def __init__(self,
pmin=None,
pmax=None,
xmin=0,
ymin=0,
zmin=0,
xmax=1,
ymax=1,
zmax=1):
super().__init__()
self._pmin = Point()
self._pmax = Point()
if pmin is None:
pmin = [xmin, ymin, zmin]
self.pmin = pmin
if pmax is None:
pmax = [xmax, ymax, zmax]
self.pmax = pmax
# assert self.pmin <= self.pmax
assert np.all(np.less_equal(self.pmin, self.pmax))
self.points.extend([self.pmin, self.pmax])
self.fmtstr = "pmin={pmin!r}, pmax={pmax!r}"
def test6():
p2 = Point(np.zeros(3), nd=2)
p3 = Point(np.zeros(2), nd=3)
assert_equal(p2, Point(np.zeros(2)))
assert_equal(p3, Point(np.zeros(3)))
assert_true(len(p2) == 2)
assert_true(len(p3) == 3)
def test_parallelepiped():
r = Parallelepiped()
assert_is_instance(r, Parallelepiped)
assert_equal(r.o, Point([0, 0, 0]))
assert_true(np.allclose(r.measure, 1.0))
assert_equal(r.centroid, Point([1, 1, 0.5]))
assert_true(r.contains([0.5, 0.5, 0.5]))
assert_false(r.contains([0, 0, 1]))
assert_is_instance(r.centroid, Point)
def test_cone():
r = Cone()
assert_is_instance(r, Cone)
assert_true(np.allclose(r.measure, 2 * np.pi / 3))
assert_equal(r.p1, Point(np.zeros(3)))
assert_equal(r.p2, Point([0, 0, 2]))
assert_true(r.contains([0, 0, 1]))
assert_false(r.contains([0, 0, 2.1]))
assert_is_instance(r.centroid, Point)
assert_is_instance(r.axis, Vector)
def generate(self):
"""Generate structure data."""
super().generate()
if self.L0 is not None and self.fix_Lz:
Lz_cutoff = 10 * self.L0 + 1
region_bounds = Cuboid(pmin=Point([-np.inf, -np.inf, 0]),
pmax=Point([np.inf, np.inf, Lz_cutoff]))
self.atoms.clip_bounds(region_bounds)
def test_triangle():
r = Triangle()
assert_is_instance(r, Triangle)
assert_equal(r.centroid, Point([1 / 3, 1 / 3]))
assert_true(np.allclose(r.measure, 0.5))
assert_equal(r.p1, Point(nd=2))
assert_equal(r.p2, Point([0, 1]))
assert_equal(r.p3, Point([1, 0]))
assert_true(r.contains([0.25, 0.25]))
assert_false(r.contains([1, 1]))
assert_is_instance(r.centroid, Point)
def test_cylinder():
r = Cylinder()
assert_is_instance(r, Cylinder)
assert_true(np.allclose(r.measure, 2 * np.pi))
assert_equal(r.p1, Point([0, 0, -1]))
assert_equal(r.p2, Point([0, 0, 1]))
assert_true(r.contains([0, 0, 0]))
assert_false(r.contains([1.1, 0, 0]))
assert_equal(r.centroid, Point())
r.p2 = [0, 0, 2]
assert_equal(r.centroid, Point([0, 0, 0.5]))
assert_is_instance(r.centroid, Point)
assert_is_instance(r.axis, Vector)
def test1():
p = Point()
assert_true(np.allclose(p, np.zeros(3)))
p = Point([0, 0, 0], dtype=float)
assert_true(np.allclose(p, np.zeros(3)))
p = Point(np.ones(3))
assert_true(np.allclose(p, np.ones(3)))
p = Point([None, None, None])
assert_true(np.allclose(p, np.zeros(3)))
p = Point(np.arange(10))
assert_true(np.allclose(p, np.arange(10)))
def test1():
print('generating graphene structure')
graphene = GrapheneGenerator(armchair_edge_length=5, zigzag_edge_length=5)
lattice = graphene.lattice
print('graphene.bounds:\n{}'.format(graphene.bounds))
print('graphene.centroid:\n{}'.format(graphene.centroid))
print('graphene.lattice:\n{}'.format(lattice))
print('graphene.lattice.a1:\n{}'.format(lattice.a1))
print('graphene.lattice.a2:\n{}'.format(lattice.a2))
print('graphene.lattice.a3:\n{}'.format(lattice.a3))
print('graphene.lattice.orientation_matrix:\n{}'.format(
lattice.orientation_matrix))
print('rotating graphene')
graphene.rotate(angle=-np.pi / 2, axis='x')
print('graphene.bounds:\n{}'.format(graphene.bounds))
print('graphene.centroid:\n{}'.format(graphene.centroid))
print('graphene.lattice:\n{}'.format(lattice))
print('graphene.lattice.a1:\n{}'.format(lattice.a1))
print('graphene.lattice.a2:\n{}'.format(lattice.a2))
print('graphene.lattice.a3:\n{}'.format(lattice.a3))
print('graphene.lattice.orientation_matrix:\n{}'.format(
lattice.orientation_matrix))
assert_true(np.allclose(lattice.angles, 3 * [90.0]))
lattice_region = Cuboid(pmax=lattice.lengths)
# lattice_region = Parallelepiped(u=lattice.a * xhat,
# v=lattice.b * yhat,
# w=lattice.c * zhat)
assert_equal(lattice_region.a, lattice.a)
assert_equal(lattice_region.b, lattice.b)
assert_equal(lattice_region.c, lattice.c)
print('lattice_region:\n{}'.format(lattice_region))
print('lattice_region.centroid:\n{}'.format(lattice_region.centroid))
print('\nrotating lattice_region')
lattice_region.rotate(transform_matrix=lattice.orientation_matrix)
# assert_equal(lattice_region.a, lattice.a)
# assert_equal(lattice_region.b, lattice.b)
# assert_equal(lattice_region.c, lattice.c)
print('lattice_region:\n{}'.format(lattice_region))
print('lattice_region.centroid:\n{}'.format(lattice_region.centroid))
print('\ncentering lattice_region on graphene centroid')
tvec = Vector(Point(graphene.centroid) - lattice_region.centroid)
lattice_region.translate(tvec)
# assert_equal(lattice_region.a, lattice.a)
# assert_equal(lattice_region.b, lattice.b)
# assert_equal(lattice_region.c, lattice.c)
print('lattice_region:\n{}'.format(lattice_region))
print('lattice_region.centroid:\n{}'.format(lattice_region.centroid))
bounding_box = generate_bounding_box(from_lattice=lattice,
center=graphene.centroid,
verbose=True)
print('bounding_box:\n{}'.format(bounding_box))
assert_equal(bounding_box, lattice_region)
print('lattice_region.lengths: {}, {}, {}'.format(lattice_region.a,
lattice_region.b,
lattice_region.c))
def contains(self, point):
"""Test region membership of `point` in :class:`Ellipsoid`.
Parameters
----------
point : array_like
Returns
-------
:class:`~python:bool`
`True` if `point` is within :class:`Ellipsoid`,
`False` otherwise
Notes
-----
A `point` :math:`(p_x, p_y, p_z)` is within the bounded region of
an ellipsoid with center :math:`(c_x, c_y, c_z)` and semi-axes lengths
:math:`r_x, r_y, r_z` if the following is true:
.. math::
\\left(\\frac{p_x - c_x}{r_x}\\right)^2 +
\\left(\\frac{p_y - c_y}{r_y}\\right)^2 +
\\left(\\frac{p_z - c_z}{r_z}\\right)^2\\le 1
"""
px, py, pz = Point(point)
cx, cy, cz = self.center
rx, ry, rz = self.rx, self.ry, self.rz
q1 = (px - cx)**2 / rx**2
q2 = (py - cy)**2 / ry**2
q3 = (pz - cz)**2 / rz**2
return q1 + q2 + q3 <= 1.0
def contains(self, point):
"""Test region membership of `point` in :class:`Sphere`.
Parameters
----------
point : array_like
Returns
-------
:class:`~python:bool`
`True` if `point` is within :class:`Sphere`,
`False` otherwise.
Notes
-----
A `point` :math:`(p_x, p_y, p_z)` is within the bounded region
of a sphere with center :math:`(h, k, l)` and radius :math:`r`
if the following is true:
.. math::
(p_x - h)^2 + (p_y - k)^2 + (p_z - l)^2 \\le r^2
"""
x, y, z = Point(point)
h, k, l = self.center
r = self.r
return (x - h)**2 + (y - k)**2 + (z - l)**2 <= r**2
def centroid(self):
""":class:`Triangle` centroid, :math:`(c_x, c_y)`.
Computed as 2D :class:`Point` :math:`(c_x, c_y)` with
coordinates:
.. math::
c_x = \\frac{x_1 + x_2 + x_3}{3}
c_y = \\frac{y_1 + y_2 + y_3}{3}
Returns
-------
:class:`Point`
2D :class:`Point` of centroid.
"""
x1, y1 = self.p1
x2, y2 = self.p2
x3, y3 = self.p3
cx = (x1 + x2 + x3) / 3
cy = (y1 + y2 + y3) / 3
return Point([cx, cy])
def __init__(self, o=None, u=None, v=None, w=None):
self._o = Point()
self._u = Vector()
self._v = Vector()
self._w = Vector()
super().__init__()
if o is None:
o = [0, 0, 0]
self.o = o
if u is None:
u = [1, 0, 0]
self.u = u
if v is None:
v = [1, 1, 0]
self.v = v
if w is None:
w = [0, 1, 1]
self.w = w
self.points.append(self.o)
self.vectors.extend([self.u, self.v, self.w])
self.fmtstr = "o={o!r}, u={u!r}, v={v!r}, w={w!r}"
def contains(self, point):
"""Test region membership of `point` in :class:`Square`.
Parameters
----------
point : array_like
Returns
-------
:class:`~python:bool`
`True` if `point` is within :class:`Square`,
`False` otherwise.
Notes
-----
A `point` :math:`(p_x, p_y)` is within the bounded region of a
square with center :math:`(c_x, c_y)` and side length :math:`a`
if the following is true:
.. math::
c_i - \\frac{a}{2}\\le p_i\\le c_i + \\frac{a}{2}\\forall
i\\in \\{x, y\\}
"""
px, py = Point(point)
cx, cy = self.center
a = self.a
xmin = cx - a / 2
xmax = cx + a / 2
ymin = cy - a / 2
ymax = cy + a / 2
return (px >= xmin) and (px <= xmax) and (py >= ymin) and (py <= ymax)
def centroid(self):
"""Paralleogram centroid, :math:`(c_x, c_y)`.
Computed as the 2D point :math:`(c_x, c_y)` with coordinates:
.. math::
c_x = o_x + \\frac{u_x + v_x}{2}
c_y = o_y + \\frac{u_y + v_y}{2}
where :math:`(o_x, o_y)`, :math:`(u_x, u_y)`, and :math:`(v_x, v_y)`
are the :math:`(x, y)` coordinates of the origin :math:`o`
and :math:`(x, y)` components of the direction vectors
:math:`\\mathbf{u}` and :math:`\\mathbf{v}`, respectively.
Returns
-------
:class:`Point`
2D :class:`Point` of centroid.
"""
ox, oy = self.o
ux, uy = self.u
vx, vy = self.v
cx = ox + (ux + vx) / 2
cy = oy + (uy + vy) / 2
return Point([cx, cy])
def test13():
latt = Crystal3DLattice(a=4.0, b=4.0, c=4.0, alpha=90, beta=90, gamma=90)
print(latt)
p = [2.1, 0.9, 0.5]
assert_true(
np.allclose(latt.wrap_fractional_coordinate(p), Point(
(0.1, 0.9, 0.5))))
def __init__(self, p1=None, p2=None, r=1):
super().__init__()
self._p1 = Point()
self._p2 = Point()
if p1 is None:
p1 = [0, 0, -1]
if p2 is None:
p2 = [0, 0, 1]
self.p1 = p1
self.p2 = p2
self.points.extend([self.p1, self.p2])
self.r = r
self.fmtstr = "p1={p1!r}, p2={p2!r}, r={r:.3f}"
def test_rectangle():
r = Rectangle()
assert_is_instance(r, Rectangle)
assert_equal(r.measure, 1)
assert_equal(r.centroid, Point([0.5, 0.5]))
assert_true(r.contains(r.centroid))
assert_false(r.contains([1.1, 1.1]))
assert_is_instance(r.centroid, Point)
def test_ellipsoid():
r = Ellipsoid()
assert_is_instance(r, Ellipsoid)
assert_equal(r.centroid, Point([0, 0, 0]))
assert_true(np.allclose(r.measure, 4 / 3 * np.pi))
assert_true(r.contains(r.centroid))
assert_false(r.contains([1.01, 1.01, 1.01]))
assert_is_instance(r.centroid, Point)
def test_square():
r = Square()
assert_is_instance(r, Square)
assert_equal(r.measure, 1)
assert_equal(r.centroid, Point([0, 0]))
assert_true(r.contains([0, 0]))
assert_false(r.contains([1, 1]))
assert_is_instance(r.centroid, Point)
def test_cuboid():
r = Cuboid()
assert_is_instance(r, Cuboid)
assert_equal(r.centroid, Point([0.5, 0.5, 0.5]))
assert_true(np.allclose(r.measure, 1.0))
assert_true(r.contains(r.centroid))
assert_false(r.contains([-0.1, 0, 0]))
assert_is_instance(r.centroid, Point)
def test_cube():
r = Cube()
assert_is_instance(r, Cube)
assert_equal(r.centroid, Point([0, 0, 0]))
assert_true(np.allclose(r.measure, 1.0))
assert_true(r.contains([0, 0, 0]))
assert_false(r.contains([1, 1, 1]))
assert_is_instance(r.centroid, Point)
def test_circle():
r = Circle()
assert_is_instance(r, Circle)
assert_equal(r.measure, np.pi)
assert_equal(r.centroid, Point([0, 0]))
assert_equal(r.r, 1.0)
assert_true(r.contains([0, 0]))
assert_false(r.contains([1.1, 0]))
assert_is_instance(r.centroid, Point)
def test_sphere():
r = Sphere()
assert_is_instance(r, Sphere)
assert_equal(r.center, Point([0, 0, 0]))
assert_equal(r.r, 1.0)
assert_true(np.allclose(r.measure, 4 / 3 * np.pi))
assert_true(r.contains([0, 0, 0]))
assert_false(r.contains([1.1, 1.1, 1.1]))
assert_is_instance(r.centroid, Point)
def __init__(self, pmin=None, pmax=None, xmin=0, ymin=0, xmax=1, ymax=1):
super().__init__()
self._pmin = Point(nd=2)
self._pmax = Point(nd=2)
if pmin is None:
pmin = [xmin, ymin]
self.pmin = pmin
if pmax is None:
pmax = [xmax, ymax]
self.pmax = pmax
self.points.append([self.pmin, self.pmax])
self.fmtstr = "pmin={pmin!r}, pmax={pmax!r}"
def contains(self, point):
"""Test region membership of `point` in :class:`Cone`.
Parameters
----------
point : array_like
Returns
-------
:class:`~python:bool`
`True` if `point` is within :class:`Cone`,
`False` otherwise.
Notes
-----
A `point` :math:`(p_x, p_y, p_z)` is within the bounded region
of a cone with a base of radius :math:`r` centered at
:math:`p_1=(x_1, y_1, z_1)` and tip at :math:`p_2 = (x_2, y_2, z_2)`
if the following is true:
.. math::
0\\le q\\le 1\\land
(x_1 - p_x + (x_2 - x_1) q)^2 +
(y_1 - p_y + (y_2 - y_1) q)^2 +
(z_1 - p_z + (z_2 - z_1) q)^2 \\le r^2 q^2
where :math:`q` is:
.. math::
q = \\frac{(p_x - x_1)(x_2 - x_1) +
(p_y - y_1)(y_2 - y_1) +
(p_z - z_1)(z_2 - z_1)}{(x_2 - x_1)^2 +
(y_2 - y_1)^2 + (z_2 - z_1)^2}
"""
px, py, pz = Point(point)
x1, y1, z1 = self.p1
x2, y2, z2 = self.p2
r = self.r
q1 = ((px - x1) * (x2 - x1) +
(py - y1) * (y2 - y1) +
(pz - z1) * (z2 - z1)) / \
((x2 - x1) ** 2 + (y2 - y1) ** 2 + (z2 - z1) ** 2)
q2 = (x1 - px + (x2 - x1) * q1) ** 2 + \
(y1 - py + (y2 - y1) * q1) ** 2 + \
(z1 - pz + (z2 - z1) * q1) ** 2
q3 = r**2 * q1**2
return (not np.allclose(x1, x2) or not np.allclose(y1, y2) or
not np.allclose(z1, z2)) and r > 0 and q1 >= 0 and q1 <= 1 \
and q2 <= q3
def __init__(self, p1=None, p2=None, p3=None):
super().__init__()
self._p1 = Point(nd=2)
self._p2 = Point(nd=2)
self._p3 = Point(nd=2)
if p1 is None:
p1 = [0, 0]
if p2 is None:
p2 = [0, 1]
if p3 is None:
p3 = [1, 0]
self.p1 = p1
self.p2 = p2
self.p3 = p3
self.points.extend([self.p1, self.p2, self.p3])
self.fmtstr = "p1={p1!r}, p2={p2!r}, p3={p3!r}"
def test_point_rotation():
assert_true(
np.allclose(rotate(Point([1.0, 0.0]), np.pi / 2), np.array([0.0,
1.0])))
with assert_raises(ValueError):
np.allclose(rotate(Point([1.0, 0.0, 0.0]), angle=np.pi / 2),
np.array([0.0, 1.0, 0.0]))
assert_true(
np.allclose(
rotate(Point([1.0, 0.0, 0.0]),
angle=np.pi / 2,
axis=Vector([1.0, 0.0, 0.0])), np.array([1.0, 0.0, 0.0])))
assert_true(
np.allclose(
rotate(Point([0.0, 1.0, 0.0]),
angle=np.pi / 2,
axis=Vector([1.0, 0.0, 0.0])), np.array([0.0, 0.0, 1.0])))
def i(self, value):
"""Set :math:`i_x, i_y, i_z` image flags.
Parameters
----------
value : array_like
"""
if not isinstance(value, (list, np.ndarray)):
raise TypeError('Expected an array_like object')
self._i[:] = Point(value, nd=3, dtype=int)
def test3():
p = Point([1.0, 0.0, 0.0])
p.rotate(np.pi/2, rot_axis='z')
assert_true(np.allclose(p, np.array([0, 1, 0])))
p.rotate(np.pi/2, rot_axis='z')
assert_true(np.allclose(p, np.array([-1, 0, 0])))
p.rotate(np.pi/2, rot_axis='z')
assert_true(np.allclose(p, np.array([0, -1, 0])))
p.rotate(np.pi/2, rot_axis='z')
assert_true(np.allclose(p, np.array([1, 0, 0])))
p.rotate(np.pi/2, rot_axis=[0, 0, 1], rot_point=[1, 1, 0])
assert_true(np.allclose(p, np.array([2, 1, 0])))
