#!/usr/bin/env python
# coding: utf-8

# In this post, we're going to produce a couple of animations related to typical sound sources encountered in the study of acoustics: monopole, dipole and quadrupole sources (using `holoviews` with the `matplotlib` backend).

# We start by creating an $(x, y)$ grid of space.

# In[1]:


import numpy as np
import holoviews as hv
hv.extension('matplotlib', logo=False)


# In[2]:


x = np.linspace(-15, 15, num=100)
y = np.linspace(-15, 15, num=100)

X, Y = np.meshgrid(x, y)


# Using this grid, we can build a phase map for a monopole source. By phase map, I mean the change in phase, at the selected frequency that a radial wave would incur by propagating from the origin to the point of the grid.

# In[3]:


r = np.sqrt(X**2 + Y**2)
phase_map1= np.exp(1j * r)

hv.QuadMesh((X, Y, np.real(phase_map1)))


# We can animate this phase map by adding a phase term that varies as a function of time. If we discretize a single period in a given number of frames and loop over the frames, we can generate an "infinite" animation. Let's try this!

# In[4]:


N = 15


# In[5]:


get_ipython().run_cell_magic('output', "holomap='scrubber'", "hmap1 = hv.HoloMap({i: hv.QuadMesh((X, Y, np.real(phase_map1* np.exp(-1j * i / N * 2 * np.pi))), \n                                   label='monopole') for i in range(N)}).opts(colorbar=True)\nhmap1\n")


# Let's apply the same logic to a dipole, made out of two sources a fraction of a wavelength apart and out of phase.

# In[6]:


delta = 2.5
r1 = np.sqrt((X-delta)**2 + Y**2)
r2 = np.sqrt((X+delta)**2 + Y**2)
phase_map2 = .5 * np.exp(1j * r1) - .5 * np.exp(1j * r2)


# In[7]:


get_ipython().run_cell_magic('output', "holomap='scrubber'", "hmap2 = hv.HoloMap({i: hv.QuadMesh((X, Y, np.real(phase_map2 * np.exp(-1j * i / N * 2 * np.pi))), \n                                   label='dipole') for i in range(N)}).opts(colorbar=True)\nhmap2\n")


# Finally, the same formulas apply to a quadripole source, which is made out of four sources, two of them being out of phase.

# In[8]:


gamma = 4.5
r1 = np.sqrt((X - gamma)**2 + (Y - gamma)**2)
r2 = np.sqrt((X - gamma)**2 + (Y + gamma)**2)
r3 = np.sqrt((X + gamma)**2 + (Y - gamma)**2)
r4 = np.sqrt((X + gamma)**2 + (Y + gamma)**2)
phase_map3 = .25 * np.exp(1j * r1) - .25 * np.exp(1j * r2) + .25 * np.exp(1j * r3) - .25 * np.exp(1j * r4)


# In[9]:


get_ipython().run_cell_magic('output', "holomap='scrubber'", "hmap3 = hv.HoloMap({i: hv.QuadMesh((X, Y, np.real(phase_map3 * np.exp(-1j * i / N * 2 * np.pi))), \n                                   label='quadrupole') for i in range(N)}).opts(colorbar=True)\nhmap3\n")


# As a final step, let's add a point cloud of particle moving on top of these monopole source. We first randomly create some points:

# In[10]:


M = 400
Xm = x.min() + np.random.rand(M) * (x.max() - x.min())
Ym = y.min() + np.random.rand(M) * (y.max() - y.min())
Rm = np.sqrt(Xm**2 + Ym**2)
Tm = np.arctan2(Ym, Xm)


# Build a phase map, using the same formula as before, but inserting the coordinates of the points.

# In[11]:


points = np.c_[Rm * np.cos(Tm), Rm * np.sin(Tm)]
phase_map4 = 1j * np.exp(1j * 1 * Rm)


# And then we animate it using an oscillation in time.

# In[12]:


get_ipython().run_cell_magic('output', "holomap='scrubber'", "hmap4 = hv.HoloMap({i: hv.Points(points + np.c_[np.real(phase_map4 * np.cos(Tm) * np.exp(-1j * i / N * 2 * np.pi)),\n                                               np.real(phase_map4 * np.sin(Tm) * np.exp(-1j * i / N * 2 * np.pi))], \n                                                   label='points') for i in range(N)})\nhmap4\n")


# The structure of the wave is visualized thanks to the particle displacement.

# Using the nice plotting API of `holoviews`, we can even overlay this animation with our previous monopole field animation:

# In[13]:


get_ipython().run_cell_magic('output', "holomap='scrubber'", 'hmap1 * hmap4.opts(show_legend=False)\n')


# If you like this sort of animations, a fantastic resource for endless variations on the "wavy" theme can be found at [Bees and bombs](https://twitter.com/beesandbombs).

# *This post was entirely written using the IPython notebook. Its content is BSD-licensed. You can see a static view or download this notebook with the help of nbviewer at [20190129_MonopoleDipoleQuadrupole.ipynb](http://nbviewer.ipython.org/urls/raw.github.com/flothesof/posts/master/20190129_MonopoleDipoleQuadrupole.ipynb).*