{
"nbformat": 4,
"nbformat_minor": 2,
"metadata": {
"colab": {
"name": "pytransform3d.ipynb",
"provenance": [],
"collapsed_sections": [],
"toc_visible": true,
"authorship_tag": "ABX9TyPxLHH6VLyllr+m+6zECs9E",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"source": [
"# pytransform3d\n",
"\n",
"
"
],
"metadata": {
"id": "view-in-github",
"colab_type": "text"
}
},
{
"cell_type": "code",
"execution_count": null,
"source": [
"# !pip install pytransform3d"
],
"outputs": [],
"metadata": {
"id": "h5TI-Y228cNt"
}
},
{
"cell_type": "code",
"execution_count": 4,
"source": [
"import matplotlib.pyplot as plt\n",
"from pytransform3d.transformations import plot_transform\n",
"from pytransform3d.plot_utils import make_3d_axis\n",
"\n",
"ax = make_3d_axis(ax_s=1, unit=\"m\", n_ticks=6)\n",
"plot_transform(ax=ax)\n",
"plt.tight_layout()\n",
"plt.show()"
],
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
""
],
"image/png": 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"
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
],
"metadata": {
"id": "43b8grRa7u2h",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 297
},
"outputId": "58f60aec-12e0-4868-b8fe-1283f3cb2d22"
}
},
{
"cell_type": "code",
"execution_count": 6,
"source": [
"import numpy as np\n",
"import pytransform3d.rotations as pr\n",
"\n",
"a = np.array([0.6, 0.3, 0.9])\n",
"b = np.array([0.4, 0.8, 0.2])\n",
"\n",
"ax = pr.plot_basis()\n",
"pr.plot_bivector(ax=ax, a=a, b=b)\n",
"ax.view_init(azim=20, elev=20)\n",
"ax.set_xlim((0, 1))\n",
"ax.set_ylim((0, 1))\n",
"ax.set_zlim((0, 1))\n",
"plt.tight_layout()\n",
"plt.show()"
],
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"/usr/local/lib/python3.7/dist-packages/numpy/lib/function_base.py:380: RuntimeWarning: Mean of empty slice.\n",
" avg = a.mean(axis)\n",
"/usr/local/lib/python3.7/dist-packages/numpy/core/_methods.py:170: RuntimeWarning: invalid value encountered in double_scalars\n",
" ret = ret.dtype.type(ret / rcount)\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
""
],
"image/png": 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"
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 369
},
"id": "vlpvnhBf9Cz-",
"outputId": "758a047c-7534-4ac3-de86-628faebf1a34"
}
},
{
"cell_type": "markdown",
"source": [
"## Construct Rotation Matrix from Two Vectors\n",
"We compute rotation matrix from two vectors that form a plane. The x-axis will point in the same direction as the first vector, the y-axis corresponds to the normalized vector rejection of b on a, and the z-axis is the cross product of the other basis vectors."
],
"metadata": {
"id": "s6Hnn8vd_4Wm"
}
},
{
"cell_type": "code",
"execution_count": 8,
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from pytransform3d.rotations import (matrix_from_two_vectors, plot_basis, random_vector)\n",
"from pytransform3d.plot_utils import plot_vector\n",
"\n",
"\n",
"random_state = np.random.RandomState(1)\n",
"a = random_vector(random_state, 3) * 0.3\n",
"b = random_vector(random_state, 3) * 0.3\n",
"R = matrix_from_two_vectors(a, b)\n",
"\n",
"ax = plot_vector(direction=a, color=\"r\")\n",
"plot_vector(ax=ax, direction=b, color=\"g\")\n",
"plot_basis(ax=ax, R=R)\n",
"plt.show()"
],
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
""
],
"image/png": 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"
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 248
},
"id": "7N3Jc6Xe8gru",
"outputId": "96fbacbf-ca88-4bae-e04a-704cb31b139b"
}
},
{
"cell_type": "markdown",
"source": [
"## Quaternion Integration\n",
"Integrate angular velocities to a sequence of quaternions."
],
"metadata": {
"id": "g8XyweYYARLn"
}
},
{
"cell_type": "code",
"execution_count": 9,
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from pytransform3d.rotations import (\n",
" quaternion_integrate, matrix_from_quaternion, plot_basis)\n",
"\n",
"\n",
"angular_velocities = np.empty((21, 3))\n",
"angular_velocities[:, :] = np.array([np.sqrt(0.5), np.sqrt(0.5), 0.0])\n",
"angular_velocities *= np.pi\n",
"\n",
"Q = quaternion_integrate(angular_velocities, dt=0.1)\n",
"ax = None\n",
"for t in range(len(Q)):\n",
" R = matrix_from_quaternion(Q[t])\n",
" p = 2 * (t/(len(Q) - 1) - 0.5) * np.ones(3)\n",
" ax = plot_basis(ax=ax, s=0.15, R=R, p=p)\n",
"plt.show()"
],
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
""
],
"image/png": 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"
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 248
},
"id": "xM9C114SARTs",
"outputId": "b457c252-4d41-4173-9b96-9d0abf3b2ed5"
}
}
]
}