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influence_coefficient_functions.py
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import numpy as np
from vector_class import Vector
from panel_class import Panel, quadPanel, triPanel
from is_inside_polygon import is_inside_polygon
def Src_influence_coeff(r_p:Vector, panel:Panel, alpha=10):
n = panel.num_vertices
r_vertex = panel.r_vertex_local
r_cp = panel.r_cp
R = panel.R
r = r_p - r_cp
r_local = r.transformation(R)
r = r_local
if r.norm() >= alpha * panel.char_length:
B = panel.area/r.norm()
elif r.z == 0:
B = 0
for i in range(n-1, -1, -1):
# panel numbering follow counter clock wise direction
# Hess and Smith integrals are calculated with clock wise ordering
a = (i+1)%n # 0, 3, 2, 1 (cw) (instead 0, 1, 2, 3 (cw))
b = i # 3, 2, 1, 0, (clock wise) (instead 1, 2, 3, 0 (cw))
r_ab = r_vertex[b] - r_vertex[a]
d_ab = r_ab.norm()
r_a = r - r_vertex[a]
r_a = r_a.norm()
r_b = r - r_vertex[b]
r_b = r_b.norm()
first_term = (
(r.x - r_vertex[a].x) * (r_vertex[b].y - r_vertex[a].y)
- (r.y - r_vertex[a].y) * (r_vertex[b].x - r_vertex[a].x)
)
first_term = first_term/d_ab
if (r_a + r_b - d_ab) == 0:
# point p coincide lies on a panel's edge
# log term ---> inf => B ---> inf
log_term = 0
else:
# katz & Plotkin
log_term = np.log((r_a + r_b + d_ab)/(r_a + r_b - d_ab))
# paper of Lothar birk
# log_term = np.log((r_a + r_b - d_ab)/(r_a + r_b + d_ab))
B = B + first_term * log_term
else:
B = 0
for i in range(n-1, -1, -1):
# panel numbering follow counter clock wise direction
# Hess and Smith integrals are calculated with clock wise ordering
a = (i+1)%n # 0, 3, 2, 1 (cw) (instead 0, 1, 2, 3 (cw))
b = i # 3, 2, 1, 0, (clock wise) (instead 1, 2, 3, 0 (cw))
r_ab = r_vertex[b] - r_vertex[a]
d_ab = r_ab.norm()
r_a = r - r_vertex[a]
r_a = r_a.norm()
r_b = r - r_vertex[b]
r_b = r_b.norm()
first_term = (
(r.x - r_vertex[a].x) * (r_vertex[b].y - r_vertex[a].y)
- (r.y - r_vertex[a].y) * (r_vertex[b].x - r_vertex[a].x)
)
first_term = first_term/d_ab
# katz & Plotkin
log_term = np.log((r_a + r_b + d_ab)/(r_a + r_b - d_ab))
# paper of Lothar birk
# log_term = np.log((r_a + r_b - d_ab)/(r_a + r_b + d_ab))
if (r_vertex[b].x - r_vertex[a].x) == 0:
m_ab = np.inf
else:
m_ab = ( (r_vertex[b].y - r_vertex[a].y)
/(r_vertex[b].x - r_vertex[a].x) )
e_a = (r.x - r_vertex[a].x)**2 + r.z**2
e_b = (r.x - r_vertex[b].x)**2 + r.z**2
h_a = (r.x - r_vertex[a].x)*(r.y - r_vertex[a].y)
h_b = (r.x - r_vertex[b].x)*(r.y - r_vertex[b].y)
arctan_term = ( np.arctan((m_ab*e_a - h_a)/(r.z*r_a))
- np.arctan((m_ab*e_b - h_b)/(r.z*r_b)) )
# Katz & Plotkin
# B = B + first_term * log_term - np.abs(r.z) * arctan_term
# paper of Lothar birk
B = B + first_term * log_term - r.z * arctan_term
B = - 1/(4 * np.pi) * B
return B
def Dblt_influence_coeff(r_p:Vector, panel:Panel, alpha=10):
n = panel.num_vertices
r_vertex = panel.r_vertex_local
r_cp = panel.r_cp
R = panel.R
r = r_p - r_cp
r_local = r.transformation(R)
r = r_local
if r.norm() >= alpha * panel.char_length:
C = - 1/(4*np.pi) * ( panel.area * r.z)/(r.norm()**3)
elif r.z == 0:
point = (r.x, r.y)
polygon = [(r_vertex[i].x, r_vertex[i].y) for i in range(n)]
if is_inside_polygon(polygon, point):
# point p lies on panel's surface as z-->0
# C = - 0.5 # if z--> +0
C = 0.5 # if z--> -0
else:
# point p lies outside of panel's surface as z-->0
C = 0
else:
C = 0
for i in range(n-1, -1, -1):
# panel numbering follow counter clock wise direction
# Hess and Smith integrals are calculated with clock wise ordering
a = (i+1)%n # 0, 3, 2, 1 (cw) (instead 0, 1, 2, 3 (cw))
b = i # 3, 2, 1, 0, (clock wise) (instead 1, 2, 3, 0 (cw))
r_a = r - r_vertex[a]
r_a = r_a.norm()
r_b = r - r_vertex[b]
r_b = r_b.norm()
if (r_vertex[b].x - r_vertex[a].x) == 0:
m_ab = np.inf
else:
m_ab = ( (r_vertex[b].y - r_vertex[a].y)
/(r_vertex[b].x - r_vertex[a].x) )
e_a = (r.x - r_vertex[a].x)**2 + r.z**2
e_b = (r.x - r_vertex[b].x)**2 + r.z**2
h_a = (r.x - r_vertex[a].x)*(r.y - r_vertex[a].y)
h_b = (r.x - r_vertex[b].x)*(r.y - r_vertex[b].y)
arctan_term = ( np.arctan((m_ab*e_a - h_a)/(r.z*r_a))
- np.arctan((m_ab*e_b - h_b)/(r.z*r_b)) )
C = C + arctan_term
C = - 1/(4*np.pi) * C
return C
def influence_coeff(r_p:Vector, panel:Panel, alpha=10):
n = panel.num_vertices
r_vertex = panel.r_vertex_local
r_cp = panel.r_cp
R = panel.R
r = r_p - r_cp
r_local = r.transformation(R)
r = r_local
if r.norm() >= alpha * panel.char_length:
B = panel.area/r.norm()
C = ( panel.area * r.z)/(r.norm()**3)
elif r.z == 0:
point = (r.x, r.y)
polygon = [(r_vertex[i].x, r_vertex[i].y) for i in range(n)]
if is_inside_polygon(polygon, point):
# point p lies on panel's surface as z-->0
# C = 2 * np.pi # if z--> +0
C = -2 * np.pi # if z--> -0
else:
# point p lies outside of panel's surface as z-->0
C = 0
B = 0
for i in range(n-1, -1, -1):
# panel numbering follow counter clock wise direction
# Hess and Smith integrals are calculated with clock wise ordering
a = (i+1)%n # 0, 3, 2, 1 (cw) (instead 0, 1, 2, 3 (cw))
b = i # 3, 2, 1, 0, (clock wise) (instead 1, 2, 3, 0 (cw))
r_ab = r_vertex[b] - r_vertex[a]
d_ab = r_ab.norm()
r_a = r - r_vertex[a]
r_a = r_a.norm()
r_b = r - r_vertex[b]
r_b = r_b.norm()
first_term = (
(r.x - r_vertex[a].x) * (r_vertex[b].y - r_vertex[a].y)
- (r.y - r_vertex[a].y) * (r_vertex[b].x - r_vertex[a].x)
)
first_term = first_term/d_ab
if (r_a + r_b - d_ab) == 0:
# point p coincide lies on a panel's edge
# log term ---> inf => B ---> inf
log_term = 0
else:
# katz & Plotkin
log_term = np.log((r_a + r_b + d_ab)/(r_a + r_b - d_ab))
# paper of Lothar birk
# log_term = np.log((r_a + r_b - d_ab)/(r_a + r_b + d_ab))
B = B + first_term * log_term
else:
B = 0
C = 0
for i in range(n-1, -1, -1):
# panel numbering follow counter clock wise direction
# Hess and Smith integrals are calculated with clock wise ordering
a = (i+1)%n # 0, 3, 2, 1 (cw) (instead 0, 1, 2, 3 (cw))
b = i # 3, 2, 1, 0, (clock wise) (instead 1, 2, 3, 0 (cw))
r_ab = r_vertex[b] - r_vertex[a]
d_ab = r_ab.norm()
r_a = r - r_vertex[a]
r_a = r_a.norm()
r_b = r - r_vertex[b]
r_b = r_b.norm()
first_term = (
(r.x - r_vertex[a].x) * (r_vertex[b].y - r_vertex[a].y)
- (r.y - r_vertex[a].y) * (r_vertex[b].x - r_vertex[a].x)
)
first_term = first_term/d_ab
# katz & Plotkin
log_term = np.log((r_a + r_b + d_ab)/(r_a + r_b - d_ab))
# paper of Lothar birk
# log_term = np.log((r_a + r_b - d_ab)/(r_a + r_b + d_ab))
if (r_vertex[b].x - r_vertex[a].x) == 0:
m_ab = np.inf
else:
m_ab = ( (r_vertex[b].y - r_vertex[a].y)
/(r_vertex[b].x - r_vertex[a].x) )
e_a = (r.x - r_vertex[a].x)**2 + r.z**2
e_b = (r.x - r_vertex[b].x)**2 + r.z**2
h_a = (r.x - r_vertex[a].x)*(r.y - r_vertex[a].y)
h_b = (r.x - r_vertex[b].x)*(r.y - r_vertex[b].y)
arctan_term = ( np.arctan((m_ab*e_a - h_a)/(r.z*r_a))
- np.arctan((m_ab*e_b - h_b)/(r.z*r_b)) )
# Katz & Plotkin
# B = B + first_term * log_term - np.abs(r.z) * arctan_term
# paper of Lothar birk
B = B + first_term * log_term - r.z * arctan_term
# Katz & Plotkin
C = C + arctan_term
B = - 1/(4 * np.pi) * B
C = - 1/(4 * np.pi) * C
return B, C
if __name__=='__main__':
from matplotlib import pyplot as plt
vertex1 = Vector((-1, -1, 1))
vertex2 = Vector((1, -1, 1))
vertex3 = Vector((1, 1, 1))
vertex4 = Vector((-1, 1, 1))
# Quadrilateral panel
panel = quadPanel(vertex1, vertex2, vertex3, vertex4)
# Triangular panel
# panel = triPanel(vertex1, vertex2, vertex3)
r_p = panel.r_cp
C = Dblt_influence_coeff(r_p, panel)
B = Src_influence_coeff(r_p, panel)
print("C = " + str(C) + "\nB = " + str(B))
B, C = influence_coeff(r_p, panel)
print("C = " + str(C) + "\nB = " + str(B))
# plot panel
ax = plt.axes(projection='3d')
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
ax.set_xlim(-5, 5)
ax.set_ylim(-5, 5)
ax.set_zlim(-5, 5)
# ax.view_init(0, 0)
x = []
y = []
z = []
for i in range(panel.num_vertices+1):
i = i % panel.num_vertices
x.append(panel.r_vertex[i].x)
y.append(panel.r_vertex[i].y)
z.append(panel.r_vertex[i].z)
ax.plot3D(x, y, z, color='k', label='panel')
ax.quiver(panel.r_cp.x, panel.r_cp.y, panel.r_cp.z,
panel.n.x, panel.n.y, panel.n.z,
color='r', label='normal vector n')
ax.quiver(panel.r_cp.x, panel.r_cp.y, panel.r_cp.z,
panel.l.x, panel.l.y, panel.l.z,
color='b', label='longidutinal vector l')
ax.quiver(panel.r_cp.x, panel.r_cp.y, panel.r_cp.z,
panel.m.x, panel.m.y, panel.m.z,
color='g', label='transverse vector m')
ax.legend()
plt.show()