def is_point_inside_cell(cell, point):
"""
Checks if a given triple-vector is inside the cell given by the basis matrix in cell
"""
p1 = FracVector((0, 0, 0))
p2 = cell[0]
p3 = cell[1]
p4 = cell[0] + cell[1]
p5 = cell[2]
p6 = cell[0] + cell[2]
p7 = cell[1] + cell[2]
p8 = cell[0] + cell[1] + cell[2]
tetras = [None] * 6
tetras[0] = [p1, p2, p3, p6]
tetras[1] = [p2, p3, p4, p6]
tetras[2] = [p3, p4, p6, p8]
tetras[3] = [p3, p6, p7, p8]
tetras[4] = [p3, p5, p6, p7]
tetras[5] = [p1, p3, p5, p6]
for tetra in tetras:
if is_point_inside_tetra(tetra, point):
return True
return False
def niggli_to_metric(niggli):
niggli = FracVector.use(niggli)
m = niggli.noms
# Since the niggli matrix contains 2*the product of the off diagonal elements, we increase the denominator by cell.denom*2
return FracVector(
((2 * m[0][0], m[1][2], m[1][1]), (m[1][2], 2 * m[0][1], m[1][0]),
(m[1][1], m[1][0], 2 * m[0][2])), niggli.denom * 2).simplify()
def is_point_inside_tetra(tetra, point):
"""
Checks if a point is inside the tretrahedra spanned by the coordinates in tetra
"""
D0 = FracVector(((tetra[0][0], tetra[0][1], tetra[0][2],
1), (tetra[1][0], tetra[1][1], tetra[1][2],
1), (tetra[2][0], tetra[2][1], tetra[2][2], 1),
(tetra[3][0], tetra[3][1], tetra[3][2], 1)))
D1 = FracVector(((point[0], point[1], point[2],
1), (tetra[1][0], tetra[1][1], tetra[1][2],
1), (tetra[2][0], tetra[2][1], tetra[2][2], 1),
(tetra[3][0], tetra[3][1], tetra[3][2], 1)))
D2 = FracVector(((tetra[0][0], tetra[0][1], tetra[0][2],
1), (point[0], point[1], point[2],
1), (tetra[2][0], tetra[2][1], tetra[2][2], 1),
(tetra[3][0], tetra[3][1], tetra[3][2], 1)))
D3 = FracVector(((tetra[0][0], tetra[0][1], tetra[0][2],
1), (tetra[1][0], tetra[1][1], tetra[1][2],
1), (point[0], point[1], point[2], 1),
(tetra[3][0], tetra[3][1], tetra[3][2], 1)))
D4 = FracVector(((tetra[0][0], tetra[0][1], tetra[0][2],
1), (tetra[1][0], tetra[1][1], tetra[1][2],
1), (tetra[2][0], tetra[2][1], tetra[2][2], 1),
(point[0], point[1], point[2], 1)))
d0 = D0.det()
if d0 < 0:
s0 = -1
else:
s0 = 1
d1 = D1.det()
d2 = D2.det()
d3 = D3.det()
d4 = D4.det()
if abs(d0) == 0:
return False
if (d1.sign() == s0 or d1 == 0) and (d2.sign() == s0 or d2 == 0) and (
d3.sign() == s0 or d3 == 0) and (d4.sign() == s0 or d4 == 0):
return True
return False
def is_any_part_of_cube_inside_cell(cell, midpoint, side):
"""
Checks if any part of a cube is inside the cell spanned by the vectors in cell
"""
ps = [
midpoint + FracVector((x, y, z)) * side for x in [-1, 1]
for y in [-1, 1] for z in [-1, 1]
]
for p in ps:
if is_point_inside_cell(cell, p):
return True
return False
def metric_to_niggli(cell):
m = cell.noms
return FracVector(
((m[0][0], m[1][1], m[2][2]), (2 * m[1][2], 2 * m[0][2], 2 * m[0][1])),
cell.denom).simplify()