def bezier_spline_aerofoil(file_path):
"""
creates a Bezier spline aerofoil with
certain lower curve control points
"""
# control points
p = np.array([[1.0, 0.0], [0.5, 0.08], [0.0, -0.05]])
q = np.array([[0.0, 0.1], [0.4, 0.2], [1.0, 0.0]])
# weights
zp = np.array([1, 1, 1, 1])
zq = np.array([1, 1, 1, 1])
# calculate degree
n = np.float(p.shape[0])
m = np.float(p.shape[0])
# calculate connection point
q_start = p_end = (n / (m + n)) * p[-1, :] + (m / (m + n)) * q[0, :]
# and add to control points
pp = np.vstack([p, p_end])
qq = np.vstack([q_start, q])
lower = rational_bezier(pp, zp)
upper = rational_bezier(qq, zq)
# open .dat file for writing to
data_file = open(file_path + "aerofoil.dat", "w")
# write lower surface to file
for i in range(0, 100):
data_file.write("%.11f %.11f\n" % (lower[i, 0], lower[i, 1]))
# for windows use " " instead of "\t"
# write upper surface to file
for i in range(0, 101):
data_file.write("%.11f %.11f\n" % (upper[i, 0], upper[i, 1]))
# for windows use " " instead of "\t"
# close .dat file
data_file.close()
def parametric_aerofoil(w):
p = np.array([[1, 0], [0.5, 0.08], [0.0, -0.05]])
q = np.array([[0, 0.1], [0.4, 0.2], [1, 0.0]])
# weights
zp = np.array([1, 1, 1, 1])
zq = np.array([1, 1, w, 1])
# calculate degree
n = np.float(np.shape(p)[0])
m = np.float(np.shape(p)[0])
# calculate connection point
q_start = p_end = (n / (m + n)) * p[-1, :] + (m / (m + n)) * q[0, :]
# and add to control points
pp = np.vstack([p, p_end])
qq = np.vstack([q_start, q])
# calculate two curves
lower = rational_bezier(pp, zp)
upper = rational_bezier(qq, zq)
points = np.vstack([lower[0:100], upper])
return points
def parametric_aerofoil(w, file_path):
"""
Generates and saves a parametric bezier spline aerofoil.
w -- weighting of points
If w is a float it is used as the weighting of point u(2)
If w is an array it must contain four values, used as weighitngs of
points u(1), u(2), l(1), l(2) respectively.
file_path -- path to write aerofoil.dat within
"""
lower = np.array([[1.0, 0.0],
[0.5, 0.08],
[0.0, -0.05]])
n = float(len(lower))
upper = np.array([[0.0, 0.1],
[0.4, 0.2],
[1.0, 0.0]])
m = float(len(upper))
connect = np.add(np.multiply(upper[0], m / (m + n)),
np.multiply(lower[n - 1], n / (m + n)))
lower = np.concatenate((lower, [connect]))
upper = np.concatenate(([connect], upper))
if type(w) is float or type(w) is np.float64:
l_bez = lab1.rational_bezier(lower, [1, 1, 1, 1])
u_bez = lab1.rational_bezier(upper, [1, 1, w, 1])
else:
l_bez = lab1.rational_bezier(lower, [1, w[2], w[3], 1])
u_bez = lab1.rational_bezier(upper, [1, w[0], w[1], 1])
u_bez = np.delete(u_bez, 0, axis=0)
aero_spline = np.concatenate((l_bez, u_bez), axis=0)
aerofoil_file = open(file_path + "aerofoil.dat", "w")
aerofoil_file.write("MyFoil\n" + serialize_array(aero_spline).strip())
def bezier_spline_aerofoil():
# define the control points:
#p = np.array(...)
#q = np.array(...)
### BEGIN SOLUTION
p = np.array([[1, 0.0], [0.5, 0.08], [0.0, -0.05]])
q = np.array([[0.0, 0.1], [0.4, 0.2], [1, 0.0]])
### END SOLUTION
# weights
zp = np.array([1, 1, 1, 1])
zq = np.array([1, 1, 1, 1])
# calculate degree
#n = ...
#m = ...
### BEGIN SOLUTION
n = np.float(np.shape(p)[0])
m = np.float(np.shape(p)[0])
### END SOLUTION
# calculate connection point
# q_start = p_end = ...
### BEGIN SOLUTION
q_start = p_end = (n/(m+n))*p[-1,:]+(m/(m+n))*q[0,:]
### END SOLUTION
# and add to control points
pp = np.vstack([p, p_end])
qq = np.vstack([q_start, q])
# calculate two curves
# lower = ...
# upper = ...
### BEGIN SOLUTION
lower = rational_bezier(pp, zp)
upper = rational_bezier(qq, zq)
### END SOLUTION
# and join together (removing repeat point at leading edge):
### BEGIN SOLUTION
points = np.vstack([lower[0:100], upper])
### END SOLUTION
return points
def bezier_spline_aerofoil(file_path):
""" Generates and saves a bezier spline aerofoil with predefined values """
lower = np.array([[1.0, 0.0],
[0.5, 0.08],
[0.0, -0.05]])
n = float(len(lower))
upper = np.array([[0.0, 0.1],
[0.4, 0.2],
[1.0, 0.0]])
m = float(len(upper))
connect = np.add(np.multiply(upper[0], m / (m + n)),
np.multiply(lower[n - 1], n / (m + n)))
lower = np.concatenate((lower, [connect]))
upper = np.concatenate(([connect], upper))
l_bez = lab1.rational_bezier(lower, [1, 1, 1, 1])
u_bez = lab1.rational_bezier(upper, [1, 1, 1, 1])
u_bez = np.delete(u_bez, len(u_bez) - 1, axis=0)
aero_spline = np.concatenate((l_bez, u_bez))
aerofoil_file = open(file_path + "aerofoil.dat", "w")
aerofoil_file.write("MyFoil\n" + serialize_array(aero_spline).strip())
