def find_bin(line): truth_cases = [] for i in range(len(pent_polygons)): plane0 = Plane(Point3D(pent_polygons[i][0]), Point3D(pent_polygons[i][1]), Point3D(pent_polygons[i][2])) search_line = Line3D(Point3D(line), Point3D(0,0,0)) plane_search_intersection = plane0.intersection(search_line)[0].evalf() point_plane_dist = plane0.distance(Point3D(line)).evalf() intersectionX = plane_search_intersection.x intersectionY = plane_search_intersection.y intersectionZ = plane_search_intersection.z intersection_line = (intersectionX, intersectionY, intersectionZ) print i true_or_false = check_projections(pent_polygons[i], intersection_line) print i for j in range(3): temp_string = 'xyz' if true_or_false[j] == 1: truth_cases.append((i,temp_string[j],point_plane_dist,'pent')) for i in range(len(hex_polygons)): plane0 = Plane(Point3D(hex_polygons[i][0]), Point3D(hex_polygons[i][1]), Point3D(hex_polygons[i][2])) search_line = Line3D(Point3D(line), Point3D(0,0,0)) plane_search_intersection = plane0.intersection(search_line)[0].evalf() point_plane_dist = plane0.distance(Point3D(line)).evalf() intersectionX = plane_search_intersection.x intersectionY = plane_search_intersection.y intersectionZ = plane_search_intersection.z intersection_line = (intersectionX, intersectionY, intersectionZ) print i true_or_false = check_projections(hex_polygons[i], intersection_line) print i for j in range(3): temp_string = 'xyz' if true_or_false[j] == 1: truth_cases.append((i,temp_string[j],point_plane_dist,'hex')) print truth_cases
def ransac(self, triangulated_points):
""" Feature rejection function
:param triangulated_points: np array, (num_features, 3) all triangulated points
:return bestinliers: (N, ), indices of the inliers, where N is the total number of inliers
"""
# we only expect to have the 5-10% outliers, so we'll set the minimum inliers
# to be 92% of the total number of features.
num_features = triangulated_points.shape[0]
# tunable parameters
mininliers = .92 * num_features
alpha = 0.042
maxinliers = 0
sympy_points = np.ndarray((num_features, 3))
for j in range(num_features):
sympy_points[j] = Point3D(triangulated_points[j, 0],
triangulated_points[j, 1],
triangulated_points[j, 2])
# make an array of possible indices that we will randomly draw from
for i in range(1000):
# select 3 random points from triangulated points to compute a plane
rand_pts = np.random.choice(triangulated_points.shape[0], 3)
normal, d = self.compute_plane(triangulated_points[rand_pts, :])
# make the points into a plane object
plane = Plane(Point3D(triangulated_points[rand_pts[0], :]),
normal_vector=normal)
# compute the reprojection error for all the points
reproj = np.ndarray((num_features, ))
for j in range(num_features):
reproj[j] = plane.distance(Point3D(sympy_points[j, :]))
# print(reproj)
inliers = reproj < alpha
ninliers = np.sum(inliers)
# update the max values if applicable
if ninliers > maxinliers:
maxinliers = ninliers
bestinliers = inliers
# check exit condition
if maxinliers > mininliers:
print('required', i + 1,
'RANSAC attempts to remove outliers.')
break
print('number of inliers: ' + str(maxinliers))
# returns the inlier indices, not the actual values
return bestinliers
return float(ag)
toArray = lambda x: np.array(x).astype(float)
def degreeOfVictor(p1, p2):
p1, p2 = map(toArray, (p1, p2))
dotProduct = (p1 * p2).sum()
norm = lambda p: (p**2).sum()**0.5
angle = dotProduct / (norm(p1) * norm(p2))
arccosDegree = lambda x: np.degrees(np.arccos(x))
degree = arccosDegree(angle)
return degree
#%%
if __name__ == '__main__':
po = Point3D(0, 0, 0)
# print fitPointsToPlane(points)
a.distance(po)
l = Line3D((0, 0, 0), (1, 0, 0))
l2 = Line3D((0, 1, 0), (0, 1, 1))
a = Plane(Point3D(1, 1, 1), normal_vector=(1, 1, 1))
b = a.perpendicular_line(Point3D(0, 0, 0))
points = (1, 0, 0), (0, 1, 0), (0, 0, 1), (0.1, 0.1, 0.1)
a.distance(Point3D(0, 0, 0))
pass
def site_descriptors(self, COsites=[]):
'''
Calculate site specific descriptors
'''
# when the site indices are not provided
if COsites == []:
self.get_COsites()
else:
self.COsites = COsites
# Numbef of sites
self.Nsites = len(self.COsites)
if self.Nsites == 3: self.sitetype = 'hollow'
if self.Nsites == 2: self.sitetype = 'bridge'
if self.Nsites == 1: self.sitetype = 'top'
#indices of Pd atom at CO binding sites
COsites_Pdi = []
for s in range(len(self.COsites)):
COsites_Pdi.append('Pd' + str(self.COsites[s]))
# Get CO site position - the mean of Pd pos at the site
COsites_Pdpos = []
for i in self.COsites:
COsites_Pdpos.append(self.atoms[i].position)
self.site_pos = np.mean(COsites_Pdpos, axis=0)
# Add a facticious C to the end
atoms_C = self.atoms.copy()
atoms_C.append(Atom('C', position=self.site_pos))
# all Pd-site bond length
Pd_site = atoms_C.get_distances(-1, self.Pdi, mic=True)
# sorted Pd-site bond length
Pd_site, _ = sort_i_and_d(Pd_site, self.Pdi)
# Site distance to neighboring Pd atoms
Pd_site_CO = np.array(Pd_site[:len(self.COsites)])
#NN dataframe at CO binding site only
PdNN_CO = self.PdNN.loc[:, COsites_Pdi]
# Aprroximate Bond lengths by site-Pd length
if not COsites == []:
PdC3 = np.zeros(3)
PdC3[:len(self.COsites)] = Pd_site_CO
# Bond lengths
self.PdC1 = PdC3[0]
self.PdC2 = PdC3[1]
self.PdC3 = PdC3[2]
'''
Weighted average for NN1, NN2, GCN
'''
#weights based on 1 over CO-Pd distance
if self.Nsites == 1: # for top site
norm_weights = np.ones(1) #avoid zero division problem
else:
norm_weights = (1 / Pd_site_CO) / np.sum(1 / Pd_site_CO)
# CN1 and CN2
self.CN1 = np.dot(norm_weights, PdNN_CO.loc['NN1'].values)
self.CN2 = np.dot(norm_weights, PdNN_CO.loc['NN2'].values)
# GCNs
cn_max = [12, 18, 22]
NN1_site = []
#Iterate through each atom at the site
for i in self.COsites:
for j in self.Pd1NN['Pd' + str(i)]:
NN1_site += list(self.Pd1NN['Pd' + str(j)])
#Find non-repeating NN1 atoms for the site
NN1_site = list(set(NN1_site))
# Take out the atoms at the site
NN1_site = [ni for ni in NN1_site if ni not in list(self.COsites)]
#Add up CN numbers for those NN1 atoms
gcn_sum = 0
for ni in NN1_site:
gcn_sum += self.PdNN.loc['NN1']['Pd' + str(ni)]
#Normalize by the max GCNs
self.GCN = gcn_sum / cn_max[self.Nsites - 1]
'''
'''
#Weighted average for OCN and CeCN
'''
PdONN_CO = []
PdCeNN_CO = []
for si in COsites_Pdi:
PdONN_CO.append(self.PdONN[si])
PdCeNN_CO.append(self.PdCeNN[si])
self.OCN1 = np.dot(np.array(PdONN_CO), norm_weights)
self.CeCN1 = np.dot(np.array(PdCeNN_CO), norm_weights)
'''
'''
Calculate distance to the support
'''
#take the distance of CO to Ce plane (determined by 3 Ce points)
# as the distance to support
Ce_plane = Plane(Point3D(self.atoms[self.Cei[0]].position),
Point3D(self.atoms[self.Cei[1]].position),
Point3D(self.atoms[self.Cei[2]].position))
self.Dsupport = float(Ce_plane.distance(Point3D(self.site_pos)))
def alignMono(entry,
prec=1E-4,
seed_index=0,
supercell=2,
c_mag=50,
dist_from_plane=0):
"""
Align a 2D material such that the 'c' vector is perpendicular to the
in-plane lattice vectors
inputs
--------
entry (list): A set of components necessary for the TSA.
Makes it easier to parallelize with this as
the input
--structure (Structure): pymatgen Structure object
--tol (float): The scaling for the atomic bonds
--mp_id (str): The label for the entry, commonly
the MaterialsProject ID
prec (float): The precision to compare magnitude of vectors
representing the bonds in the system
seed_index (int): The site to use as the starting point for the
TSA. Typically does not impact the results, but
will if the structure is a bipartide or has
mixed dimensionality
supercell (int): The supercell size to generate for
periodic networks
c_mag (float): The magnitude to make the non-periodic vectors
dist_from_plane (float): Maximum distance an atom can be from the
plane parallel to the monolayer. Is relevant
when the atoms in the monolayer are spread
across periodic boundary conditions in the
unit cell
returns
--------
list1 (list): -fractional coordinates in new lattice
-new lattice (a,b,c)
-species associated with each site
list1 (list): -fractional coordinates in new lattice
-new lattice (b,a,c)
-species associated with each site
"""
# Keep original copy of structure
s = copy.deepcopy(entry[0])
new_latt = getNewLattice(entry,
dim=2,
prec=prec,
seed_index=seed_index,
supercell=supercell,
c_mag=c_mag)
# Identify plane to translate atoms towards
plane = Plane(Point3D(s.sites[seed_index].coords),
normal_vector=new_latt[2])
# Create list of translationss
trans = list(itertools.product([1, -1, 0], repeat=3))
lat = s.lattice.as_dict()['matrix']
final_sites = []
i = 0
# Ensure that the atoms are nearby each other
for site in s.sites:
point = Point3D(site.coords)
if plane.distance(point) < dist_from_plane:
final_sites.append(site.coords)
else:
news = []
# translate atomic sites to see which position is closest to plane
for t in trans:
point = Point3D(site.coords + np.dot(np.transpose(lat), t))
news.append([float(plane.distance(point)), t])
news.sort(key=lambda x: x[0])
final_sites.append(site.coords +
np.dot(np.transpose(lat), news[0][1]))
i += 1
# Create new lattice matricies
lat1 = np.array([new_latt[0], new_latt[1], new_latt[2]])
lat2 = np.array([new_latt[1], new_latt[0], new_latt[2]])
# Generate atomic fractions
new_fracs1 = np.linalg.solve(lat1.T, np.array(final_sites).T).T
new_fracs2 = np.linalg.solve(lat2.T, np.array(final_sites).T).T
species = s.species
return ([species, new_fracs1, lat1], [species, new_fracs2, lat2])
zLP1 = Lparam[_sage_const_2].subs(t=tt)
# запишем наши объекты через sympy
from sympy import Plane, Point, Point3D, Line3D
Psp = Plane(Point3D(pointP), normal_vector=n)
M1sp = Point3D(M1)
prtemp = Psp.projection(M1sp)
# проекция M1 на P
prM1P = vector([prtemp.x._sage_(), prtemp.y._sage_(), prtemp.z._sage_()])
# наша L через sympy
Lsp = Line3D(pointL, point2L)
prtemp = Lsp.projection(M1sp)
# проекция M1 на L
prM1L = vector([prtemp.x._sage_(), prtemp.y._sage_(), prtemp.z._sage_()])
# расстояние от M2 до P2
P2sp = Plane(Point3D(M1), normal_vector=n2)
dM2P2 = P2sp.distance(Point3D(M2))
# плоскость через M1 и L
P6 = Simp_Plane(Make_Plane(M1, pointL - M1, sL))
# проекция L1 на P
# уравнение L1 в параметрическом виде
pointL1 = vector([
M2[_sage_const_0] + a[_sage_const_0],
M2[_sage_const_1] + a[_sage_const_1],
M2[_sage_const_2] + a[_sage_const_2]
])
M2sp = Point3D(M2)
pointL1sp = Point3D(pointL1)
# проекция M2 на P
prtemp = Psp.projection(M2sp)
prM2P = vector([prtemp.x._sage_(), prtemp.y._sage_(), prtemp.z._sage_()])
# проекция pointL1 на P