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@mgeier
Forked from moble/CompareSquads.ipynb
Last active May 27, 2023 09:35
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Compare quaternion interpolation methods
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{
"cells": [
{
"cell_type": "raw",
"id": "6a781d91-4dc5-4112-af17-64e4fb693688",
"metadata": {
"execution": {
"iopub.execute_input": "2023-05-25T13:18:59.236802Z",
"iopub.status.busy": "2023-05-25T13:18:59.236454Z",
"iopub.status.idle": "2023-05-25T13:19:02.951756Z",
"shell.execute_reply": "2023-05-25T13:19:02.949886Z",
"shell.execute_reply.started": "2023-05-25T13:18:59.236777Z"
},
"tags": []
},
"source": [
"import sys\n",
"from pathlib import Path\n",
"\n",
"executable = str(Path(sys.executable).resolve())\n",
"\n",
"! {executable} -m pip install numpy matplotlib quaternionic splines"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "f81ec81d-1da8-4df5-b942-d6e1c262c0b0",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"import quaternionic\n",
"from splines.quaternion import Squad, CatmullRom, UnitQuaternion, canonicalized\n",
"from helper import angles2quat, animate_rotations, display_animation"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "a9874dc2-42ad-45e3-99f7-3ff40a33ea83",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"# Some helpful utilities for converting between `splines` and `quaternionic`\n",
"\n",
"def uq(q):\n",
" return UnitQuaternion.from_unit_xyzw(q.vector.tolist() + [q.w[()],])\n",
"\n",
"def q(uq):\n",
" try:\n",
" iterator = iter(uq)\n",
" except TypeError:\n",
" return quaternionic.array(uq.wxyz)\n",
" else:\n",
" return quaternionic.array([uqi.wxyz for uqi in uq])\n",
"\n",
"class QuaternionicSquad:\n",
" def __init__(self, Rs, t):\n",
" self.Rs = Rs\n",
" self.grid = t\n",
" def evaluate(self, t):\n",
" try:\n",
" iterator = iter(t)\n",
" except TypeError:\n",
" return uq(quaternionic.squad(self.Rs, self.grid, np.array([t])[0]))\n",
" else:\n",
" return list(map(uq, quaternionic.squad(self.Rs, self.grid, np.array(t))))"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "39708d61-b5d9-4d8b-a61e-e54a3b9542f7",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"def evaluate(spline, frames=200):\n",
" times = np.linspace(\n",
" spline.grid[0], spline.grid[-1], frames, endpoint=False)\n",
" return spline.evaluate(times)"
]
},
{
"cell_type": "markdown",
"id": "6e53ab72-b3da-4754-a438-c37a150cd500",
"metadata": {},
"source": [
"To show the phenomenon, we need a large angle,\n",
"followed by multiple small angles\n",
"with large changes in rotation axis in between.\n",
"\n",
"See https://splines.readthedocs.io/en/0.3.0/euclidean/catmull-rom-properties.html#Wrong-Tangent-Vectors\n",
"for a similar situation in the context of Euclidean splines."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "33e0a5d6-571e-47ab-a23e-8eb56e804183",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"rotations = [\n",
" angles2quat(0, 0, 0),\n",
" angles2quat(90, 0, -45),\n",
" angles2quat(-45, 45, -90),\n",
" angles2quat(135, -35, 90),\n",
" angles2quat(134.5, -34, 91),\n",
" angles2quat(134.8, -33, 89),\n",
" angles2quat(90, 0, 0),\n",
"]\n",
"\n",
"rotations_periodic = list(canonicalized(rotations + rotations[:1]))\n",
"\n",
"# centripetal parameterization\n",
"angles = np.array([\n",
" a.rotation_to(b).angle\n",
" for a, b in zip(rotations_periodic, rotations_periodic[1:])])\n",
"t = times = np.concatenate([[0], np.cumsum(np.sqrt(angles))])"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "e383735b-747d-4902-82e7-4194015429b4",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"cr = CatmullRom(rotations, times, endconditions='closed')"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "4ba800cd-59ed-4256-939e-5e4ec9d7c48c",
"metadata": {},
"outputs": [],
"source": [
"sq = Squad(rotations, times)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "53be7a68-d47a-454f-95d3-441925916f1e",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"Rs = q(rotations_periodic)\n",
"\n",
"qs = QuaternionicSquad(Rs, t)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "b3ab58ca-aafd-4b3a-b565-e10a651f45b2",
"metadata": {
"tags": []
},
"outputs": [
{
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"\n",
" /* Define the Animation class */\n",
" function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
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" }\n",
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"\n",
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" document.getElementById(this.img_id).src =\n",
" this.frames[this.current_frame].src;\n",
" document.getElementById(this.slider_id).value = this.current_frame;\n",
" }\n",
"\n",
" Animation.prototype.next_frame = function()\n",
" {\n",
" this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
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"\n",
" Animation.prototype.previous_frame = function()\n",
" {\n",
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