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Merge pull request #70 from gouarin/superellipsoid
add superellipsoid example
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‎examples/superellipsoid.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# How to use pythreejs to plot a superellipsoid"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"A superellipsoid is given by a parametric function and the equation is very similar to an ellipse equation. We only have different exponents which give us different shapes. For more informations: https://en.wikipedia.org/wiki/Superellipsoid.\n",
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"\n",
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"The idea of this example is to construct the mesh of the square $[0, 1]\\times[0,1]$ and to do a projection of these points on the superillipse which is the 2D shape and then to do a spherical product to have the 3D shape."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"\n",
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"n = 10 # number of discretisation points for the square in each direction \n",
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"x_box = np.concatenate((np.linspace(-1, 1., n), np.ones(n-2), np.linspace(1, -1., n), -np.ones(n-2)))\n",
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"y_box = np.concatenate((-np.ones(n-1), np.linspace(-1, 1., n), np.ones(n-2), np.linspace(1, -1., n-1, endpoint=False)))\n",
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"nx_box = x_box.size\n",
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"\n",
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"coords = np.empty((nx_box**2, 3))\n",
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"\n",
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"def superellipse(rx, ry, m):\n",
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" \"\"\"\n",
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" superellipse formula with the projection of the unit square\n",
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" \n",
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" Parameters\n",
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" ----------\n",
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" rx : the radius in the x direction \n",
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" ry : the radius in the y direction \n",
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" m : the exponent of the superellipse\n",
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" \n",
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" Output\n",
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" ------\n",
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" the coordinates of the superellipse\n",
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" \"\"\"\n",
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" return x_box*rx*(1. - .5*np.abs(y_box)**(2./m))**(m/2.), y_box*ry*(1. - .5*np.abs(x_box)**(2./m))**(m/2.)\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"def superellipsoid(rx, ry, rz, m1, m2):\n",
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" \"\"\"\n",
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" superellipsoid formula with the spherical product of two superellipse\n",
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" and update of the global coords array\n",
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" \n",
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" Parameters\n",
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" ----------\n",
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" rx : the radius in the x direction \n",
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" ry : the radius in the y direction \n",
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" rz : the radius in the z direction \n",
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" m1 : the exponent of the first superellipse\n",
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" m2 : the exponent of the second superellipse\n",
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" \"\"\" \n",
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" gx, gy = superellipse(1, 1, m2)\n",
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" hx, hy = superellipse(1, 1, m1)\n",
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"\n",
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" \n",
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" coords[:, 0] = rx*(gx[np.newaxis, :]*hx[:, np.newaxis]).flatten()\n",
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" coords[:, 1] = ry*(gx[np.newaxis, :]*hy[:, np.newaxis]).flatten()\n",
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" coords[:, 2] = rz*(gy[np.newaxis, :]*np.ones(hx.size)[:, np.newaxis]).flatten()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"# superellipsoid parameters\n",
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"rx = ry = rz = 1.\n",
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"m1 = m2 = 1.\n",
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"\n",
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"superellipsoid(rx, ry, rz, m1, m2)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"We construct the triangulation by using the ConveHull function in scipy."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"import scipy.spatial as spatial\n",
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"\n",
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"cvx = spatial.ConvexHull(coords)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"from pythreejs import *\n",
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"from IPython.display import display\n",
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"\n",
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"surf_g = PlainGeometry(vertices=coords.tolist(), faces=cvx.simplices.tolist())\n",
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"surf = Mesh(geometry=surf_g, material=BasicMaterial(color='green', wireframe=True))\n",
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"scene = Scene(children=[surf, AmbientLight(color='#777777')])\n",
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"c = PerspectiveCamera(position=[2, 2, 3], up=[0, 0, 1],\n",
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" children=[DirectionalLight(color='white',\n",
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" position=[3, 5, 1],\n",
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" intensity=0.6)])\n",
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"renderer = Renderer(camera=c, scene=scene, controls=[OrbitControls(controlling=c)])\n",
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"display(renderer)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"from ipywidgets import FloatSlider, HBox, VBox\n",
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"\n",
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"m1_slider, m2_slider = (FloatSlider(description='m1', min=0.01, max=4.0, step=0.01, value=m1,\n",
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" continuous_update=False, orientation='vertical'),\n",
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" FloatSlider(description='m2', min=0.01, max=4.0, step=0.01, value=m2,\n",
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" continuous_update=False, orientation='vertical'))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"rx_slider, ry_slider, rz_slider = (FloatSlider(description='rx', min=0.01, max=10.0, step=0.01, value=rx, \n",
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" continuous_update=False, orientation='horizontal'),\n",
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" FloatSlider(description='ry', min=0.01, max=10.0, step=0.01, value=ry, \n",
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" continuous_update=False, orientation='horizontal'),\n",
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" FloatSlider(description='rz', min=0.01, max=10.0, step=0.01, value=rz, \n",
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" continuous_update=False, orientation='horizontal'))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"def update(change):\n",
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" superellipsoid(rx_slider.value, ry_slider.value, rz_slider.value, \n",
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" m1_slider.value, m2_slider.value)\n",
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" surf_g.vertices = coords.tolist()\n",
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" \n",
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"m1_slider.observe(update, names=['value'])\n",
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"m2_slider.observe(update, names=['value'])\n",
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"rx_slider.observe(update, names=['value'])\n",
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"ry_slider.observe(update, names=['value'])\n",
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"rz_slider.observe(update, names=['value'])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"VBox([HBox([renderer, m1_slider, m2_slider]), rx_slider, ry_slider, rz_slider])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"anaconda-cloud": {},
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"kernelspec": {
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"display_name": "Python [conda root]",
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"language": "python",
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"name": "conda-root-py"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.5.2"
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},
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"widgets": {
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"state": {
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"5eb4554c95814fc6b83135c8b1a7a5ee": {
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"views": [
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{
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"cell_index": 8
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}
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]
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},
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"b9b3e029e6554c0caee4a3cd691eb821": {
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"views": [
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{
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"cell_index": 12
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}
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},
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"version": "1.2.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 1
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}

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