4d-interpolation-arc-length.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "using https://splines.readthedocs.io/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import HTML\n",
    "from matplotlib.animation import FuncAnimation\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import splines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from splines.quaternion import Quaternion\n",
    "from helper import angles2quat, animate_rotations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "rotations = [\n",
    "    angles2quat(0, 0, 0),\n",
    "    angles2quat(45, 0, 0),\n",
    "    angles2quat(90, 45, 0),\n",
    "    angles2quat(90, 90, 0),\n",
    "    angles2quat(91, 91, 0),\n",
    "    angles2quat(180, 0, 90),\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`alpha=0.5`: centripetal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "vertices = [q.xyzw for q in rotations]\n",
    "s1 = splines.CatmullRom(vertices, alpha=0.5, endconditions='closed')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "s1.grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "s2 = splines.ConstantSpeedAdapter(s1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "s2.grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "times1 = np.linspace(s1.grid[0], s1.grid[-1], 100)\n",
    "times2 = np.linspace(s2.grid[0], s2.grid[-1], 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "normalized1 = [Quaternion(w, (x, y, z)).normalize() for x, y, z, w in s1.evaluate(times1)]\n",
    "normalized2 = [Quaternion(w, (x, y, z)).normalize() for x, y, z, w in s2.evaluate(times2)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ani = animate_rotations({\n",
    "    'non-constant speed': normalized1,\n",
    "    'constant speed': normalized2,\n",
    "}, figsize=(6, 3), interval=60)\n",
    "display(HTML(ani.to_jshtml(default_mode='loop')))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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