Added hypercube on a string example

content/2DPGA/ex_2dpga_hypercube_on_string.ipynb

@@ -0,0 +1,207 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "169aa061-abb7-4888-83cb-088b0ad87af9",
+   "metadata": {},
+   "source": [
+    "# Hypercube on a string\n",
+    "\n",
+    "A demo of the famous tesseract on a string! More info can be found here: https://enki.ws/ganja.js/examples/pga_dyn.html"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "2dc7b21b-034b-42e9-ad83-05d9605de074",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Note: you may need to restart the kernel to use updated packages.\n"
+     ]
+    }
+   ],
+   "source": [
+    "%pip install -q kingdon anywidget==0.9.9"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "ebb1e69c-7bb1-4eeb-a6a0-dbf06c76c4d4",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "from kingdon import Algebra\n",
+    "from sympy import cos, sin, Symbol\n",
+    "import ipywidgets"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "6dd82824-271e-4b23-a547-993d9c771149",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def euler(f,y,h):\n",
+    "    return [yi + h*fi for yi, fi in zip(y, f(*y))]\n",
+    "\n",
+    "def RK4(f,y,h):\n",
+    "    k1 = f(*y)\n",
+    "    k2 = f(*[yi + 0.5*h*k1i for yi, k1i in zip(y, k1)])\n",
+    "    k3 = f(*[yi + 0.5*h*k2i for yi, k2i in zip(y, k2)])\n",
+    "    k4 = f(*[yi + h*k3i for yi, k3i in zip(y, k3)])\n",
+    "    return [yi + (h/3)*(k2i + k3i + (k1i + k4i)*0.5) \n",
+    "            for yi, k1i, k2i, k3i, k4i in zip(y, k1, k2, k3, k4)]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a48fa9e9-b26b-4d5a-b2e7-4c2d12e5a8ca",
+   "metadata": {},
+   "source": [
+    "Hint: try increasing $d$!"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "0d34bcef-2f02-49ff-955a-87fd3d694147",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "d = 2\n",
+    "alg = Algebra(d, 0, 1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "0ffd82d4-cfba-41e5-879e-f9ad4e284f20",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "points = [\n",
+    "    alg.vector([1.0, *(float(x)-0.5 for x in bin(i)[2:].zfill(d))]).dual()\n",
+    "    for i in range(2**d)\n",
+    "]\n",
+    "edges = [\n",
+    "    [a, b]\n",
+    "    for i, a in enumerate(points)\n",
+    "    for j, b in enumerate(points)\n",
+    "    if not (i<=j or (i ^ j) & ((i ^ j) - 1))\n",
+    "]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "be300f39-b86d-4121-997b-a647a37e0348",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Gravitational force and spring constant\n",
+    "fg = alg.multivector(e02=-9.81)\n",
+    "spring_constant = 12\n",
+    "# attach = alg.evenmv(e=1, e02=-0.25) >> points[2**d-1]\n",
+    "attach = alg.evenmv(e=1, e02=-1) * points[2**d-1]\n",
+    "\n",
+    "def force(M, B):\n",
+    "    gravitational = (M.reverse() >> fg).dual()\n",
+    "    hooke = -spring_constant*((M.reverse() >> attach) & points[2**d-1])\n",
+    "    damping = (-0.25 * B).dual()\n",
+    "    return hooke + gravitational + damping\n",
+    "\n",
+    "state = [\n",
+    "    alg.evenmv(e=1, e01=0.0, e02=0.0, e12=0.0),           # The starting position and orientation in space. (identity) \n",
+    "    alg.multivector(e01=0.0, e02=0.0, e12=-0.2)           # The starting linear and rotational velocity in body.\n",
+    "]\n",
+    "\n",
+    "dState = lambda M, B: [                                   # Change in M and B\n",
+    "    -0.5 * M * B,\n",
+    "    (force(M, B) +  B.cp(B.dual())).undual()\n",
+    "]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "9a395761-71f5-4854-aaf0-b675d922f3d0",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "cd4171369bfa4943be2358538a1971ad",
+       "version_major": 2,
+       "version_minor": 1
+      },
+      "text/plain": [
+       "GraphWidget(cayley=[['1', 'e0', 'e1', 'e2', 'e01', 'e02', 'e12', 'e012'], ['e0', '0', 'e01', 'e02', '0', '0', …"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def graph_func():\n",
+    "    global state\n",
+    "    \n",
+    "    for _ in range(10):\n",
+    "        state = euler(dState, state, 1/600)\n",
+    "    # state = RK4(dState, state, 1/60)\n",
+    "    new_edges = [[state[0] >> p for p in edge] for edge in edges]\n",
+    "\n",
+    "    return [\n",
+    "        *new_edges,\n",
+    "        0x007799,\n",
+    "        attach, \n",
+    "        [attach, state[0] >> points[2**d-1]],\n",
+    "    ]\n",
+    "\n",
+    "alg.graph(\n",
+    "    graph_func,\n",
+    "    animate=True,\n",
+    "    scale=0.5,\n",
+    "    lineWidth=6,\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "bfac1ff2-0180-40b4-ac7e-2b63834811ca",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.10.14"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

jp_app_launcher_config.yaml

@@ -38,6 +38,12 @@
   type: notebook
   catalog: 2DPGA
 
+- title: Tesseract on a string
+  source: content/2DPGA/ex_2dpga_hypercube_on_string.ipynb
+  icon: images/pga2d_hypercube_on_string.svg
+  type: notebook
+  catalog: 2DPGA
+
 - title: Pointcloud Fitting
   source: content/ex_pointcloud.ipynb
   type: notebook