def intersect_line(self, Z1, Z2):
"""Return a list (0, 1 or 2 complex) of coordinates of the
intersection of the segment with a line defined by two complex
Parameters
----------
self : Segment
A Segment object
Returns
-------
Z_list: list
Complex coordinates of the intersection (if any,
return [begin, end] if the segment is part of the line)
"""
Z3 = self.begin
Z4 = self.end
Z_list = inter_line_line(Z1, Z2, Z3, Z4)
if len(Z_list) == 0:
# No intersection
return []
elif len(Z_list) == 1:
# One intersect. Is it between begin and end or not ?
Z_int = Z_list[0]
Seg_len = self.comp_length()
if np_abs(Z_int - Z3) <= Seg_len and np_abs(Z_int - Z4) <= Seg_len:
return [Z_int]
else:
return []
elif len(Z_list) == 2:
# The segment is on the line
return [Z3, Z4]
def build_geometry(self, alpha=0, delta=0, is_simplified=False):
"""Compute the curve (Segment) needed to plot the Slot.
The ending point of a curve is the starting point of the next curve in
the list
Parameters
----------
self : HoleM57
A HoleM57 object
alpha : float
Angle to rotate the slot (Default value = 0) [rad]
delta : complex
Complex to translate the slot (Default value = 0)
is_simplified : bool
True to avoid line superposition
Returns
-------
surf_list: list
List of SurfLine needed to draw the HoleM57
"""
if self.get_is_stator(): # check if the slot is on the stator
st = "S"
else:
st = "R"
Rbo = self.get_Rbo()
# "Tooth" angle (P1',0,P1)
alpha_T = 2 * arcsin(self.W3 / (2 * (Rbo - self.H1)))
# magnet pole pitch angle (Z1,0,Z1')
alpha_S = (2 * pi / self.Zh) - alpha_T
# Angle (P1,P1',P4') and (P5',P4', )
alpha = (pi - self.W0) / 2
# Half slot pitch
hssp = pi / self.Zh
Z1 = (Rbo - self.H1) * exp(-1j * alpha_S / 2)
x11 = 2 * sin(alpha_S / 2) * (Rbo - self.H1) # Distance from P1 to P1'
# In rect triangle P4, P1, perp (P1,P1') with P4
H = tan(alpha) * (x11 / 2 - self.W1 / 2)
Z4 = Z1.real - H - 1j * self.W1 / 2
x45 = self.H2 / cos(alpha) # distance from P4 to P5
Z5 = Z4 - x45
# Get coordinates of "random" points on (P5,P8) and (P1,P8)
# In ref P4 center and P1 on X+ axis
Z58 = (self.W4 - 1j * self.H2) * exp(1j * angle(Z1 - Z4)) + Z4
# In the tooth ref
Z18 = (Rbo - self.H1 - self.H2 + 1j * self.W3 / 2) * exp(-1j * hssp)
Z8 = inter_line_line(Z5, Z58, Z1, Z18)[0]
# In ref "b" P4 center and P1 on X+ axis
Z8b = (Z8 - Z4) * exp(-1j * angle(Z1 - Z4))
Z2 = (Z8b + 1j * self.H2 - self.W2) * exp(1j * angle(Z1 - Z4)) + Z4
Z3 = (Z8b + 1j * self.H2 - self.W2 - self.W4) * exp(
1j * angle(Z1 - Z4)) + Z4
Z7 = (Z8b - self.W2) * exp(1j * angle(Z1 - Z4)) + Z4
Z6 = (Z8b - self.W2 - self.W4) * exp(1j * angle(Z1 - Z4)) + Z4
# Symmetry
Z1s = Z1.conjugate()
Z2s = Z2.conjugate()
Z3s = Z3.conjugate()
Z4s = Z4.conjugate()
Z5s = Z5.conjugate()
Z6s = Z6.conjugate()
Z7s = Z7.conjugate()
Z8s = Z8.conjugate()
surf_list = list()
# Z_list = array([Z1, Z2, Z3, Z4, Z5, Z6, Z7, Z8])
# plt.plot(Z_list.real, Z_list.imag, "x r")
# for ii in range(8):
# plt.text(Z_list[ii].real, Z_list[ii].imag, "Z" + str(ii + 1))
# plt.show()
# Check schematics:
assert abs(abs(Z7 - Z8) - self.W2) < 1e-6
assert abs(abs(Z6 - Z7) - self.W4) < 1e-6
assert abs(abs(Z2 - Z3) - self.W4) < 1e-6
assert abs(abs(Z2 - Z7) - self.H2) < 1e-6
assert abs(abs(Z4 - Z4s) - self.W1) < 1e-6
assert abs(abs(Z5 - Z5s) - self.W1) < 1e-6
# TODO: Create all the surfaces for all the cases
# (with/without magnet W1>0 or W1=0)
# Air surface (W3) with magnet_0
curve_list_air = list()
curve_list_air.append(Segment(Z1, Z2))
curve_list_air.append(Segment(Z2, Z7))
if self.W2 > 0:
curve_list_air.append(Segment(Z7, Z8))
curve_list_air.append(Segment(Z8, Z1))
# initiating the label of the line on the air surface
curve_list_air = set_name_line(curve_list_air, "hole_1_line")
point_ref = (Z1 + Z2 + Z7 + Z8) / 4
S1 = SurfLine(line_list=curve_list_air, label="Air", point_ref=point_ref)
# Magnet_0 surface
curve_list_mag = list()
if is_simplified:
curve_list_mag.append(Segment(Z7, Z2))
curve_list_mag.append(Segment(Z3, Z6))
else:
curve_list_mag.append(Segment(Z2, Z3))
curve_list_mag.append(Segment(Z3, Z6))
curve_list_mag.append(Segment(Z6, Z7))
curve_list_mag.append(Segment(Z7, Z2))
# initiating the label of the line of the magnet surface
curve_list_mag = set_name_line(curve_list_mag, "magnet_1_line")
point_ref = (Z2 + Z3 + Z6 + Z7) / 4
S2 = SurfLine(
line_list=curve_list_mag,
label="Magnet" + st + "_N_R0_T0_S0",
point_ref=point_ref,
)
# Air surface with magnet_0 and W1 > 0
curve_list_air = list()
curve_list_air.append(Segment(Z4, Z5))
curve_list_air.append(Segment(Z5, Z6))
curve_list_air.append(Segment(Z6, Z3))
if abs(Z4 - Z3) > 1e-6:
curve_list_air.append(Segment(Z3, Z4))
# initiating the label of the line on the air surface
curve_list_air = set_name_line(curve_list_air, "hole_2_line")
point_ref = (Z6 + Z5 + Z4) / 3
S3 = SurfLine(line_list=curve_list_air, label="Air", point_ref=point_ref)
# Symmetry Air surface (W3) with magnet_1
curve_list_air = list()
curve_list_air.append(Segment(Z2s, Z1s))
curve_list_air.append(Segment(Z1s, Z8s))
if self.W2 > 0:
curve_list_air.append(Segment(Z8s, Z7s))
curve_list_air.append(Segment(Z7s, Z2s))
point_ref = (Z1s + Z2s + Z8s + Z7s) / 4
# initiating the label of the line on the air surface
curve_list_air = set_name_line(curve_list_air, "hole_3_line")
S4 = SurfLine(line_list=curve_list_air, label="Air", point_ref=point_ref)
# magnet_1 surface
curve_list_mag = list()
if is_simplified:
curve_list_mag.append(Segment(Z2s, Z7s))
curve_list_mag.append(Segment(Z6s, Z3s))
else:
curve_list_mag.append(Segment(Z3s, Z2s))
curve_list_mag.append(Segment(Z2s, Z7s))
curve_list_mag.append(Segment(Z7s, Z6s))
curve_list_mag.append(Segment(Z6s, Z3s))
point_ref = (Z3s + Z2s + Z7s + Z6s) / 4
# initiating the label of the line on the magnet surface
curve_list_mag = set_name_line(curve_list_mag, "magnet_2_line")
S5 = SurfLine(
line_list=curve_list_mag,
label="Magnet" + st + "_N_R0_T1_S0",
point_ref=point_ref,
)
# Air surface with magnet_1 and W1 > 0
curve_list_air = list()
curve_list_air.append(Segment(Z3s, Z6s))
curve_list_air.append(Segment(Z6s, Z5s))
curve_list_air.append(Segment(Z5s, Z4s))
if abs(Z4 - Z3) > 1e-6:
curve_list_air.append(Segment(Z4s, Z3s))
point_ref = (Z3s + Z6s + Z5s) / 3
# initiating the label of the line on the air surface
curve_list_air = set_name_line(curve_list_air, "hole_4_line")
S6 = SurfLine(line_list=curve_list_air, label="Air", point_ref=point_ref)
# Air surface between magnet_0 and magnet_1 with W1 == 0
curve_list_air = list()
curve_list_air.append(Segment(Z3, Z4))
curve_list_air.append(Segment(Z4, Z3s))
curve_list_air.append(Segment(Z3s, Z6s))
curve_list_air.append(Segment(Z6s, Z5))
curve_list_air.append(Segment(Z5, Z6))
curve_list_air.append(Segment(Z6, Z3))
# initiating the label of the line on the air surface
curve_list_air = set_name_line(curve_list_air, "hole_2_line")
point_ref = (Z5 + Z4) / 2
S7 = SurfLine(line_list=curve_list_air, label="Air", point_ref=point_ref)
# Create the surface list by selecting the correct ones
if self.magnet_0 and self.magnet_1 and self.W1 > 0:
surf_list = [S1, S2, S3, S6, S5, S4]
elif self.magnet_0 and self.magnet_1 and self.W1 == 0:
surf_list = [S1, S2, S7, S5, S4]
# elif self.magnet_0 and not self.magnet_1 and self.W1 > 0:
# surf_list = [S1, S2, S3, S9]
# elif self.magnet_0 and not self.magnet_1 and self.W1 == 0:
# surf_list = [S1, S2, S10]
# elif not self.magnet_0 and self.magnet_1 and self.W1 > 0:
# surf_list = [S8, S6, S5, S4]
# elif not self.magnet_0 and self.magnet_1 and self.W1 == 0:
# surf_list = [S11, S5, S4]
# elif not self.magnet_0 and not self.magnet_1 and self.W1 > 0:
# surf_list = [S8, S9]
# elif not self.magnet_0 and not self.magnet_1 and self.W1 == 0:
# surf_list = [S12]
# Apply the transformations
for surf in surf_list:
surf.rotate(alpha)
surf.translate(delta)
return surf_list
def _comp_point_coordinate(self):
"""Compute the point coordinates needed to plot the Slot.
Parameters
----------
self : HoleM53
A HoleM53 object
Returns
-------
point_dict: dict
A dict of the slot coordinates
"""
Rext = self.get_Rext()
# "Tooth" angle (P1',0,P1)
alpha_T = 2 * arcsin(self.W3 / (2 * (Rext - self.H1)))
# magnet pole pitch angle (Z1,0,Z1')
alpha_S = (2 * pi / self.Zh) - alpha_T
# Angle (P1,P1',P4') and (P5',P4', )
alpha = (pi - self.W0) / 2
# Half slot pitch
hssp = pi / self.Zh
Z1 = (Rext - self.H1) * exp(-1j * alpha_S / 2)
x11 = 2 * sin(alpha_S / 2) * (Rext - self.H1) # Distance from P1 to P1'
# In rect triangle P4, P1, perp (P1,P1') with P4
H = tan(alpha) * (x11 / 2 - self.W1 / 2)
Z4 = Z1.real - H - 1j * self.W1 / 2
x45 = self.H2 / cos(alpha) # distance from P4 to P5
Z5 = Z4 - x45
# Get coordinates of "random" points on (P5,P8) and (P1,P8)
# In ref P4 center and P1 on X+ axis
Z58 = (self.W4 - 1j * self.H2) * exp(1j * angle(Z1 - Z4)) + Z4
# In the tooth ref
Z18 = (Rext - self.H1 - self.H2 + 1j * self.W3 / 2) * exp(-1j * hssp)
Z8 = inter_line_line(Z5, Z58, Z1, Z18)[0]
# In ref "b" P4 center and P1 on X+ axis
Z8b = (Z8 - Z4) * exp(-1j * angle(Z1 - Z4))
Z9 = (Z8b + 1j * self.H2) * exp(1j * angle(Z1 - Z4)) + Z4
Z2 = (Z8b + 1j * self.H2 - self.W2) * exp(1j * angle(Z1 - Z4)) + Z4
Z3 = (Z8b + 1j * self.H2 - self.W2 - self.W4) * exp(
1j * angle(Z1 - Z4)) + Z4
Z7 = (Z8b - self.W2) * exp(1j * angle(Z1 - Z4)) + Z4
Z6 = (Z8b - self.W2 - self.W4) * exp(1j * angle(Z1 - Z4)) + Z4
point_dict = dict()
point_dict["Z1"] = Z1
point_dict["Z2"] = Z2
point_dict["Z3"] = Z3
point_dict["Z4"] = Z4
point_dict["Z5"] = Z5
point_dict["Z6"] = Z6
point_dict["Z7"] = Z7
point_dict["Z8"] = Z8
point_dict["Z9"] = Z9
# Symmetry
point_dict["Z1s"] = Z1.conjugate()
point_dict["Z2s"] = Z2.conjugate()
point_dict["Z3s"] = Z3.conjugate()
point_dict["Z4s"] = Z4.conjugate()
point_dict["Z5s"] = Z5.conjugate()
point_dict["Z6s"] = Z6.conjugate()
point_dict["Z7s"] = Z7.conjugate()
point_dict["Z8s"] = Z8.conjugate()
point_dict["Z9s"] = Z9.conjugate()
point_dict["Zc0"] = inter_line_line(Z3, Z2, point_dict["Z3s"],
point_dict["Z2s"])[0]
return point_dict