply given by the ratio of first component of the 4-velocity in the orthonormal frame between the two ends of the geodesic." ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [], "source": [ "%%cython\n", "from libc.math cimport cos, sin, acos, sqrt, abs, atan2\n", "cimport cython\n", "from __main__ import profile\n", "from __main__ import xyz_to_spherical\n", "from __main__ import spherical_to_xyz\n", "from __main__ import temp_to_XYZ\n", "\n", "@cython.boundscheck(False)\n", "@cython.wraparound(False)\n", "cpdef tuple intersection(list curve, float m, float alpha, float beta, \n", " float dmin, float dmax):\n", " \"\"\"\n", " Return True if the curve intersect the disk comprised between dmin \n", " and dmax tilted of angles alpha and beta\n", " \"\"\"\n", " cdef float x, y, z\n", " cdef float x2, y2, z2\n", " cdef float r, theta, phi\n", " cdef int n, i\n", " cdef float t\n", " cdef float sinalpha, cosalpha\n", " cdef float sinbeta, cosbeta\n", " cdef float X, Y, Z\n", " cdef float X0, Y0, Z0\n", " cdef float dt, dt0, dr, dtheta, dphi\n", " cdef float dx, dy, dz\n", " cdef float th, rho, doppler, beta_rel\n", " X, Y, Z = 0., 0., 0. # return values\n", " # 20 percent speed gain\n", " sinalpha = sin(alpha)\n", " cosalpha = cos(alpha)\n", " sinbeta = sin(beta)\n", " cosbeta = cos(beta)\n", " n = len(curve)\n", " r, theta, phi = curve[0][2:5]\n", " dt0 = curve[1][1]-curve[0][1]\n", " # rotations\n", " x, y, z = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta)\n", " x, y, z = x, y*cos(beta)-z*sin(beta), z*cos(beta)+y*sin(beta)\n", " z = z*cos(alpha)+x*sin(alpha)\n", " for i in range(1, n): \n", " r = curve[i][2]\n", " theta = curve[i][3]\n", " phi = curve[i][4]\n", " # rotations\n", " x2, y2, z2 = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta)\n", " y2, z2 = y2*cosbeta-z2*sinbeta, z2*cosbeta+y2*sinbeta\n", " x2, z2 = x2*cosalpha-z2*sinalpha, z2*cosalpha+x2*sinalpha\n", " if z!=z2:\n", " t = z/(z-z2)\n", " if t>=0 and t<1 and curve[i][2]>dmin and curve[i][2]" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%display plain\n", "data = np.zeros( (ny, nx, 3), dtype=float )\n", "render()\n", "data_rgb = XYZ_to_RGB(data)\n", "img4 = toimage(data_rgb)\n", "img4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Second relativistic effect: aberration (forward focalisation)\n", "\n", "One last thing we didn't take into account is that a moving object that emits isotropic light at rest doesn't do so when in motion. The classical aberration formula reads:\n", "\n", "$$\\theta' = \\arccos \\left( \\frac{\\cos \\theta -\\beta}{1-\\beta \\cos \\theta} \\right)$$\n", "\n", "In the rest frame, the number of light rays emanating from the object at an angle $\\theta'$ is constant, equal to $\\frac{dN}{d\\theta'}$.\n", "\n", "By using chain derivation, in the moving frame :\n", "\n", "$$\\frac{dN}{d\\theta} = \\frac{dN}{d\\theta'} \\frac{d\\theta'}{d\\theta}$$\n", "\n", "As we can see, the number of rays per unit angle is multiplied by $\\frac{d\\theta'}{d\\theta}$. Let's plot this function for multiple values of $\\beta$." ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [], "source": [ "beta = var('beta')" ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [], "source": [ "thp = acos((cos(th)-beta)/(1-beta*cos(th)))" ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle -\\frac{\\frac{{\\left(\\beta - \\cos\\left({\\theta}\\right)\\right)} \\beta \\sin\\left({\\theta}\\right)}{{\\left(\\beta \\cos\\left({\\theta}\\right) - 1\\right)}^{2}} + \\frac{\\sin\\left({\\theta}\\right)}{\\beta \\cos\\left({\\theta}\\right) - 1}}{\\sqrt{-\\frac{{\\left(\\beta - \\cos\\left({\\theta}\\right)\\right)}^{2}}{{\\left(\\beta \\cos\\left({\\theta}\\right) - 1\\right)}^{2}} + 1}}\\)" ], "text/latex": [ "$\\displaystyle -\\frac{\\frac{{\\left(\\beta - \\cos\\left({\\theta}\\right)\\right)} \\beta \\sin\\left({\\theta}\\right)}{{\\left(\\beta \\cos\\left({\\theta}\\right) - 1\\right)}^{2}} + \\frac{\\sin\\left({\\theta}\\right)}{\\beta \\cos\\left({\\theta}\\right) - 1}}{\\sqrt{-\\frac{{\\left(\\beta - \\cos\\left({\\theta}\\right)\\right)}^{2}}{{\\left(\\beta \\cos\\left({\\theta}\\right) - 1\\right)}^{2}} + 1}}$" ], "text/plain": [ "-((beta - cos(th))*beta*sin(th)/(beta*cos(th) - 1)^2 + sin(th)/(beta*cos(th) - 1))/sqrt(-(beta - cos(th))^2/(beta*cos(th) - 1)^2 + 1)" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%display latex\n", "diff(thp,th)" ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [], "source": [ "aberration = abs(diff(thp,th)) # abs needed if we want negative angles" ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 10 graphics primitives" ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P = plot(aberration.subs(beta=0.), [-pi*.99,pi*.99])\n", "for i in range(1,10):\n", " P += plot(aberration.subs({beta: 0.1*i}), [-pi*.99,pi*.99])\n", "P.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see, the effect does focus rays toward the direction of motion. One can also check that the integral does not depend on $\\beta$.\n", "\n", "This is a fast cython implementation:" ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [], "source": [ "%%cython\n", "from libc.math cimport cos, sin ,sqrt\n", "\n", "cpdef float focalisation_factor(float th, float beta):\n", " # uses an other expression stricly equal, but faster to compute.\n", " return (cos(th)*(cos(th)+beta)+sin(th)**2)/\\\n", " (sin(th)**2*sqrt(1-beta**2)+1/sqrt(1-beta**2)*(beta+cos(th))**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, this is the final code for the intersection: " ] }, { "cell_type": "code", "execution_count": 91, "metadata": {}, "outputs": [], "source": [ "%%cython\n", "from libc.math cimport cos, sin, acos, sqrt, abs, atan2\n", "cimport cython\n", "from __main__ import profile\n", "from __main__ import xyz_to_spherical\n", "from __main__ import spherical_to_xyz\n", "from __main__ import temp_to_XYZ\n", "from __main__ import focalisation_factor\n", "\n", "@cython.boundscheck(False)\n", "@cython.wraparound(False)\n", "cpdef tuple intersection(list curve, float m, float alpha, float beta, \n", " float dmin, float dmax):\n", " cdef float x, y, z\n", " cdef float x2, y2, z2\n", " cdef float r, theta, phi\n", " cdef int n, i\n", " cdef float t\n", " cdef float sinalpha, cosalpha\n", " cdef float sinbeta, cosbeta\n", " cdef float X, Y, Z\n", " cdef float X0, Y0, Z0\n", " cdef float dt, dt0, dr, dtheta, dphi\n", " cdef float dx, dy, dz\n", " cdef float th, rho, doppler, beta_rel\n", " X, Y, Z = 0., 0., 0. # return values\n", " # 20 percent speed gain\n", " sinalpha = sin(alpha)\n", " cosalpha = cos(alpha)\n", " sinbeta = sin(beta)\n", " cosbeta = cos(beta)\n", " n = len(curve)\n", " r, theta, phi = curve[0][2:5]\n", " dt0 = curve[1][1]-curve[0][1]\n", " # rotations\n", " x, y, z = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta)\n", " x, y, z = x, y*cos(beta)-z*sin(beta), z*cos(beta)+y*sin(beta)\n", " z = z*cos(alpha)+x*sin(alpha)\n", " for i in range(1, n): \n", " r = curve[i][2]\n", " theta = curve[i][3]\n", " phi = curve[i][4]\n", " # rotations\n", " x2, y2, z2 = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta)\n", " y2, z2 = y2*cosbeta-z2*sinbeta, z2*cosbeta+y2*sinbeta\n", " x2, z2 = x2*cosalpha-z2*sinalpha, z2*cosalpha+x2*sinalpha\n", " if z!=z2:\n", " t = z/(z-z2)\n", " if t>=0 and t<1 and curve[i][2]>dmin and curve[i][2]" ] }, "execution_count": 92, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%display plain\n", "data = np.zeros( (ny, nx, 3), dtype=float )\n", "render()\n", "data_rgb = XYZ_to_RGB(data)\n", "img5 = toimage(data_rgb)\n", "# img5.save(\"my_home_made_black_hole.png\") # uncomment to save\n", "img5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The difference with the previous image seems small, but that's only because the translation to RGB introduces luminosity clipping. In fact, the white area is twice as bright in the new picture." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion\n", "\n", "Here is a small recap of all the steps we went through:\n", "\n", "### Geometric image:" ] }, { "cell_type": "code", "execution_count": 93, "metadata": {}, "outputs": [ { "data": { "image/jpeg": 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"text/plain": [ "" ] }, "execution_count": 93, "metadata": {}, "output_type": "execute_result" } ], "source": [ "img1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Disk thickness:" ] }, { "cell_type": "code", "execution_count": 94, "metadata": {}, "outputs": [ { "data": { "image/jpeg": 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"text/plain": [ "" ] }, "execution_count": 94, "metadata": {}, "output_type": "execute_result" } ], "source": [ "img2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Black body object:" ] }, { "cell_type": "code", "execution_count": 95, "metadata": {}, "outputs": [ { "data": { "image/jpeg": 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"text/plain": [ "" ] }, "execution_count": 95, "metadata": {}, "output_type": "execute_result" } ], "source": [ "img3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Doppler effect added:" ] }, { "cell_type": "code", "execution_count": 96, "metadata": {}, "outputs": [ { "data": { "image/jpeg": 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", "text/plain": [ "" ] }, "execution_count": 96, "metadata": {}, "output_type": "execute_result" } ], "source": [ "img4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Relativistic aberration added:" ] }, { "cell_type": "code", "execution_count": 97, "metadata": {}, "outputs": [ { "data": { "image/jpeg": 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", 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