def area(self):
# Returns the area of the polygon, in nondimensional (normalized to chord^2) units.
x = self.x()
y = self.y()
x_n = np.roll(x, -1) # x_next, or x_i+1
y_n = np.roll(y, -1) # y_next, or y_i+1
a = x * y_n - x_n * y # a is the area of the triangle bounded by a given point, the next point, and the origin.
A = 0.5 * np.sum(a) # area
return A
def area(self) -> float:
"""
Returns the area of the polygon.
"""
x = self.x()
y = self.y()
x_n = np.roll(x, -1) # x_next, or x_i+1
y_n = np.roll(y, -1) # y_next, or y_i+1
a = x * y_n - x_n * y # a is the area of the triangle bounded by a given point, the next point, and the origin.
A = 0.5 * np.sum(a) # area
return A
def centroid(self):
# Returns the centroid of the polygon, in nondimensional (chord-normalized) units.
x = self.x()
y = self.y()
x_n = np.roll(x, -1) # x_next, or x_i+1
y_n = np.roll(y, -1) # y_next, or y_i+1
a = x * y_n - x_n * y # a is the area of the triangle bounded by a given point, the next point, and the origin.
A = 0.5 * np.sum(a) # area
x_c = 1 / (6 * A) * np.sum(a * (x + x_n))
y_c = 1 / (6 * A) * np.sum(a * (y + y_n))
centroid = np.array([x_c, y_c])
return centroid
def centroid(self) -> np.ndarray:
"""
Returns the centroid of the polygon as a 1D np.ndarray of length 2.
"""
x = self.x()
y = self.y()
x_n = np.roll(x, -1) # x_next, or x_i+1
y_n = np.roll(y, -1) # y_next, or y_i+1
a = x * y_n - x_n * y # a is the area of the triangle bounded by a given point, the next point, and the origin.
A = 0.5 * np.sum(a) # area
x_c = 1 / (6 * A) * np.sum(a * (x + x_n))
y_c = 1 / (6 * A) * np.sum(a * (y + y_n))
centroid = np.array([x_c, y_c])
return centroid
def Ixx(self):
# Returns the nondimensionalized Ixx moment of inertia, taken about the centroid.
x = self.x()
y = self.y()
x_n = np.roll(x, -1) # x_next, or x_i+1
y_n = np.roll(y, -1) # y_next, or y_i+1
a = x * y_n - x_n * y # a is the area of the triangle bounded by a given point, the next point, and the origin.
A = 0.5 * np.sum(a) # area
x_c = 1 / (6 * A) * cas.sum1(a * (x + x_n))
y_c = 1 / (6 * A) * cas.sum1(a * (y + y_n))
centroid = np.array([x_c, y_c])
Ixx = 1 / 12 * np.sum(a * (y**2 + y * y_n + y_n**2))
Iuu = Ixx - A * centroid[1]**2
return Iuu
def Ixy(self):
# Returns the nondimensionalized product of inertia, taken about the centroid.
x = self.x()
y = self.y()
x_n = np.roll(x, -1) # x_next, or x_i+1
y_n = np.roll(y, -1) # y_next, or y_i+1
a = x * y_n - x_n * y # a is the area of the triangle bounded by a given point, the next point, and the origin.
A = 0.5 * np.sum(a) # area
x_c = 1 / (6 * A) * np.sum(a * (x + x_n))
y_c = 1 / (6 * A) * np.sum(a * (y + y_n))
centroid = np.array([x_c, y_c])
Ixy = 1 / 24 * np.sum(a *
(x * y_n + 2 * x * y + 2 * x_n * y_n + x_n * y))
Iuv = Ixy - A * centroid[0] * centroid[1]
return Iuv
def Iyy(self):
"""
Returns the nondimensionalized Iyy moment of inertia, taken about the centroid.
"""
x = self.x()
y = self.y()
x_n = np.roll(x, -1) # x_next, or x_i+1
y_n = np.roll(y, -1) # y_next, or y_i+1
a = x * y_n - x_n * y # a is the area of the triangle bounded by a given point, the next point, and the origin.
A = 0.5 * np.sum(a) # area
x_c = 1 / (6 * A) * np.sum(a * (x + x_n))
y_c = 1 / (6 * A) * np.sum(a * (y + y_n))
centroid = np.array([x_c, y_c])
Iyy = 1 / 12 * np.sum(a * (x**2 + x * x_n + x_n**2))
Ivv = Iyy - A * centroid[0]**2
return Ivv
def test_roll_casadi_2d():
a = np.array([[1, 2, 3], [4, 5, 6]])
b = cas.SX(a)
assert np.all(cas.DM(np.roll(b, 1, axis=1)) == np.roll(a, 1, axis=1))
def test_roll_casadi():
b = np.array([[3, 1, 2]])
a = cas.SX(b)
assert np.all(cas.DM(np.roll(a, 1)) == b)
def test_roll_onp():
a = [1, 2, 3]
b = [3, 1, 2]
assert np.all(np.roll(a, 1) == b)
