Geometric algebra implementation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b09f7672",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "## gimped version of multivec 3d (algebra in plane only now)\n",
    "## eats a vector [a,x,y,xy]\n",
    "## a is scalar part, x,y are vector parts, xy is bivector part\n",
    "class MultiVec2d:\n",
    "    def __init__(self,dvec):\n",
    "        a= dvec[0]# scalar part\n",
    "        x=dvec[1] # e1 vector part\n",
    "        y=dvec[2] # so on\n",
    "        xy=dvec[3] # e1 e2 bivector part\n",
    "        \n",
    "        self.e0=a # scalar part\n",
    "        self.e1 = x # e1 vector part\n",
    "        self.e2 = y # so on\n",
    "        self.e12 = xy # e1 e2 bivector part\n",
    "        \n",
    "        self.vrep= np.array(dvec)\n",
    "        self.gpmatrix = np.array([[a,x,y,-1*xy],\n",
    "                                  [x,a,xy,-1*y],\n",
    "                                  [y,-1*xy,a,x],\n",
    "                                  [xy,-1*y,x,a]\n",
    "                                  ])\n",
    "    def __mul__(self,other):\n",
    "        return(MultiVec2d(self.gpmatrix.dot(other.vrep)))\n",
    "    def __add__(self,other):\n",
    "        return(MultiVec2d(self.vrep+other.vrep))\n",
    "    \n",
    "    def latexPrintSum(self):\n",
    "        a = str(self.e0)+'*1+'+str(self.e1)+r'e_1+'+str(self.e2)+','+str(self.e12)+r'e_1\\land e_2'\n",
    "        ax = plt.axes([0,0,0.3,0.3]) #left,bottom,width,height\n",
    "        ax.set_xticks([])\n",
    "        ax.set_yticks([])\n",
    "        ax.axis('off')\n",
    "        plt.text(0.4,0.4,'$%s$' %a,size=20,color=\"black\")\n",
    "        plt.show()\n",
    "    def latexPrintVec(self):\n",
    "        a = r'['+str(self.e0)+','+str(self.e1)+','+str(self.e2)+','+str(self.e12)+r']'\n",
    "        ax = plt.axes([0,0,0.3,0.3]) #left,bottom,width,height\n",
    "        ax.set_xticks([])\n",
    "        ax.set_yticks([])\n",
    "        ax.axis('off')\n",
    "        plt.text(0.4,0.4,'$%s$' %a,size=20,color=\"black\")\n",
    "        plt.show()\n",
    "\n",
    "a = MultiVec2d([0,1,0,0])\n",
    "b = MultiVec2d([0,0,1,0])\n",
    "i=a*b\n",
    "z=a+b\n",
    "z.latexPrintVec()\n",
    "g=z*i\n",
    "g.latexPrintVec()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6cbd0910",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f827d711",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "class MultiVec3d:\n",
    "    def __init__(self,dvec):\n",
    "        ## expects a numpy datavector\n",
    "        a= dvec[0]# scalar part\n",
    "        x=dvec[1] # e1 vector part\n",
    "        y=dvec[2] # so on\n",
    "        z=dvec[3]\n",
    "        xy=dvec[4] # e1 e2 bivector part\n",
    "        yz=dvec[5]\n",
    "        zx=dvec[6]\n",
    "        xyz=dvec[7] # e1e2e3 trivector part\n",
    "        \n",
    "        self.e0=a # scalar part\n",
    "        self.e1 = x # e1 vector part\n",
    "        self.e2 = y # so on\n",
    "        self.e3 = z\n",
    "        self.e12 = xy # e1 e2 bivector part\n",
    "        self.e23 = yz\n",
    "        self.e31 = zx\n",
    "        self.e123 = xyz # e1e2e3 trivector part\n",
    "        \n",
    "        self.vrep= np.array(dvec)\n",
    "        self.gpmatrix = np.array([[a,x,y,z,-1*xy,-1*yz,-1*zx,-1*xyz],\n",
    "                                  [x,a,xy,-1*zx,-1*y,-1*xyz,z,-1*yz],\n",
    "                                  [y,-1*xy,a,yz,x,-1*z,-1*xyz,-1*zx],\n",
    "                                  [z,zx,-1*yz,a,-1*xyz,y,-1*x,-1*xy],\n",
    "                                  [xy,-1*y,x,xyz,a,zx,-1*yz,z],\n",
    "                                  [yz,xyz,-1*z,y,-1*zx,a,xy,x],\n",
    "                                  [zx,z,xyz,-1*x,yz,-1*xy,a,y],\n",
    "                                  [xyz,yz,zx,xy,z,x,y,a]\n",
    "                                  ])\n",
    "    def __mul__(self,other):\n",
    "        return(MultiVec3d(self.gpmatrix.dot(other.vrep)))\n",
    "    def __add__(self,other):\n",
    "        v1=self.vrep\n",
    "        v2=other.vrep\n",
    "        return(MultiVec3d(v1+v2))\n",
    "    def __sub__(self,other):\n",
    "        v1=self.vrep\n",
    "        v2=other.vrep\n",
    "        return(MultiVec3d(v1-v2))\n",
    "    def __truediv__(self,other):\n",
    "        mag=self.dp(self)\n",
    "        mag=abs(mag.e0)\n",
    "        if mag != 0:\n",
    "            invrs=MultiVec3d([1/mag,0,0,0,0,0,0,0])\n",
    "            return(other*invrs)\n",
    "        else:\n",
    "            return(other)\n",
    "\n",
    "    ## dot product\n",
    "    def dp(self,other):\n",
    "        half=MultiVec3d([0.5,0,0,0,0,0,0,0])\n",
    "        return(half*((self*other)+(other*self)))\n",
    "    ## wedge product\n",
    "    def wedge(self,other):\n",
    "        half=MultiVec3d([0.5,0,0,0,0,0,0,0])\n",
    "        return(half*((self*other)-(other*self)))\n",
    "    \n",
    "    def latexPrintSum(self):\n",
    "        a = str(self.e0)+'*1+'+str(self.e1)+r'e_1+'+str(self.e2)+r'e_2+'+str(self.e3)+r'e_3+'+str(self.e12)+r'e_1\\land e_2+'+str(self.e23)+r'e_2\\land e_3+'+str(self.e31)+r'e_3\\land e_1+'+str(self.e123)+r'e_1\\land e_2 \\land e_3'\n",
    "        ax = plt.axes([0,0,0.3,0.3]) #left,bottom,width,height\n",
    "        ax.set_xticks([])\n",
    "        ax.set_yticks([])\n",
    "        ax.axis('off')\n",
    "        plt.text(0.4,0.4,'$%s$' %a,size=20,color=\"black\")\n",
    "        plt.show()\n",
    "    def latexPrintVec(self):\n",
    "        a = r'['+str(self.e0)+','+str(self.e1)+','+str(self.e2)+','+str(self.e3)+','+str(self.e12)+','+str(self.e23)+','+str(self.e31)+','+str(self.e123)+r']'\n",
    "        ax = plt.axes([0,0,0.3,0.3]) #left,bottom,width,height\n",
    "        ax.set_xticks([])\n",
    "        ax.set_yticks([])\n",
    "        ax.axis('off')\n",
    "        plt.text(0.4,0.4,'$%s$' %a,size=20,color=\"black\")\n",
    "        plt.show()\n",
    "\n",
    "a = MultiVec3d([0,1,0,0,0,0,0,0]) ## canonical basis vectors\n",
    "b = MultiVec3d([0,0,1,0,0,0,0,0])\n",
    "c = MultiVec3d([0,0,0,1,0,0,0,0]) \n",
    "i=a*b\n",
    "j=b*c\n",
    "k=c*a\n",
    "\n",
    "(((a+b)/a)).latexPrintVec()\n",
    "#(i*i).latexPrintVec(),j.latexPrintVec(),k.latexPrintVec(),(i*c).latexPrintVec()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6db59ecb",
   "metadata": {},
   "source": [
    "# boilerplate for mathbox"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e0ec6b62",
   "metadata": {},
   "outputs": [],
   "source": [
    "import json\n",
    "import numpy as np\n",
    "from IPython.display import HTML, Javascript, display\n",
    "\n",
    "def json_numpy_serialzer(o):\n",
    "    '''Helper function to serialize NumPy arrays.'''\n",
    "    if isinstance(o, np.ndarray):\n",
    "        return o.tolist()\n",
    "    raise TypeError(\"{} of type {} is not JSON serializable\".format(repr(o), type(o)))\n",
    "\n",
    "def jsglobal(**params):\n",
    "    '''Populate JS global namespace with provided Python obejcts.'''\n",
    "    code = [];\n",
    "    for name, value in params.items():\n",
    "        jsdata = json.dumps(value, default=json_numpy_serialzer)\n",
    "        code.append(\"window.{} = {};\".format(name, jsdata))\n",
    "    display(Javascript(\"\\n\".join(code)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d4043635",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "// Loading the compiled MathBox bundle.\n",
       "require.config({\n",
       "    paths: {\n",
       "        mathBox: '//cdn.rawgit.com/unconed/mathbox/eaeb8e15/build/mathbox-bundle'\n",
       "    }\n",
       "});\n",
       "\n",
       "// Helper function that setups WebGL context and initializes MathBox.\n",
       "window.with_mathbox = function(element, func) {\n",
       "    require(['mathBox'], function(){\n",
       "        var mathbox = mathBox({\n",
       "          plugins: ['core', 'controls', 'cursor', 'mathbox'],\n",
       "          controls: { klass: THREE.OrbitControls },\n",
       "          mathbox: {inspect: false},\n",
       "          element: element[0],\n",
       "          loop: {start: false},\n",
       "            \n",
       "        });\n",
       "        var three = mathbox.three;\n",
       "        three.renderer.setClearColor(new THREE.Color(0xFFFFFF), 1.0);\n",
       "        three.camera.position.set(-1, 1, 2);\n",
       "        three.controls.noKeys = true;\n",
       "        \n",
       "        three.element.style.height = \"400px\";\n",
       "        three.element.style.width = \"100%\";\n",
       "        \n",
       "        function isInViewport(element) {\n",
       "          var rect = element.getBoundingClientRect();\n",
       "          var html = document.documentElement;\n",
       "          var w = window.innerWidth || html.clientWidth;\n",
       "          var h = window.innerHeight || html.clientHeight;\n",
       "          return rect.top < h && rect.left < w && rect.bottom > 0 && rect.right > 0;\n",
       "        }\n",
       "        \n",
       "        // Running update/render loop only for visible plots.\n",
       "        var intervalId = setInterval(function(){\n",
       "            if (three.element.offsetParent === null) {\n",
       "                clearInterval(intervalId);\n",
       "                three.destroy();\n",
       "                return;\n",
       "            }\n",
       "            var visible = isInViewport(three.canvas);\n",
       "            if (three.Loop.running != visible) {\n",
       "                visible? three.Loop.start() : three.Loop.stop();\n",
       "            }\n",
       "        }, 100);\n",
       "\n",
       "        func(mathbox);\n",
       "        \n",
       "        window.dispatchEvent(new Event('resize'));\n",
       "    })\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%javascript\n",
    "\n",
    "// Loading the compiled MathBox bundle.\n",
    "require.config({\n",
    "    paths: {\n",
    "        mathBox: '//cdn.rawgit.com/unconed/mathbox/eaeb8e15/build/mathbox-bundle'\n",
    "    }\n",
    "});\n",
    "\n",
    "// Helper function that setups WebGL context and initializes MathBox.\n",
    "window.with_mathbox = function(element, func) {\n",
    "    require(['mathBox'], function(){\n",
    "        var mathbox = mathBox({\n",
    "          plugins: ['core', 'controls', 'cursor', 'mathbox'],\n",
    "          controls: { klass: THREE.OrbitControls },\n",
    "          mathbox: {inspect: false},\n",
    "          element: element[0],\n",
    "          loop: {start: false},\n",
    "            \n",
    "        });\n",
    "        var three = mathbox.three;\n",
    "        three.renderer.setClearColor(new THREE.Color(0xFFFFFF), 1.0);\n",
    "        three.camera.position.set(-1, 1, 2);\n",
    "        three.controls.noKeys = true;\n",
    "        \n",
    "        three.element.style.height = \"400px\";\n",
    "        three.element.style.width = \"100%\";\n",
    "        \n",
    "        function isInViewport(element) {\n",
    "          var rect = element.getBoundingClientRect();\n",
    "          var html = document.documentElement;\n",
    "          var w = window.innerWidth || html.clientWidth;\n",
    "          var h = window.innerHeight || html.clientHeight;\n",
    "          return rect.top < h && rect.left < w && rect.bottom > 0 && rect.right > 0;\n",
    "        }\n",
    "        \n",
    "        // Running update/render loop only for visible plots.\n",
    "        var intervalId = setInterval(function(){\n",
    "            if (three.element.offsetParent === null) {\n",
    "                clearInterval(intervalId);\n",
    "                three.destroy();\n",
    "                return;\n",
    "            }\n",
    "            var visible = isInViewport(three.canvas);\n",
    "            if (three.Loop.running != visible) {\n",
    "                visible? three.Loop.start() : three.Loop.stop();\n",
    "            }\n",
    "        }, 100);\n",
    "\n",
    "        func(mathbox);\n",
    "        \n",
    "        window.dispatchEvent(new Event('resize'));\n",
    "    })\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3acaf04",
   "metadata": {},
   "source": [
    "# surface plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "44a56d3c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "with_mathbox(element, function(mathbox) {\n",
       "   mathbox.cartesian({},{rotation:(t)=>[0, 0, 0]}) // Setup rotating the coordinate frame\n",
       "     .camera( { proxy: true, position: [0, 0, 1],lookAt:[0,0,0] } )\n",
       "     .grid({axes: [1, 2]})  // Add a grid to it.\n",
       "     .area({width:50, height:50,                       // This defines 2D data source, sampled from JS callback \n",
       "            expr: function(emit, x, y, i, j, t){\n",
       "              var rho = Math.sqrt(x*x+y*y);\n",
       "              var z = Math.sin(rho*10-t*0.5)*0.2 + 0.3;\n",
       "              var r =  (.5  + 0.5* Math.sin(y*t));\n",
       "              var g = (.5  + 0.5* Math.cos(y));\n",
       "              var b = y;\n",
       "              emit(x, y, z);\n",
       "           }})\n",
       "     .surface({color:'#AAA', shaded:true})             // Adding surface primitives, that draw data provided by \n",
       "     .surface({color:'#55A', lineX:true, lineY:true, fill:false, zBias:1}); // the last defined datasource.\n",
       "})\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%javascript\n",
    "with_mathbox(element, function(mathbox) {\n",
    "   mathbox.cartesian({},{rotation:(t)=>[0, 0, 0]}) // Setup rotating the coordinate frame\n",
    "     .camera( { proxy: true, position: [0, 0, 1],lookAt:[0,0,0] } )\n",
    "     .grid({axes: [1, 2]})  // Add a grid to it.\n",
    "     .area({width:50, height:50,                       // This defines 2D data source, sampled from JS callback \n",
    "            expr: function(emit, x, y, i, j, t){\n",
    "              var rho = Math.sqrt(x*x+y*y);\n",
    "              var z = Math.sin(rho*10-t*0.5)*0.2 + 0.3;\n",
    "              var r =  (.5  + 0.5* Math.sin(y*t));\n",
    "              var g = (.5  + 0.5* Math.cos(y));\n",
    "              var b = y;\n",
    "              emit(x, y, z);\n",
    "           }})\n",
    "     .surface({color:'#AAA', shaded:true})             // Adding surface primitives, that draw data provided by \n",
    "     .surface({color:'#55A', lineX:true, lineY:true, fill:false, zBias:1}); // the last defined datasource.\n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "2280088c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "with_mathbox(element, function(mathbox) {\n",
       "\n",
       "mathbox.camera( { proxy: true, position: [0, 0, 4],lookAt:[0,0,0] } )\n",
       "\n",
       "var W = 512, H = 256;\n",
       "mathbox\n",
       "  .rtt({width:W, height:H, type:\"float\", id:\"rtt\"}) // offscreen rendering\n",
       "    // main simulation shader code\n",
       "    .shader({code:`\n",
       "      uniform vec2 dataSize;\n",
       "      uniform vec2 spot;\n",
       "      uniform vec2 fk;\n",
       "      vec4 getsample(vec2 p);\n",
       "      vec2 sample(vec2 p) {\n",
       "        return getsample(mod(p, dataSize)).xy;\n",
       "      }\n",
       "      vec4 main(vec2 p) {\n",
       "        if (length(spot-p)<2.0) {\n",
       "          return vec4(0.0, 0.5, 0.0, 0.0);\n",
       "        }\n",
       "        float f = fk.x, k = fk.y;\n",
       "        const vec2 dx=vec2(1.,0.0), dy=vec2(0.0,1.);\n",
       "        vec2 v = sample(p);\n",
       "        vec2 lap = sample(p+dx)+sample(p-dx)+sample(p+dy)+sample(p-dy)-4.0*v;\n",
       "        float rate = v.x * v.y * v.y;\n",
       "        vec2 dv = vec2(0.2, 0.1)*lap + vec2(-rate, rate);\n",
       "        dv += vec2(f * (1.0 - v.x), -(f + k) * v.y);\n",
       "        v = clamp(v+dv, 0.0, 1.0);\n",
       "        return vec4(v, 0.0, 0.0);\n",
       "      }`, fk:[0.034, 0.056]}, {spot:(t)=>[(t*0.02+0.75)%1*W, (t*0.12+0.5)%1*H]})\n",
       "      .play({  // animate Gray-Scott reaction-diffusion parameters\n",
       "        loop: true, to:4, pace:3.0,\n",
       "        script:[\n",
       "          {fk:[0.034, 0.056]}, \n",
       "          {fk:[0.029, 0.057]},\n",
       "          {fk:[0.014, 0.054]},\n",
       "          {fk:[0.025, 0.060]},\n",
       "          {fk:[0.034, 0.056]}]})\n",
       "      .resample({indices:2}).compose() // this triggers Render-to-Texture pass\n",
       "   .end() // back from offscreen rendering\n",
       "\n",
       "   .cartesian({}, {rotation:(t)=>[t*0.0+1.5, 0, 0]})\n",
       "       // shader to compute surface colors\n",
       "       .shader({code:`\n",
       "          vec4 sample(vec4 p);\n",
       "          uniform vec4 dataSize;\n",
       "          const float pi = 3.141593;\n",
       "          vec4 main(vec4 p) {\n",
       "            float v = sample(p).y;\n",
       "            vec2 pq = p.xy/(dataSize.xy-1.0)*2.0*pi;\n",
       "            return vec4(pq.x/5.0, pq.y/5.0, 0.0, 1.0);\n",
       "          }\n",
       "         `}).resample()\n",
       "       // shader to compute 3d positions of torus vertices\n",
       "       .shader({code:`\n",
       "         uniform vec4 dataSize;\n",
       "         const float pi = 3.141593;\n",
       "         vec4 sample(vec4 p);\n",
       "         vec4 main(vec4 p) {\n",
       "           float v = sample(p).y;\n",
       "           vec2 pq = p.xy/(dataSize.xy-1.0)*2.0*pi;\n",
       "           float r = v*0.2 + 0.3;\n",
       "           float a = 0.7 + r*cos(pq.y);\n",
       "           return vec4(pq.x, 0, pq.y, 0.0);\n",
       "         }`}).resample({source:'#rtt'})\n",
       "       // draw the torus!\n",
       "       .surface({shaded:true, closedX:true, colors:'<<', color:\"#fff\"});\n",
       "\n",
       "   // this hack triggers RTT pass multiple times per frame for faster simulation\n",
       "   mathbox.three.on('update', function(){\n",
       "     var rtt = mathbox.select('rtt')[0].controller.rtt;\n",
       "     for (var i=0; i<5; ++i)\n",
       "       rtt.render()\n",
       "   })\n",
       "})\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%javascript\n",
    "with_mathbox(element, function(mathbox) {\n",
    "\n",
    "mathbox.camera( { proxy: true, position: [0, 0, 4],lookAt:[0,0,0] } )\n",
    "\n",
    "var W = 512, H = 256;\n",
    "mathbox\n",
    "  .rtt({width:W, height:H, type:\"float\", id:\"rtt\"}) // offscreen rendering\n",
    "    // main simulation shader code\n",
    "    .shader({code:`\n",
    "      uniform vec2 dataSize;\n",
    "      uniform vec2 spot;\n",
    "      uniform vec2 fk;\n",
    "      vec4 getsample(vec2 p);\n",
    "      vec2 sample(vec2 p) {\n",
    "        return getsample(mod(p, dataSize)).xy;\n",
    "      }\n",
    "      vec4 main(vec2 p) {\n",
    "        if (length(spot-p)<2.0) {\n",
    "          return vec4(0.0, 0.5, 0.0, 0.0);\n",
    "        }\n",
    "        float f = fk.x, k = fk.y;\n",
    "        const vec2 dx=vec2(1.,0.0), dy=vec2(0.0,1.);\n",
    "        vec2 v = sample(p);\n",
    "        vec2 lap = sample(p+dx)+sample(p-dx)+sample(p+dy)+sample(p-dy)-4.0*v;\n",
    "        float rate = v.x * v.y * v.y;\n",
    "        vec2 dv = vec2(0.2, 0.1)*lap + vec2(-rate, rate);\n",
    "        dv += vec2(f * (1.0 - v.x), -(f + k) * v.y);\n",
    "        v = clamp(v+dv, 0.0, 1.0);\n",
    "        return vec4(v, 0.0, 0.0);\n",
    "      }`, fk:[0.034, 0.056]}, {spot:(t)=>[(t*0.02+0.75)%1*W, (t*0.12+0.5)%1*H]})\n",
    "      .play({  // animate Gray-Scott reaction-diffusion parameters\n",
    "        loop: true, to:4, pace:3.0,\n",
    "        script:[\n",
    "          {fk:[0.034, 0.056]}, \n",
    "          {fk:[0.029, 0.057]},\n",
    "          {fk:[0.014, 0.054]},\n",
    "          {fk:[0.025, 0.060]},\n",
    "          {fk:[0.034, 0.056]}]})\n",
    "      .resample({indices:2}).compose() // this triggers Render-to-Texture pass\n",
    "   .end() // back from offscreen rendering\n",
    "\n",
    "   .cartesian({}, {rotation:(t)=>[t*0.0+1.5, 0, 0]})\n",
    "       // shader to compute surface colors\n",
    "       .shader({code:`\n",
    "          vec4 sample(vec4 p);\n",
    "          uniform vec4 dataSize;\n",
    "          const float pi = 3.141593;\n",
    "          vec4 main(vec4 p) {\n",
    "            float v = sample(p).y;\n",
    "            vec2 pq = p.xy/(dataSize.xy-1.0)*2.0*pi;\n",
    "            return vec4(pq.x/5.0, pq.y/5.0, 0.0, 1.0);\n",
    "          }\n",
    "         `}).resample()\n",
    "       // shader to compute 3d positions of torus vertices\n",
    "       .shader({code:`\n",
    "         uniform vec4 dataSize;\n",
    "         const float pi = 3.141593;\n",
    "         vec4 sample(vec4 p);\n",
    "         vec4 main(vec4 p) {\n",
    "           float v = sample(p).y;\n",
    "           vec2 pq = p.xy/(dataSize.xy-1.0)*2.0*pi;\n",
    "           float r = v*0.2 + 0.3;\n",
    "           float a = 0.7 + r*cos(pq.y);\n",
    "           return vec4(pq.x, 0, pq.y, 0.0);\n",
    "         }`}).resample({source:'#rtt'})\n",
    "       // draw the torus!\n",
    "       .surface({shaded:true, closedX:true, colors:'<<', color:\"#fff\"});\n",
    "\n",
    "   // this hack triggers RTT pass multiple times per frame for faster simulation\n",
    "   mathbox.three.on('update', function(){\n",
    "     var rtt = mathbox.select('rtt')[0].controller.rtt;\n",
    "     for (var i=0; i<5; ++i)\n",
    "       rtt.render()\n",
    "   })\n",
    "})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eabb935e",
   "metadata": {},
   "source": [
    "# passing datapoints\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "451dfd01",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "window.POS = [[-0.021712612066011223, 0.019946908931671718, 0.48508510856524284], [0.0327273957661201, 0.1138860251409253, 0.6685505902762708], [0.07692444531243454, 0.24035530188976806, 0.7943782658085321], [0.1702318453305351, 0.3548976717778088, 0.8734043162384201], [0.2787613469893774, 0.46941649386835466, 0.9415880012813798], [0.30062903587649853, 0.6324125668553141, 1.0356344745792456], [0.3885564727678274, 0.6928208184672779, 1.0128685551846488], [0.45599225293545126, 0.7523575353306768, 0.992430641038287], [0.4571169204470674, 0.8321116789067495, 0.9234562293651387], [0.5077310292328631, 0.9025071251788233, 0.7923438405529885], [0.5831815777901931, 0.8954726925739621, 0.6496760767980221], [0.6239593660611535, 1.0010948355577993, 0.5328431087788859], [0.6851540088017171, 1.011884826260192, 0.3508969811207159], [0.7352006375983341, 0.981815384666931, 0.1530262735660855], [0.7632562168236227, 0.9934318565456078, 0.006785026185938909], [0.8093345534511676, 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      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make an array of 3d points.\n",
    "np.random.seed(123)\n",
    "t = np.linspace(0, 2*np.pi, 1000)\n",
    "x, y, z = np.sin(t*10), np.sin(t*20), np.sin(t*30+0.5)\n",
    "pos = np.vstack([x, y, z]).T\n",
    "pos += np.random.normal(size=pos.shape)*0.02\n",
    "\n",
    "jsglobal(POS=pos) # Pass this array to JS-world as a global variable \"POS\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9a0043a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "with_mathbox(element, function(mathbox) {\n",
       "    mathbox.cartesian({},{rotation:(t)=>[0, t*0.1, 0]})\n",
       "      .grid({axes: [1, 3]})\n",
       "      // Now we can see the data on JS side!\n",
       "      .array({data:POS, channels:3, live:false})\n",
       "      .point({color:\"#55a\"})\n",
       "      .line({width:1.0})\n",
       "})\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%javascript\n",
    "with_mathbox(element, function(mathbox) {\n",
    "    mathbox.cartesian({},{rotation:(t)=>[0, t*0.1, 0]})\n",
    "      .grid({axes: [1, 3]})\n",
    "      // Now we can see the data on JS side!\n",
    "      .array({data:POS, channels:3, live:false})\n",
    "      .point({color:\"#55a\"})\n",
    "      .line({width:1.0})\n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7e2af7db",
   "metadata": {},
   "outputs": [],
   "source": [
    "  var mathbox = mathBox({\n",
    "      plugins: ['core', 'controls', 'cursor', 'mathbox'],\n",
    "      controls: {klass: THREE.OrbitControls}\n",
    "    });\n",
    "    if (mathbox.fallback) throw \"WebGL not supported\"\n",
    "\n",
    "    var three = mathbox.three;\n",
    "    three.renderer.setClearColor(new THREE.Color(0xFFFFFF), 1.0);\n",
    "\tvar camera = mathbox.camera( { proxy: true, position: [0, 0, 3] } );\n",
    "\t\n",
    "\t// save the view as a variable to simplify accessing it later\n",
    "    var view = mathbox.cartesian( {range: [[xMin, xMax], [yMin, yMax]], scale: [2,1]} );\n",
    "\n",
    "\t// axes\n",
    "\tvar xAxis = view.axis( {axis: 1, width: 8, detail: 40, color:\"red\"} );\n",
    "    var xScale = view.scale( {axis: 1, divide: 10, nice:true, zero:true} );\n",
    "    var xTicks = view.ticks( {width: 5, size: 15, color: \"red\", zBias:2} );\n",
    "    var xFormat = view.format( {digits: 2, font:\"Arial\", weight: \"bold\", style: \"normal\", source: xScale} );\n",
    "    var xTicksLabel = view.label( {color: \"red\", zIndex: 1, offset:[0,-20], points: xScale, text: xFormat} );\n",
    "\t\n",
    "\tvar yAxis = view.axis( {axis: 2, width: 8, detail: 40, color:\"green\"} );\n",
    "    var yScale = view.scale( {axis: 2, divide: 5, nice:true, zero:false} );\n",
    "    var yTicks = view.ticks( {width: 5, size: 15, color: \"green\", zBias:2} );\n",
    "    var yFormat = view.format( {digits: 2, font:\"Arial\", weight: \"bold\", style: \"normal\", source: yScale} );\n",
    "    var yTicksLabel = view.label( {color: \"green\", zIndex: 1, offset:[0,0], points: yScale, text: yFormat} );\n",
    "\t\n",
    "\t// grid\n",
    "\tvar grid = view.grid( {width: 2, divideX: 20, divideY: 10, opacity:0.25} );\n",
    "\t\n",
    "\tvar graphData = view.interval({\n",
    "        expr: function (emit, x, i, t)\n",
    "\t\t{\n",
    "          emit( x, x*x );\n",
    "        },\n",
    "\t\twidth: 256,\t\n",
    "\t\tchannels: 2,\n",
    "    });\n",
    "\t\n",
    "    var graphView = view.line( {width: 4, color: \"blue\"} );\n",
    "\t  \n",
    "\t// parameters used by dat.gui\n",
    "var functionText = \"sin(a*x + b)\";\n",
    "var a = 1, b = 1;\n",
    "var\txMin = -3, xMax = 3, yMin = -1,\tyMax = 1;\n",
    "\n",
    "var updateGraphFunc = function() \n",
    "{ \n",
    "\tvar yFunc = Parser.parse( functionText ).toJSFunction( ['x'] );\n",
    "\tgraphData.set(\"expr\", \n",
    "\t    function (emit, x, i, t) \n",
    "\t\t{ \n",
    "\t\t    var y = yFunc(x);\n",
    "\t\t\temit( x, y );\n",
    "\t\t\t}\n",
    "\t);\n",
    "\tview.set(\"range\", [[xMin, xMax], [yMin, yMax]]); \n",
    "}\n",
    "\n",
    "var updateGraph = function() { updateGraphFunc(); };\n",
    "\n",
    "    // GUI controls\n",
    "\n",
    "var gui = new dat.GUI();\n",
    "gui.add( this, 'functionText' ).name('y = f(x) = ');\n",
    "\n",
    "var folder0 = gui.addFolder('Parameters');\n",
    "var aGUI = folder0.add( this, 'a' ).min(0).max(5).step(0.01).name('a = ');\n",
    "var bGUI = folder0.add( this, 'b' ).min(0).max(5).step(0.01).name('b = ');\n",
    "folder0.open();\n",
    "\n",
    "var folder1 = gui.addFolder('Window Range');\n",
    "var xMinGUI = folder1.add( this, 'xMin' );\n",
    "var xMaxGUI = folder1.add( this, 'xMax' );\n",
    "var yMinGUI = folder1.add( this, 'yMin' );\n",
    "var yMaxGUI = folder1.add( this, 'yMax' );\n",
    "folder1.open();\n",
    "\n",
    "gui.add( this, 'updateGraph' ).name(\"Update Graph\");\n",
    "\n",
    "// onChange or onFinishChange\n",
    "aGUI.onChange( updateGraphFunc );\n",
    "bGUI.onChange( updateGraphFunc );\n",
    "xMinGUI.onChange( updateGraphFunc );\n",
    "xMaxGUI.onChange( updateGraphFunc );\n",
    "yMinGUI.onChange( updateGraphFunc );\n",
    "yMaxGUI.onChange( updateGraphFunc );\n",
    "\n",
    "gui.open();\n",
    "\n",
    "// do this last so all structures are set up, all parameters defined\n",
    "updateGraphFunc();\n",
    "\n"
   ]
  }
 ],
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