{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" \n",
" "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"from lets_plot import *\n",
"\n",
"LetsPlot.setup_html()"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def bottle(theta, phi):\n",
" x = -2/15*np.cos(theta)*(3*np.cos(phi) - \n",
" 30*np.sin(theta) + \n",
" 90*np.cos(theta)**4*np.sin(theta) - \n",
" 60*np.cos(theta)**6*np.sin(theta) + \n",
" 5*np.cos(theta)*np.cos(phi)*np.sin(theta))\n",
" y = -1/15*np.sin(theta)*(3*np.cos(phi) - \n",
" 3*np.cos(theta)**2*np.cos(phi) - \n",
" 48*np.cos(theta)**4*np.cos(phi) + \n",
" 48*np.cos(theta)**6*np.cos(phi) - 60*np.sin(theta) + \n",
" 5*np.cos(theta)*np.cos(phi)*np.sin(theta) -\n",
" 5*np.cos(theta)**3*np.cos(phi)*np.sin(theta)-\n",
" 80*np.cos(theta)**5*np.cos(phi)*np.sin(theta)+\n",
" 80*np.cos(theta)**7*np.cos(phi)*np.sin(theta))\n",
" z = 2/15*(3 + 5*np.cos(theta)*np.sin(theta))*np.sin(phi)\n",
" return x, y, z"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"n = 100"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"theta = np.linspace(0, np.pi, n)\n",
"phi = np.linspace(0, 2*np.pi, n)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"thetas, phis = np.meshgrid(theta, phi)\n",
"theta, phi = thetas.reshape(-1), phis.reshape(-1)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"x, y, z = bottle(theta, phi)\n",
"X = np.vstack((x, y, z)).T"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"def rotation_matrices(theta_x, theta_y, theta_z):\n",
" Rx = [[1, 0, 0],\n",
" [0, np.cos(theta_x), -np.sin(theta_x)],\n",
" [0, np.sin(theta_x), np.cos(theta_x)]]\n",
" Ry = [[np.cos(theta_y), 0, np.sin(theta_y)], \n",
" [0, 1, 0], \n",
" [-np.sin(theta_y), 0, np.cos(theta_y)]]\n",
" Rz = [[np.cos(theta_z), -np.sin(theta_z), 0], \n",
" [np.sin(theta_z), np.cos(theta_z), 0], \n",
" [0, 0, 1]]\n",
" return Rx, Ry, Rz"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"Rx, Ry, Rz = rotation_matrices(np.pi/6, np.pi/6, np.pi/6)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"X_rotated = ((X.dot(Rx)).dot(Ry)).dot(Rz)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"data = pd.DataFrame(X_rotated, columns=['x', 'y', 'z'])\n",
"data['cross-sectional'] = np.tile(np.arange(n), n)\n",
"data['longitudinal'] = np.repeat(np.arange(n), n)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"p = ggplot(data) \\\n",
" + geom_path(aes(x='x', y='y', group='longitudinal'), alpha=0.5, color='gray', sampling='none')\n",
"p += theme(axis_text='blank', axis_ticks='blank', axis_line='blank', axis_title='blank')\n",
"p"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"p += geom_path(aes(x='x', y='y', group='cross-sectional'), alpha=0.2, color='gray', sampling='none')\n",
"p"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.9.5"
}
},
"nbformat": 4,
"nbformat_minor": 2
}