élasticité, geometrie

Source

L'installation Elasticité dynamique agit comme un filtre et génère de nouveaux espaces démultipliés, comme un empilement quasi infini d'horizons. Par principe de réflexion, la pièce absorbe l'image de l'environnement et accumule les points de vue ; le mouvement permanent requalifie continuellement ce qui est regardé et entendu.

Ce post implémente une configuration favorisant des angles droits.

In [1]:
%load_ext autoreload
%autoreload 2
In [2]:
import elasticite as el
import numpy as np
duration = el.get_default_args(el.EdgeGrid.render)['duration']

angles perpendiculaires

In [3]:
%%writefile ../scenario_line_geometry.py
#!/usr/bin/env python
# -*- coding: utf8 -*-

import elasticite as el
import numpy as np

class EdgeGrid(el.EdgeGrid):
    def champ(self):
        if self.structure: N_lame = self.N_lame-self.struct_N
        else: N_lame = self.N_lame

        force = np.zeros_like(self.lames[2, :N_lame])
        damp_min = 0.5
        damp_tau = 10.
        damp = lambda t: damp_min + (1.-damp_min)*np.exp(-np.abs(np.mod(t+self.period/2, self.period)-self.period/2)/damp_tau)

        smooth_tau = 15
        smooth = lambda t: 1.-np.exp(-np.abs(np.mod(t+self.period/2, self.period)-self.period/2)**2/smooth_tau**2)
        
        damp_angle_tau = 8.
        damp_angle = lambda t: 1.-np.exp(-(np.mod(t+self.period/2, self.period)-self.period/2)**2/2/damp_angle_tau**2)
        xf = lambda t: location[0]
        zf = lambda t: location[2] + 3.5 * np.sin(2*np.pi*(t)/self.period)

        noise = lambda t: .5 * smooth(t)#* np.exp((np.cos(2*np.pi*((t-0.) / 6. + x))-1.)/ .1**2)
        #damp = lambda t: 0.001 #* np.exp(np.cos(t / 6.) / 3.**2)
        colin_t = lambda t: -.2 * smooth(t) #*np.exp((np.cos(2*np.pi*((t-3.) / 6. + y))-1.)/ .3**2)
        colin_d = lambda d: np.exp(-d**2/2/.25**2) #np.exp(-np.log((d+1.e-12)/.05)**2/2/1.5)

        
        #delta_angle = np.mod(self.angle_relatif()-np.pi/3., 2*np.pi/3)
        delta_angle = self.angle_relatif()[:N_lame, :N_lame]-np.pi/2.
        #delta_angle *= np.sign(delta_angle)
        D = self.distance(do_torus=True)[:N_lame, :N_lame]
        force  += 1. * colin_t(self.t) * np.sum(np.sin(2*delta_angle)*colin_d(D), axis=1) * smooth(self.t)
        #force += force_/np.abs(force_**2).sum()
        force -= 12 * (np.mod(self.lames[2, :N_lame]+np.pi/2, np.pi) - np.pi/2) * (1- smooth(self.t) )
        force += noise(self.t)*np.pi*np.random.randn(N_lame)
        force -= damp(self.t) * self.lames[3, :N_lame]/self.dt
        force *= .03
        force = 2. * np.tanh(force)
        return force
    

if __name__ == "__main__":
    import sys
    if len(sys.argv)>1: mode = sys.argv[1]
    else: mode = 'both'
    filename = None
    filename = 'mat/line_geometry.npy'
    e = EdgeGrid(N_lame=25, grid_type='line', mode=mode, verb=False, filename=filename, period=4*60.)
    el.main(e)

    

Overwriting ../scenario_line_geometry.py
In [4]:
%cd ..
!rm mat/line_geometry.npy
%run  scenario_line_geometry.py writer
%cd posts

/Users/laurentperrinet/cloud_nas/science/elasticte
/Users/laurentperrinet/cloud_nas/science/elasticte/posts
In [5]:
import matplotlib
%matplotlib inline
import matplotlib.pyplot as plt

z = np.load('../mat/line_geometry.npy')
fig, ax = plt.subplots(figsize=(15, 3))
#_ = ax.plot(z[:, 0])
_ = ax.plot(z[:, 0], z[:, 1:])
No description has been provided for this image

45 deg

In [6]:
%%writefile ../scenario_line_geometry_45deg.py
#!/usr/bin/env python
# -*- coding: utf8 -*-

import elasticite as el
import numpy as np

class EdgeGrid(el.EdgeGrid):
    def champ(self):
        if self.structure: N_lame = self.N_lame-self.struct_N
        else: N_lame = self.N_lame

        force = np.zeros_like(self.lames[2, :N_lame])
        damp_min = 0.4
        damp_tau = 14.
        damp = lambda t: damp_min + (1.-damp_min)*np.exp(-np.abs(np.mod(t+self.period/2, self.period)-self.period/2)/damp_tau)

        smooth = lambda t: 1.-np.exp(-np.abs(np.mod(t+self.period/2, self.period)-self.period/2)**2/damp_tau**2)
        on_off = lambda t, freq: (np.sin(2*np.pi*t/self.period*freq) > 0.)

        noise = lambda t: .5 * smooth(t)
        
        force -= 7.5 * (np.mod(self.lames[2, :N_lame]+np.pi/2, np.pi) - np.pi/2 -np.pi/4) *smooth(self.t) *on_off(self.t, 3)
        force -= 40 * (np.mod(self.lames[2, :N_lame]+np.pi/2, np.pi) - np.pi/2) * (1- smooth(self.t) ) *(1-on_off(self.t, 3))
        force += noise(self.t)*np.pi*np.random.randn(N_lame)
        force -= damp(self.t) * self.lames[3, :N_lame]/self.dt
        force *= .01
        force = 2 * np.tanh(force)
        return force    

if __name__ == "__main__":
    import sys
    if len(sys.argv)>1: mode = sys.argv[1]
    else: mode = 'both'
    filename = None
    filename = 'mat/line_geometry_45deg.npy'
    e = EdgeGrid(N_lame=25, grid_type='line', mode=mode, verb=False, filename=filename, period=4*60.)
    el.main(e)

    

Overwriting ../scenario_line_geometry_45deg.py
In [7]:
%cd ..
!rm mat/line_geometry_45deg.npy
%run  scenario_line_geometry_45deg.py writer
%cd posts

/Users/laurentperrinet/cloud_nas/science/elasticte
/Users/laurentperrinet/cloud_nas/science/elasticte/posts
In [8]:
import matplotlib
%matplotlib inline
import matplotlib.pyplot as plt

z = np.load('../mat/line_geometry_45deg.npy')
el.check(e, z)
fig, ax = plt.subplots(figsize=(15, 3))
#_ = ax.plot(z[:, 0])
_ = ax.plot(z[:, 0], z[:, 1:])
No description has been provided for this image

90 deg

In [9]:
%%writefile ../scenario_line_geometry_90deg.py
#!/usr/bin/env python
# -*- coding: utf8 -*-

import elasticite as el
import numpy as np

class EdgeGrid(el.EdgeGrid):
    def champ(self):
        if self.structure: N_lame = self.N_lame-self.struct_N
        else: N_lame = self.N_lame

        force = np.zeros_like(self.lames[2, :N_lame])
        damp_min = 0.7
        damp_tau = 14.
        damp = lambda t: damp_min + (1.-damp_min)*np.exp(-np.abs(np.mod(t+self.period/2, self.period)-self.period/2)/damp_tau)

        smooth = lambda t: 1.-np.exp(-np.abs(np.mod(t+self.period/2, self.period)-self.period/2)**2/damp_tau**2)
        on_off = lambda t, freq: (np.sin(2*np.pi*t/self.period*freq) > 0.)

        noise = lambda t: .2 * smooth(t)
        
        force -= 7.5 * (np.mod(self.lames[2, :N_lame], np.pi) -np.pi/2 ) *smooth(self.t) * on_off(self.t, 3)
        force -= 40 * (np.mod(self.lames[2, :N_lame]+np.pi/2, np.pi) - np.pi/2) * (1- smooth(self.t) ) * (1-on_off(self.t, 3))
        force += noise(self.t)*np.pi*np.random.randn(N_lame)
        force -= damp(self.t) * self.lames[3, :N_lame]/self.dt
        force *= .01
        force = 2 * np.tanh(force)
        return force    

if __name__ == "__main__":
    import sys
    if len(sys.argv)>1: mode = sys.argv[1]
    else: mode = 'both'
    filename = None
    filename = 'mat/line_geometry_90deg.npy'
    e = EdgeGrid(N_lame=25, grid_type='line', mode=mode, verb=False, filename=filename, period=4*60.)
    el.main(e)

    

Overwriting ../scenario_line_geometry_90deg.py
In [10]:
%cd ..
!rm mat/line_geometry_90deg.npy
%run  scenario_line_geometry_90deg.py writer
%cd posts

/Users/laurentperrinet/cloud_nas/science/elasticte
/Users/laurentperrinet/cloud_nas/science/elasticte/posts
In [11]:
import matplotlib
%matplotlib inline
import matplotlib.pyplot as plt

z = np.load('../mat/line_geometry_90deg.npy')
el.check(e, z)
fig, ax = plt.subplots(figsize=(15, 3))
#_ = ax.plot(z[:, 0])
_ = ax.plot(z[:, 0], z[:, 1:])
No description has been provided for this image

angles structure

on s'oriente vers les angles parallèles aux structures

In [12]:
%%writefile ../scenario_line_geometry_structure.py
#!/usr/bin/env python
# -*- coding: utf8 -*-

import elasticite as el
import numpy as np

class EdgeGrid(el.EdgeGrid):
    def champ(self):
        if self.structure: N_lame = self.N_lame-self.struct_N
        else: N_lame = self.N_lame

        force = np.zeros_like(self.lames[2, :N_lame])
        damp_min = 0.8
        damp_tau = 15.
        damp = lambda t: damp_min #+ (1.-damp_min)*np.exp(-np.abs(np.mod(t+self.period/2, self.period)-self.period/2)/damp_tau)

        smooth = lambda t: 1.-np.exp(-np.abs(np.mod(t+self.period/2, self.period)-self.period/2)**2/damp_tau**2)
        on_off = lambda t, freq: (np.sin(2*np.pi*t/self.period*freq) > 0.)

        noise = lambda t: .4 * smooth(t)
        np.random.seed(12345)
        random_timing = np.random.rand(N_lame)
        #print(np.mod(random_timing + self.t/self.period, 1))
        struct_angles = np.random.permutation( np.hstack((self.struct_angles, -np.array(self.struct_angles)))) * np.pi / 180
        #print(struct_angles, (np.mod(random_timing + self.t/self.period, 1)*len(struct_angles)).astype(np.int)) 
        angle_desired = np.zeros(N_lame)
        for i, idx in enumerate((np.mod(random_timing + self.t/self.period, 1)*len(struct_angles)).astype(np.int)):
            angle_desired[i] = struct_angles[idx]
        
        force -= 20 * (np.mod(self.lames[2, :N_lame] - angle_desired +np.pi/2, np.pi) - np.pi/2 ) * smooth(self.t)
        force -= 80 * (np.mod(self.lames[2, :N_lame] + np.pi/2, np.pi) - np.pi/2) * (1- smooth(self.t) )
        force += noise(self.t)*np.pi*np.random.randn(N_lame)
        force -= damp(self.t) * self.lames[3, :N_lame]/self.dt
        force = .02 * 100 * np.tanh(force/100)
        return force    

if __name__ == "__main__":
    import sys
    if len(sys.argv)>1: mode = sys.argv[1]
    else: mode = 'both'
    filename = None
    filename = 'mat/line_geometry_structure.npy'
    e = EdgeGrid(N_lame=25, grid_type='line', mode=mode, verb=False, filename=filename, period=4*60.)
    el.main(e)

    

Overwriting ../scenario_line_geometry_structure.py
In [13]:
%cd ..
!rm mat/line_geometry_structure.npy
%run  scenario_line_geometry_structure.py writer
%cd posts

/Users/laurentperrinet/cloud_nas/science/elasticte
/Users/laurentperrinet/cloud_nas/science/elasticte/posts
In [14]:
import matplotlib
%matplotlib inline
import matplotlib.pyplot as plt

z = np.load('../mat/line_geometry_structure.npy')
el.check(e, z)
fig, ax = plt.subplots(figsize=(15, 3))
#_ = ax.plot(z[:, 0])
_ = ax.plot(z[:, 0], z[:, 1:])
No description has been provided for this image

git

In [15]:
!git add  ../mat/line_geometry_90deg.npy  ../scenario_line_geometry_90deg.py

!git s

 M ../mat/line_geometry.npy
 M ../mat/line_geometry_45deg.npy
M  ../mat/line_geometry_90deg.npy
 M "2015-09-30 \303\251lasticit\303\251, vapory and reflections.ipynb"
 M "2015-10-14 \303\251lasticit\303\251, control scenario.ipynb"
 M "2015-11-02 \303\251lasticit\303\251 expansion en miroir - exploration param\303\250tres.ipynb"
 M "2015-11-02 \303\251lasticit\303\251 expansion en miroir - principes.ipynb"
 M "2015-11-17 \303\251lasticit\303\251 expansion en miroir - dynamique d'un point focal.ipynb"
?? ../mat/line_contraint.npy
?? ../mat/master.npy
?? __temp_ipython__.png
?? anim.gif
In [16]:
!git commit -am' scenario geometry  90deg '

[master d1079d9]  scenario geometry  90deg
 8 files changed, 1001 insertions(+), 63 deletions(-)
 rewrite mat/line_geometry.npy (82%)
 rewrite mat/line_geometry_45deg.npy (82%)
 rewrite mat/line_geometry_90deg.npy (82%)
In [17]:
! git push

Counting objects: 12, done.
Delta compression using up to 4 threads.
Compressing objects: 100% (12/12), done.
Writing objects: 100% (12/12), 9.10 MiB | 3.93 MiB/s, done.
Total 12 (delta 7), reused 0 (delta 0)
To git@git.framasoft.org:laurentperrinet/elasticte.git
   1c15145..d1079d9  master -> master