Stereographic Projections

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Face normal detection and Stereographic Projection

The projections in this package work by projecting points that lie on a sphere on a 2d disc about the equator. Points in the northern hemisphere will be mapped towards the south pole and points in the southern hemisphere will be mapped towards the northpole.

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from PyCrystallography.geometry import *
from PyCrystallography.stereographic_projection import Stereographic_projection

fig = plt.figure(0,figsize=[8,8])
ax = fig.add_subplot(111,projection='3d')
######################################
# which ever 3d model you want to load
cuboid(ax,5,5,5)
######################################
r = max(h,w,d)
points=normal_points(ax,faces,r)
Stereographic_projection(ax,points,r)
plt.show()

fig = plt.figure(0,figsize=[8,8])
ax = fig.add_subplot(111,projection='3d')
faces = pyramid(ax,1,0.5,3)
points=normal_points(ax,faces,1)
Stereographic_projection(ax,points,1,'stereographic_projection_pyramid')
plt.show()

fig = plt.figure(0,figsize=[8,8])
ax = fig.add_subplot(111,projection='3d')
faces = bipyramid(ax,1,0.5,6)
points=normal_points(ax,faces,1)
Stereographic_projection(ax,points,2,'stereographic_projection_bipyramid')
plt.show()

fig = plt.figure(0,figsize=[8,8])
ax = fig.add_subplot(111,projection='3d')
faces = prism(ax,2,2,6)
points=normal_points(ax,faces,2)
Stereographic_projection(ax,points,2,'stereographic_projection_prism')
plt.show()

fig = plt.figure(0,figsize=[8,8])
ax = fig.add_subplot(111,projection='3d')
faces = biprismid(ax,3,1,0.5,5)
points=normal_points(ax,faces,3)
Stereographic_projection(ax,points,3,'stereographic_projection_prism')
plt.show()

fig = plt.figure(0,figsize=[8,8])
ax = fig.add_subplot(111,projection='3d')
faces = tetrakis(ax,4,1)
points=normal_points(ax,faces,5)
Stereographic_projection(ax,points,5,'stereographic_projection_tetrakis')
plt.show()

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Identifying object symmetries

There are 32 point group classifications for symmetries in crystallography. They are classified by:

• mirror planes
• rotational axes (nfold)
• rotoinversion axes

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n-fold roational symmetry

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from PyCrystallography.geometry import *
from PyCrystallography.stereographic_projection import *

fig = plt.figure(0,figsize=[8,8])
ax = fig.add_subplot(111,projection='3d')
######################################
# which ever 3d model you want to load
faces=cuboid(ax,5,5,5)
######################################
points=normal_points(ax,faces,5)
northern_points,southern_points=Stereographic_projection(points,3,'test')
identify_fold_symmetry(northern_points,southern_points)

NFOLD =  5