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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']



    


















    






/usr/local/lib/python3.5/site-packages/matplotlib/__init__.py:872: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.
  warnings.warn(self.msg_depr % (key, alt_key))

















In [3]:



    


import sys
sys.path.append('..')
from scenario_line_fresnel import EdgeGrid
e = EdgeGrid(N_lame=25, grid_type='line')



    











In [4]:



    


e.lames.shape



    


















    
Out[4]:








(4, 31)

Point-Line Distance--2-Dimensional

See http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html





In [5]:



    


%matplotlib inline
%config InlineBackend.figure_format='retina'
#%config InlineBackend.figure_format = 'svg'
import matplotlib.pyplot as plt
import numpy as np
np.set_printoptions(precision=2, suppress=True)



    











In [6]:



    


particles = np.array([[.2, .3], [-.5, 1.1], [.3, .9]]).T
fig = plt.figure(figsize=(5, 5))
border = 0.0
ax = fig.add_axes((border, border, 1.-2*border, 1.-2*border), axisbg='w')
ax.plot(particles[0, 0], particles[1, 0], 'b+')
ax.plot(particles[0, 1:], particles[1, 1:], 'r')
ax.set_xlim([-1, 1])
ax.set_ylim([0, 2])
print(particles)



    


















    






[[ 0.2 -0.5  0.3]
 [ 0.3  1.1  0.9]]

projection du point sur la droite





In [7]:



    


particles = np.array([[.2, 1.4], [-.5, 1.], [.4, 1.]]).T
particles = np.array([[.2, 1.5], [-.5, .8], [.3, .9]]).T
print(particles)
P = particles[:, 0].copy()
print(P)
print(np.dot(particles[:, 1:].T, np.array([[0, 1], [-1, 0]])))
perp = np.zeros_like(P)
perp[0] = particles[1, 2] - particles[1, 1]
perp[1] = -(particles[0, 2] - particles[0, 1])
print(perp)
# distance to the line
d = perp[0]*(particles[0, 1] - particles[0, 0]) + perp[1]*(particles[1, 1] - particles[1, 0])
print(d, np.sqrt(perp[0]**2 + perp[1]**2), d/np.sqrt(perp[0]**2 + perp[1]**2))
# normalizing
#perp /= np.sqrt((perp**2).sum())
#perp /= np.sqrt(perp[0]**2 + perp[1]**2)
P += d * perp / (perp[0]**2 + perp[1]**2)
fig = plt.figure(figsize=(5, 5))
border = 0.0
ax = fig.add_axes((border, border, 1.-2*border, 1.-2*border), axisbg='w')
ax.plot(particles[0, 0], particles[1, 0], 'b+')
ax.plot(particles[0, 1:], particles[1, 1:], 'r')
ax.plot(P[0], P[1], 'gs')
ax.set_xlim([-1, 1])
ax.set_ylim([0, 2])
print(P)



    


















    






[[ 0.2 -0.5  0.3]
 [ 1.5  0.8  0.9]]
[ 0.2  1.5]
[[-0.8 -0.5]
 [-0.9  0.3]]
[ 0.1 -0.8]
0.49 0.80622577483 0.607770199487
[ 0.28  0.9 ]

shorter form





In [8]:



    


particles = np.array([[.2, 1.4], [-.5, 1.], [.4, 1.]]).T
particles = np.array([[.2, 1.5], [-.5, .8], [.3, .9]]).T
perp = np.array([particles[1, 2] - particles[1, 1], -(particles[0, 2] - particles[0, 1])])
# distance to the line
d = perp[0]*(particles[0, 1] - particles[0, 0]) + perp[1]*(particles[1, 1] - particles[1, 0])
P =  particles[:, 0] + d * perp / (perp**2).sum()

fig = plt.figure(figsize=(5, 5))
border = 0.0
ax = fig.add_axes((border, border, 1.-2*border, 1.-2*border), axisbg='w')
ax.plot(particles[0, 0], particles[1, 0], 'b+')
ax.plot(particles[0, 1:], particles[1, 1:], 'r')
ax.plot(P[0], P[1], 'gs')
ax.set_xlim([-1, 1])
ax.set_ylim([0, 2])
print(P)



    


















    






[ 0.28  0.9 ]

deducing the mirror image as twice this projection





In [9]:



    


particles = np.array([[.2, 1.4], [-.5, 1.], [.4, 1.]]).T
particles = np.array([[.2, 1.5], [-.5, .8], [.3, .9]]).T
perp = np.array([particles[1, 2] - particles[1, 1], -(particles[0, 2] - particles[0, 1])])
# distance to the line
d = perp[0]*(particles[0, 1] - particles[0, 0]) + perp[1]*(particles[1, 1] - particles[1, 0])
P =  particles[:, 0] + 2 *d * perp / (perp**2).sum()

fig = plt.figure(figsize=(5, 5))
border = 0.0
ax = fig.add_axes((border, border, 1.-2*border, 1.-2*border), axisbg='w')
ax.plot(particles[0, 0], particles[1, 0], 'b+')
ax.plot(particles[0, 1:], particles[1, 1:], 'r')
ax.plot(P[0], P[1], 'gs')
ax.set_xlim([-1, 1])
ax.set_ylim([0, 2])
print(P)



    


















    






[ 0.35  0.29]

a function





In [10]:



    


particles.T.tolist()



    


















    
Out[10]:








[[0.2, 1.5], [-0.5, 0.8], [0.3, 0.9]]

















In [11]:



    


particles = np.array([[-.5, .5],[.2, 1.5], [-.5, .8], [.3, .9]]).T
particles = np.random.rand(2, 10)
print(particles)
segment = np.array([[-.5, .5], [.5, 1.5]]).T
print(segment)
def mirror(particles, segment, alpha=1.):
    mirror = particles.copy()
    perp = np.array([segment[1][1] - segment[1][0], -(segment[0][1] - segment[0][0])])
    # distance to the line
    d = perp[0]*(segment[0][1] - particles[0, :]) + perp[1]*(segment[1, 1] - particles[1, :])
    mirror[:2, :] =  particles[:2, :] + 2. * d[np.newaxis, :] * perp[:, np.newaxis] / (perp**2).sum()
    if mirror.shape[0]>2: mirror[2, :] =  alpha * particles[2, :]
    #ind = 1-(d == np.zeros_like(d))
    return mirror#[:, ind]

particles_mirror = mirror(particles, segment)

fig = plt.figure(figsize=(5, 5))
border = 0.0
ax = fig.add_axes((border, border, 1.-2*border, 1.-2*border), axisbg='w')
ax.plot(particles[0, :], particles[1, :], 'b+')
ax.plot(segment[0, :], segment[1, :], 'r')
ax.plot(particles_mirror[0, :], particles_mirror[1, :], 'g+')
ax.plot(np.vstack((particles[0, :], particles_mirror[0, :])), np.vstack((particles[1, :], particles_mirror[1, :])), 'k--')
ax.set_xlim([-1, 1])
ax.set_ylim([0, 2])
print(particles_mirror)



    


















    






[[ 0.5   0.12  0.85  0.5   0.64  0.91  0.58  0.35  0.58  0.67]
 [ 0.81  0.02  0.62  0.04  0.89  0.29  0.94  0.94  0.38  0.81]]
[[-0.5  0.5]
 [ 0.5  1.5]]
[[-0.19 -0.98 -0.38 -0.96 -0.11 -0.71 -0.06 -0.06 -0.62 -0.19]
 [ 1.5   1.12  1.85  1.5   1.64  1.91  1.58  1.35  1.58  1.67]]

miroir d'une image et image d'un miroir

peut on simuler de façon équivalente plusieurs reflections en utilisant le miroir d'un segment





In [12]:



    


particles = np.array([[-.5, .5],[.2, 1.5], [-.5, .8], [.3, .9]]).T
particles = np.random.rand(2, 10)
print(particles)
segmentA = np.array([[-.5, .5], [.5, 1.5]]).T
segmentB = np.array([[-0., 0.], [.0, 2.]]).T
print(segmentA, segmentB)

particles_mirrorA = mirror(particles, segmentA)
particles_mirrorAB = mirror(particles_mirrorA, segmentB)
segmentB_mirrorA = mirror(segmentA, segmentB)
particles_mirrorAB_ = mirror(particles, segmentB_mirrorA)

fig = plt.figure(figsize=(15, 15))
border = 0.0
ax = fig.add_axes((border, border, 1.-2*border, 1.-2*border), axisbg='w')
ax.plot(particles[0, :], particles[1, :], 'bo')
ax.plot(segmentA[0, :], segmentA[1, :], 'r')
ax.plot(segmentB[0, :], segmentB[1, :], 'b')
ax.plot(segmentB_mirrorA[0, :], segmentB_mirrorA[1, :], 'b--')
ax.plot(particles_mirrorA[0, :], particles_mirrorA[1, :], 'go')
ax.plot(particles_mirrorAB[0, :], particles_mirrorAB[1, :], 'g+')
ax.plot(particles_mirrorAB_[0, :], particles_mirrorAB_[1, :], 'gx')
ax.plot(np.vstack((particles_mirrorA[0, :], particles_mirrorAB[0, :])), np.vstack((particles_mirrorA[1, :], particles_mirrorAB[1, :])), 'k--')
ax.plot(np.vstack((particles[0, :], particles_mirrorAB_[0, :])), np.vstack((particles[1, :], particles_mirrorAB_[1, :])), 'k-.')
ax.set_xlim([-1, 1])
ax.set_ylim([0, 2])
print(particles_mirror)



    


















    






[[ 0.31  0.97  0.45  0.7   0.06  0.21  0.24  0.25  0.68  0.76]
 [ 0.46  0.01  0.76  0.81  0.8   0.25  0.18  0.78  0.37  0.44]]
[[-0.5  0.5]
 [ 0.5  1.5]] [[-0.  0.]
 [ 0.  2.]]
[[-0.19 -0.98 -0.38 -0.96 -0.11 -0.71 -0.06 -0.06 -0.62 -0.19]
 [ 1.5   1.12  1.85  1.5   1.64  1.91  1.58  1.35  1.58  1.67]]

on applique maintenant à la structure

la structure est représentée par une liste de segments sur lesquels on a tiré des points





In [13]:



    


import elasticite as el
import numpy as np

e = el.EdgeGrid(N_lame=25, grid_type='line')
e.sample_structure()
fig, ax = e.plot_structure()
print(e.do_structure())



    


















    






[[-1.45 -3.53 -3.85  1.45  3.53  3.85]
 [ 3.11  1.36 -1.46  3.11  1.36 -1.46]
 [ 3.4   4.28  4.92 -0.26 -1.13 -1.78]]










    
























In [14]:



    


segments = e.structure_as_segments()
print(segments)



    


















    






[array([[ 0.  , -2.9 ],
       [ 3.5 ,  2.72]]), array([[-2.9 , -4.17],
       [ 2.72,  0.  ]]), array([[-4.17, -3.54],
       [ 0.  , -2.93]]), array([[ 0.  ,  2.9 ],
       [ 3.5 ,  2.72]]), array([[ 2.9 ,  4.17],
       [ 2.72,  0.  ]]), array([[ 4.17,  3.54],
       [ 0.  , -2.93]])]

















In [15]:



    


e = el.EdgeGrid(N_lame=25, grid_type='line')
e.sample_structure()
alpha = .8
particles = e.particles.copy()
particles_mirror = particles.copy()
for segment in segments:
    particles_mirror = np.hstack((particles_mirror, mirror(particles, segment, alpha)))
    #print(particles_mirror.shape)#, mirror(e.particles, np.array(segment))).shape)

e.particles = particles_mirror
fig, ax = e.plot_structure()



    


















    
























In [16]:



    


alpha *= .8
particles = e.particles.copy()
particles_mirror = particles.copy()
for segment in segments:
    particles_mirror = np.hstack((particles_mirror, mirror(particles, np.array(segment), alpha)))
    #print(particles_mirror.shape)#, mirror(e.particles, np.array(segment))).shape)

e.particles = particles_mirror
fig, ax = e.plot_structure()



    


















    
























In [17]:



    


alpha *= .8
particles = e.particles.copy()
particles_mirror = particles.copy()
for segment in segments:
    particles_mirror = np.hstack((particles_mirror, mirror(particles, np.array(segment), alpha)))
    #print(particles_mirror.shape)#, mirror(e.particles, np.array(segment))).shape)

    
e.total_width *= 1.6
e.particles = particles_mirror
fig, ax = e.plot_structure()

Summming up everything in a few functions:





In [18]:



    


e = el.EdgeGrid(N_lame=25, grid_type='line')
e.sample_structure()
fig, ax = e.plot_structure()



    


















    
























In [19]:



    


e = el.EdgeGrid(N_lame=25, grid_type='line')
e.sample_structure(N_mirror=1, alpha = .8)
e.total_width *= 1.6
fig, ax = e.plot_structure()



    


















    
























In [20]:



    


e = el.EdgeGrid(N_lame=25, grid_type='line')
e.sample_structure(N_mirror=2, alpha = .8)
fig, ax = e.plot_structure()



    


















    
























In [21]:



    


e = el.EdgeGrid(N_lame=25, grid_type='line')
e.sample_structure(N_mirror=3, alpha = .5)
fig, ax = e.plot_structure()

git





In [22]:



    


!git s
#!git add 2015-11-02\ élasticité\ expansion\ en\ m*



    


















    






?? ../.DS_Store
?? ../.dropbox
?? "../Icon\r"
?? ../__pycache__/
?? "2015-11-02 \303\251lasticit\303\251 expansion en miroir - principes.html"
?? ../scenario_grille_carre.pyc
?? ../scenario_line_contraint.pyc
?? ../scenario_line_elastic_fresnel.pyc
?? ../scenario_line_fresnel.pyc
?? ../screenshot.png
?? ../src/__pycache__/
?? ../src/elasticite.pyc
?? ../src/elasticite_blob.py

















In [23]:



    


!git commit -am' expansion - miroir de la structure - principes'



    


















    






On branch master
Your branch is ahead of 'origin/master' by 4 commits.
  (use "git push" to publish your local commits)
Untracked files:
	../.DS_Store
	../.dropbox
	"../Icon\r"
	../__pycache__/
	"2015-11-02 \303\251lasticit\303\251 expansion en miroir - principes.html"
	../scenario_grille_carre.pyc
	../scenario_line_contraint.pyc
	../scenario_line_elastic_fresnel.pyc
	../scenario_line_fresnel.pyc
	../screenshot.png
	../src/__pycache__/
	../src/elasticite.pyc
	../src/elasticite_blob.py

nothing added to commit but untracked files present

















In [24]:



    


! git push



    


















    






Counting objects: 18, done.
Delta compression using up to 8 threads.
Compressing objects: 100% (18/18), done.
Writing objects: 100% (18/18), 2.34 MiB | 0 bytes/s, done.
Total 18 (delta 11), reused 0 (delta 0)
To git@git.framasoft.org:laurentperrinet/elasticte.git
   b51b768..8bf2d9b  master -> master

Content source: laurentperrinet/elasticite

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