tree-in-wind.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A project to render a tree with leaves in the wind. Bonus points to render a shadow as well?\n",
    "\n",
    "Thus far, I've got an extremely simple rigid-body simulation working (Oliapuram & Kumar 2010). Future work would make sure I'm being faithful to their dynamics math, make the code more general, and add support for wind fields.\n",
    "\n",
    "### Refs\n",
    "\n",
    "#### Tree animation\n",
    "Oliapuram & Kumar (2010) Realtime Forest Animation in Wind\n",
    "Quigley, Yu, Huang, Lin, Fedkiw (2017) Real-time Interactive Tree Animation\n",
    "Xu, Yang, Ding, Buck-Sorlin (2020) Physics-based algorithm to simulate tree dynamics under wind load\n",
    "\n",
    "#### Mechanics\n",
    "Sussman & Wisdom, Structure + Interpretation of Mechanics https://tgvaughan.github.io/sicm/\n",
    "https://github.com/sicmutils/sicmutils\n",
    "\n",
    "#### Navier-Stokes (for wind fields)\n",
    "- https://lorenabarba.com/blog/cfd-python-12-steps-to-navier-stokes/\n",
    "- https://www.ibiblio.org/e-notes/webgl/gpu/fluid.htm\n",
    "- http://developer.download.nvidia.com/books/HTML/gpugems/gpugems_ch38.html\n",
    "- http://jamie-wong.com/2016/08/05/webgl-fluid-simulation/\n",
    "- https://github.com/amandaghassaei/FluidSimulation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as animation\n",
    "from IPython.display import HTML\n",
    "import random\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Attempting a first pass at things from Oliapuram & Kumar's Realtime Forest Animation in Wind\n",
    "\n",
    "def deg_to_rad(deg):\n",
    "    return deg/360*np.pi*2\n",
    "\n",
    "preferred = [deg_to_rad(90), deg_to_rad(60), deg_to_rad(120), deg_to_rad(90), deg_to_rad(45), deg_to_rad(90), deg_to_rad(90+45)]\n",
    "parent = [None, 0, 0, 1, 1, 2, 2] # a simple tree\n",
    "\n",
    "# Choose some random angles and see how we relax back to preferred angles\n",
    "angles = (np.array(preferred)*np.random.uniform(0.8, 1.2)).tolist()\n",
    "velo = [0 for p in preferred]\n",
    "\n",
    "k = 0.1\n",
    "kr = 0.5\n",
    "#mu = 30\n",
    "mu = 40\n",
    "\n",
    "history = []\n",
    "dt = .1\n",
    "for _ in range(int(60/dt)):\n",
    "    history.append(tuple(angles))\n",
    "\n",
    "    n_angles = list(angles)\n",
    "    n_velo = list(velo)\n",
    "    rest_child = [0 for _ in preferred]\n",
    "    rest = 0\n",
    "    for i in range(len(preferred))[::-1]:\n",
    "        rest = k * (preferred[i] - angles[i])\n",
    "        damp = -mu * velo[i] * abs(velo[i])\n",
    "        accel = (rest + damp + kr*rest_child[i]) # hack... needs mass=1\n",
    "        n_angles[i] += velo[i] * dt + accel * dt**2 / 2\n",
    "        n_velo[i] += accel * dt\n",
    "\n",
    "        # Save our restoration force for parent\n",
    "        assert parent[i] is None or parent[i] < i\n",
    "        if parent[i] is not None:\n",
    "            rest_child[parent[i]] += rest\n",
    "    angles = n_angles\n",
    "    velo = n_velo\n",
    "\n",
    "    #rest_root = k * (preferred - angles[0])\n",
    "    #velo[0] += (kr * rest_root + rest) * dt\n",
    "    #angles[0] += velo[0] * dt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = plt.figure()\n",
    "lim = 3\n",
    "plt.xlim(-lim, lim)\n",
    "plt.ylim(0, lim)\n",
    "\n",
    "angles = history\n",
    "'''\n",
    "angles = [\n",
    "    (np.pi/2, np.pi/2),\n",
    "    (1.2*np.pi/2, np.pi/2),\n",
    "    (np.pi/2, np.pi/2),\n",
    "    (0.7*np.pi/2, np.pi/2),\n",
    "    (np.pi/2, np.pi/2),\n",
    "]\n",
    "'''\n",
    "lines = [plt.plot([], [], 'r-')[0] for _ in preferred]\n",
    "plt.xticks([])\n",
    "plt.yticks([])\n",
    "\n",
    "def update_line(t):\n",
    "    points = [\n",
    "        np.array([np.cos(a), np.sin(a)])\n",
    "        for a in angles[t]\n",
    "    ]\n",
    "    for b in range(len(preferred)):\n",
    "        par = np.array([0, 0])\n",
    "        if parent[b] is not None:\n",
    "            par = points[parent[b]]\n",
    "            points[b] += par\n",
    "        lines[b].set_data(*zip(par, points[b]))\n",
    "    return []\n",
    "\n",
    "line_ani = animation.FuncAnimation(f, update_line, len(angles), fargs=(),\n",
    "                                   interval=100*dt, blit=True)\n",
    "plt.close()\n",
    "HTML(line_ani.to_html5_video())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# some sample dynamics code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "#https://www.toptal.com/game/video-game-physics-part-i-an-introduction-to-rigid-body-dynamics\n",
    "class Particle(object):\n",
    "    def __init__(self):\n",
    "        self.position = np.array([random.randint(0, 10), random.randint(0, 10)], dtype=np.float)\n",
    "        self.velocity = np.array([0., 0])\n",
    "        self.mass = 1\n",
    "\n",
    "    def step(self, force, dt):\n",
    "        acceleration = force / self.mass\n",
    "        self.velocity += acceleration * dt\n",
    "        self.position += self.velocity * dt\n",
    "\n",
    "    def __repr__(self):\n",
    "        return f'Particle(position={self.position}, velocity={self.velocity}, mass={self.mass})'\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Particle(position=[10.    0.19], velocity=[ 0.   -9.81], mass=1)]\n",
      "[Particle(position=[ 10.   -19.43], velocity=[  0.   -19.62], mass=1)]\n",
      "[Particle(position=[ 10.   -48.86], velocity=[  0.   -29.43], mass=1)]\n",
      "[Particle(position=[ 10.  -88.1], velocity=[  0.   -39.24], mass=1)]\n",
      "[Particle(position=[  10.   -137.15], velocity=[  0.   -49.05], mass=1)]\n",
      "[Particle(position=[  10.   -196.01], velocity=[  0.   -58.86], mass=1)]\n",
      "[Particle(position=[  10.   -264.68], velocity=[  0.   -68.67], mass=1)]\n",
      "[Particle(position=[  10.   -343.16], velocity=[  0.   -78.48], mass=1)]\n",
      "[Particle(position=[  10.   -431.45], velocity=[  0.   -88.29], mass=1)]\n",
      "[Particle(position=[  10.   -529.55], velocity=[  0.  -98.1], mass=1)]\n"
     ]
    }
   ],
   "source": [
    "def sim(time=10, dt=1):\n",
    "    curr = 0\n",
    "    particles = [Particle()]\n",
    "    while curr < time:\n",
    "        for particle in particles:\n",
    "            particle.step(np.array([0, -9.81 * particle.mass]), dt)\n",
    "        curr += dt\n",
    "        print(particles)\n",
    "sim()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = plt.figure()\n",
    "data = np.random.rand(2, 25)\n",
    "l, = plt.plot([], [], 'r-')\n",
    "plt.xlim(0, 1)\n",
    "plt.ylim(0, 1)\n",
    "plt.xlabel('x')\n",
    "plt.title('test')\n",
    "def update_line(num, data, line):\n",
    "    line.set_data(data[..., :num])\n",
    "    return []\n",
    "\n",
    "line_ani = animation.FuncAnimation(f, update_line, 25, fargs=(data, l),\n",
    "                                   interval=100, blit=True)\n",
    "plt.close()\n",
    "HTML(line_ani.to_html5_video())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "display_name": "Python 3",
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