{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 3D Plot of a vector field on $\\mathbb{S}^2$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we set up the notebook to display mathematical objects using LaTeX formatting:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### $\\mathbb{S}^2$ as a 2-dimensional differentiable manifold\n", "\n", "We declare $\\mathbb{S}^2$ as a differentiable manifold of dimension 2 over $\\mathbb{R}$ and endow it with the stereographic charts from the North pole (`stereoN`) and the South pole (`stereoS`):" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left(U ,\\left(\\frac{\\partial}{\\partial x },\\frac{\\partial}{\\partial y }\\right)\\right), \\left(V ,\\left(\\frac{\\partial}{\\partial {x'} },\\frac{\\partial}{\\partial {y'} }\\right)\\right), \\left(W ,\\left(\\frac{\\partial}{\\partial x },\\frac{\\partial}{\\partial y }\\right)\\right), \\left(W ,\\left(\\frac{\\partial}{\\partial {x'} },\\frac{\\partial}{\\partial {y'} }\\right)\\right)\\right]$ " ], "text/plain": [ "[Coordinate frame (U, (d/dx,d/dy)),\n", " Coordinate frame (V, (d/dxp,d/dyp)),\n", " Coordinate frame (W, (d/dx,d/dy)),\n", " Coordinate frame (W, (d/dxp,d/dyp))]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2 = Manifold(2, 'S^2', latex_name=r'\\mathbb{S}^2', start_index=1)\n", "U = S2.open_subset('U')\n", "V = S2.open_subset('V')\n", "S2.declare_union(U, V)\n", "stereoN. = U.chart()\n", "stereoS. = V.chart(r\"xp:x' yp:y'\")\n", "stereoN_to_S = stereoN.transition_map(stereoS, (x/(x^2+y^2), y/(x^2+y^2)), \n", " intersection_name='W',\n", " restrictions1= x^2+y^2!=0, \n", " restrictions2= xp^2+xp^2!=0)\n", "stereoS_to_N = stereoN_to_S.inverse()\n", "W = U.intersection(V)\n", "eU = stereoN.frame()\n", "eV = stereoS.frame()\n", "S2.frames()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Spherical coordinates

\n", "

The standard spherical (or polar) coordinates $(\\theta,\\phi)$ are defined on the open domain $A\\subset W \\subset \\mathbb{S}^2$ that is the complement of the \"origin meridian\"; since the latter is the half-circle defined by $y=0$ and $x\\geq 0$, we declare:

" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} x & = & -\\frac{\\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\theta}\\right) - 1} \\\\ y & = & -\\frac{\\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\theta}\\right) - 1} \\end{array}\\right.$ " ], "text/plain": [ "x = -cos(ph)*sin(th)/(cos(th) - 1)\n", "y = -sin(ph)*sin(th)/(cos(th) - 1)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = W.open_subset('A', coord_def={stereoN.restrict(W): (y!=0, x<0), \n", " stereoS.restrict(W): (yp!=0, xp<0)})\n", "spher. = A.chart(r'th:(0,pi):\\theta ph:(0,2*pi):\\phi')\n", "spher_to_stereoN = spher.transition_map(stereoN.restrict(A), \n", " (sin(th)*cos(ph)/(1-cos(th)),\n", " sin(th)*sin(ph)/(1-cos(th))) )\n", "spher_to_stereoN.set_inverse(2*atan(1/sqrt(x^2+y^2)), atan2(-y,-x)+pi)\n", "spher_to_stereoN.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Embedding of $\\mathbb{S}^2$ into $\\mathbb{R}^3$\n", "

Let us first declare $\\mathbb{R}^3$ as a 3-dimensional manifold covered by a single chart (the so-called Cartesian coordinates):

" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathbb{R}^3,(X, Y, Z)\\right)$ " ], "text/plain": [ "Chart (R^3, (X, Y, Z))" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R3 = Manifold(3, 'R^3', r'\\mathbb{R}^3', start_index=1)\n", "cart. = R3.chart() ; cart" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The embedding of the sphere is defined as a differential mapping $\\Phi: \\mathbb{S}^2 \\rightarrow \\mathbb{R}^3$:

" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "Phi = S2.diff_map(R3, {(stereoN, cart): [2*x/(1+x^2+y^2), 2*y/(1+x^2+y^2),\n", " (x^2+y^2-1)/(1+x^2+y^2)],\n", " (stereoS, cart): [2*xp/(1+xp^2+yp^2), 2*yp/(1+xp^2+yp^2),\n", " (1-xp^2-yp^2)/(1+xp^2+yp^2)]},\n", " name='Phi', latex_name=r'\\Phi')" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\Phi:& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R}^3 \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(\\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), \\cos\\left({\\theta}\\right)\\right) \\end{array}$ " ], "text/plain": [ "Phi: S^2 --> R^3\n", "on A: (th, ph) |--> (X, Y, Z) = (cos(ph)*sin(th), sin(ph)*sin(th), cos(th))" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.expr(stereoN.restrict(A), cart)\n", "Phi.display(spher, cart)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Let us use $\\Phi$ to draw the grid of spherical coordinates $(\\theta,\\phi)$ in terms of the Cartesian coordinates $(X,Y,Z)$ of $\\mathbb{R}^3$:

" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "graph_spher = spher.plot(chart=cart, mapping=Phi, nb_values=11, color='blue')" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph_spher" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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YrmJW4Nh/ZQUYWI9HAW78eUG+a9sAtLe359uEFLjpppseeOCBDRs23HPPPVVV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\n/Xe044wuuixwJLLh1VfzD8uBz9czbx5a3xIKfSa3qJUFj4V/i8CyXv3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MmjWr2iYMYfXq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\nMFQE47kbmpGJEyeOHDnSKLuhgfn/AThUh9RH1kNhAAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(graph_spher, viewer='tachyon')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A vector field on $\\mathbb{S}^2$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}v = \\frac{\\partial}{\\partial x } -2 \\frac{\\partial}{\\partial y }$ " ], "text/plain": [ "v = d/dx - 2 d/dy" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v = S2.vector_field(name='v')\n", "v[eU,:] = [1, -2]\n", "v.display(eU)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}v = \\left( -{x'}^{2} + 4 \\, {x'} {y'} + {y'}^{2} \\right) \\frac{\\partial}{\\partial {x'} } + \\left( -2 \\, {x'}^{2} - 2 \\, {x'} {y'} + 2 \\, {y'}^{2} \\right) \\frac{\\partial}{\\partial {y'} }$ " ], "text/plain": [ "v = (-xp^2 + 4*xp*yp + yp^2) d/dxp + (-2*xp^2 - 2*xp*yp + 2*yp^2) d/dyp" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.add_comp_by_continuation(eV, W, chart=stereoS)\n", "v.display(eV)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

A 3D view of the vector field $v$ is obtained via the embedding $\\Phi$:

" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "graph_v = v.plot(chart=cart, mapping=Phi, chart_domain=spher, nb_values=11, scale=0.2)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph_v" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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DnM6jVpoCQG3tu/ApnPAvfD0Lp4Da2g/GjRsX35iJVvaP4KPAdsMY2fvBNb1nzpw5c+bM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"text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(graph_v, viewer='tachyon')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us superpose the plot of the spherical coordinate grid:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb|<class|\\phantom{\\verb!x!}\\verb|'sage.plot.plot3d.base.Graphics3dGroup'>|$ " ], "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph = graph_spher + graph_v \n", "type(graph)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we permute `graph_v` and `graph_spher` in the graphic sum, we get an error:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb|<class|\\phantom{\\verb!x!}\\verb|'sage.plot.plot3d.base.Graphics3dGroup'>|$ " ], "text/plain": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph = graph_v + graph_spher\n", "type(graph)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "ename": "error", "evalue": "Error -3 while decompressing: invalid distance too far back", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31merror\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mgraph\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m/home/eric/sage/beta1/local/lib/python2.7/site-packages/IPython/core/displayhook.pyc\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, result)\u001b[0m\n\u001b[1;32m 244\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstart_displayhook\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 245\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwrite_output_prompt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 246\u001b[0;31m \u001b[0mformat_dict\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmd_dict\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcompute_format_data\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 247\u001b[0m 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"\u001b[0;32m/home/eric/sage/beta1/local/lib/python/zipfile.pyc\u001b[0m in \u001b[0;36mread1\u001b[0;34m(self, n)\u001b[0m\n\u001b[1;32m 682\u001b[0m data = self._decompressor.decompress(\n\u001b[1;32m 683\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_unconsumed\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 684\u001b[0;31m \u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mlen_readbuffer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mMIN_READ_SIZE\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 685\u001b[0m )\n\u001b[1;32m 686\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31merror\u001b[0m: Error -3 while decompressing: invalid distance too far back" ] } ], "source": [ "graph" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The display with tachyon viewer is fine:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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BY3DU65XwCRxu2LcDEeIDaCT9nhBnldN74okn2nMWn0/Cq+0ZIRKYCv8XZsGv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\nYUk9h031YwQUbQMcDvSN+wj2w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