def proj3to2(n: Vector) -> Matrix:
es = List([
Vector([1.0, 0.0, 0.0]),
Vector([0.0, 1.0, 0.0]),
Vector([0.0, 0.0, 1.0])
])
vs = es.fmap(lambda v: proj(v, n))
return transpose(Matrix([vs[0].unbox(), vs[1].unbox(), vs[2].unbox()]))
def test_rotate(self):
b = Box([10, 10, 10], [1.0, 2.0, 0.0], [0, 1, 0])
axis = Axis(normal=Vector([-1.0, 0.0, 0.0]),
origin=Vector([0.0, 1.0, 0.0]))
theta = math.pi / 2
b_rotate = b.rotate(axis, theta)
self.assertEqual(b_rotate,
Box([10, 10, 10], [1.0, 1.0, -1.0], [0.0, 0.0, -1.0]))
def axis_to_axis(source, target):
"""
Rotation matrix which rotate source axis to target axis.
Implemented by firstly roteta source axis to `AXES3_STD.z`, and then rotate
`AXES3_STD.z` to target axis.
"""
source, target = Vector(source), Vector(target)
# source, target = source.unbox(), target.unbox()
return z_to_axis(target)@axis_to_z(source)
def from_axis_like(cls, axis_like, possible_origin=None):
if possible_origin is None:
possible_origin = Vector([0.0, 0.0, 0.0])
if isinstance(axis_like, Axis):
normal, origin = axis_like.normal, axis_like.origin
else:
normal, origin = axis_like, possible_origin
normal, origin = Vector(normal), Vector(origin)
return Axis(normal, origin)
def test_Vector_ndarray():
v = Vector([[1, 2, 3], [4, 5, 6]])
n = np.array([[1, 4], [2, 5], [3, 6]])
assert matmul(v, n) == Vector([[14, 32], [32, 27]])
v = Vector([1, 4])
n = np.array([1, 4])
assert matmul(v, n) == np.array([17])
def axis_x_of(n: Vector) -> Vector:
"""
Returns:
x axis if z is n.
"""
# FIXME add support for AXIS, lazy vector
n = unit(Vector(n))
main_index_of_n = argmax(abs_(n))
result = [0.0, 0.0, 0.0]
main_index_of_result = (main_index_of_n + 1) % 3
result[main_index_of_result] = n[main_index_of_n]
result[main_index_of_n] = -n[main_index_of_result]
return unit(Vector(result))
def get_rot_yz(axis):
axis = Vector(axis)
# rot_y = math.acos(axis.z)
# rot_z = math.atan2(axis.y, axis.x)
rot_y = math.acos(axis[2])
rot_z = math.atan2(axis[1], axis[0])
return rot_y, rot_z
class Box(Entity):
shape: Vector = attr.ib(converter=Vector)
origin: Vector = attr.ib(converter=Vector, default=Vector([0.0, 0.0, 0.0]))
normal: Vector = attr.ib(converter=Vector, default=Vector([0.0, 0.0, 1.0]))
# __slots__ = ['shape', 'origin', 'normal']
# def __init__(self,
# shape: Vector,
# origin: Vector = None,
# normal: Vector = None):
# self.shape = Vector(shape)
# if origin is None:
# origin = Vector([0.0, 0.0, 0.0])
# self.origin = Vector(origin)
# if normal is None:
# normal = Vector([0.0, 0.0, 1.0])
# self.normal = Vector(normal)
# def rotate_on_direction(self, direction, theta):
# from .point import Point
# p_origin = Point(self.origin)
# p_normal = Point(self.normal)
# return self.replace(origin=p_origin._rotate_on_direction(direction, theta).origin,
# normal=p_normal._rotate_on_direction(direction, theta).origin)
def is_collision(self, p: 'Entity') -> bool:
from dxl.shape.data.axis import Axis
from dxl.shape.function.rotation.matrix import axis_to_z
p_tran_rot = p.translate(-self.origin).origin @ transpose(
axis_to_z(self.normal))
if ((-self.shape.x / 2 <= p_tran_rot.x < self.shape.x / 2) and
(-self.shape.y / 2 <= p_tran_rot.y < self.shape.y / 2) and
(-self.shape.z / 2 <= p_tran_rot.z < self.shape.z / 2)):
return True
else:
return False
def fmap(self, f):
return Box(self.shape, f(self.origin), f(self.normal))
def __eq__(self, b):
if not isinstance(b, Box):
return False
return all_close(self.shape, b.shape) and all_close(self.origin, b.origin) and all_close(self.normal, b.normal)
def test_init(self):
a1 = Axis(normal=Vector([0.0, 1.0, 0.0]),
origin=Vector([1.0, 2.0, 0.0]))
a2 = Axis(normal=Vector([0.0, 1.0, 0.0]))
assert all_close(a1.normal, Vector([0.0, 1.0, 0.0]))
assert all_close(a1.origin, Vector([1.0, 2.0, 0.0]))
assert all_close(a2.normal, Vector([0.0, 1.0, 0.0]))
assert all_close(a2.origin, Vector([0.0, 0.0, 0.0]))
self.assertTrue(isinstance(a1, Axis))
self.assertTrue(isinstance(a2, Axis))
class Axis(Entity):
normal: Vector = attr.ib(converter=Vector)
origin: Vector = attr.ib(converter=Vector, default=Vector([0.0, 0.0, 0.0]))
def rotate_on_direction(self, direction: Vector, theta: float):
from dxl.shape.function import rotate
return self.replace(normal=rotate(self.normal, direction, theta),
origin=rotate(self.origin, direction, theta))
def fmap(self, f):
return Axis(f(self.normal), f(self.origin))
@classmethod
def from_axis_like(cls, axis_like, possible_origin=None):
if possible_origin is None:
possible_origin = Vector([0.0, 0.0, 0.0])
if isinstance(axis_like, Axis):
normal, origin = axis_like.normal, axis_like.origin
else:
normal, origin = axis_like, possible_origin
normal, origin = Vector(normal), Vector(origin)
return Axis(normal, origin)
def test_slice():
v = Vector([1.0, 2.0])
assert v[0] == 1.0
def test_rotate_on_direction(self):
a = Axis(normal=Vector([0.0, 1.0, 0.0]),
origin=Vector([1.0, 2.0, 0.0]))
direction_x = Vector([1.0, 0.0, 0.0])
direction_y = Vector([0.0, 1.0, 0.0])
direction_z = Vector([0.0, 0.0, 1.0])
theta = math.pi / 2
a_rot_x = a.rotate_on_direction(direction_x, theta)
a_rot_y = a.rotate_on_direction(direction_y, theta)
a_rot_z = a.rotate_on_direction(direction_z, theta)
assert all_close(a_rot_x.origin, Vector([1.0, 0.0, 2.0]))
assert all_close(a_rot_x.normal, Vector([0.0, 0.0, 1.0]))
assert all_close(a_rot_y.origin, Vector([0.0, 2.0, -1.0]))
assert all_close(a_rot_y.normal, Vector([0.0, 1.0, 0.0]))
assert all_close(a_rot_z.origin, Vector([-2.0, 1.0, 0.0]))
assert all_close(a_rot_z.normal, Vector([-1.0, 0.0, 0.0]))
def test_construction(self):
ax = Axis(Vector([1.0, 0.0, 0.0]))
self.assertEqual(ax.normal.x, 1.0)
self.assertEqual(ax.normal.z, 0.0)
def theta(position):
result = np.math.acos(Vector(position).x / norm(p_xy(position)))
if Vector(position).y < 0:
result = 2 * np.pi - result
return result
def ring_id(scanner, position):
return int((Vector(position).z / scanner.axial_length + 0.5) *
scanner.nb_rings * scanner.blocks[0].grid[2])
def outer_product(a: Vector, b: Vector):
return Vector(
[a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x])
def test_Vector_Vector_ndarray():
v = Vector([[1, 1], [1, 1]])
n = np.array([[1, 1], [1, 1]])
assert all_close(project(v, n), np.array([[0.5, 0.5], [0.5, 0.5]]))
def rotate_on_direction(self, direction: Vector, theta: float):
from dxl.shape.function import rotate
return self.replace(normal=rotate(self.normal, direction, theta),
origin=rotate(self.origin, direction, theta))
def fmap(self, f):
return Axis(f(self.normal), f(self.origin))
@classmethod
def from_axis_like(cls, axis_like, possible_origin=None):
if possible_origin is None:
possible_origin = Vector([0.0, 0.0, 0.0])
if isinstance(axis_like, Axis):
normal, origin = axis_like.normal, axis_like.origin
else:
normal, origin = axis_like, possible_origin
normal, origin = Vector(normal), Vector(origin)
return Axis(normal, origin)
AXIS3_X = Axis(Vector([1.0, 0.0, 0.0]))
AXIS3_Y = Axis(Vector([0.0, 1.0, 0.0]))
AXIS3_Z = Axis(Vector([0.0, 0.0, 1.0]))
class AXES3:
x = AXIS3_X
y = AXIS3_Y
z = AXIS3_Z
def test_project_withvalue():
v1 = Vector([1.0, 0.0])
v2 = Vector([1.0, 1.0])
assert all_close(project(v1, v2), Vector([0.5, -0.5]))
def proj(v: Vector, n: Vector):
v, n = Vector(v), Vector(n)
p = project(v, n)
return Vector([p[(np.argmax(n) + i + 1) % len(p)] for i in range(v.size - 1)])
def test_matmul():
v = Vector([1.0, 1.0])
assert v@v == 2.0
assert isinstance(v@v, float)
def test_random_vectors(self, v):
rot = z_to_axis(Vector(v))
assert all_close(rot @ (AXIS3_Z.normal), v)
def test_matmul_with_nparray():
d = np.array([1.0, 1.0])
v = Vector(d)
assert v@d == 2.0
# assert d@v == 2.0
def embed2to3(n: Vector) -> Matrix:
es = List([Vector([1.0, 0.0]), Vector([0.0, 1.0])])
vs = es.fmap(lambda v: embed(v, n)).fmap(lambda v: v.unbox())
return transpose(Matrix(vs))
def test_Vector_Matrix():
v = Vector([[1, 4], [2, 5], [3, 6]])
m = Matrix([[1, 2, 3], [4, 5, 6]])
assert matmul(v, m) == Vector([[17, 22, 27], [22, 29, 36], [27, 36, 45]])
def test_Vector_Vector():
v1 = Vector([[1, 2, 3], [4, 5, 6]])
v2 = Vector([[1, 4], [2, 5], [3, 6]])
assert matmul(v1, v2) == Vector([[14, 32], [32, 27]])
def sub_box_shape(b: Box, grid: List[int]) -> Vector:
return Vector([s / g for s, g in zip(b.shape, grid)])
def axis_y_of(n: Vector) -> Vector:
n = unit(Vector(n))
return unit(outer_product(n, axis_x_of(n)))
def embed(v: Vector, n: Vector):
v, n = Vector(v), Vector(n)
from ..axes import axis_x_of, axis_y_of
return axis_x_of(n) * v.x + axis_y_of(n) * v.y
def test_Matrix_Vector():
m = Matrix([[1, 2, 3], [4, 5, 6]])
v = Vector([[1, 4], [2, 5], [3, 6]])
assert matmul(m, v) == Vector([[14, 32], [32, 27]])