def construct_single_ply_piece(self, fraction=1.0):
"""Construct a ply piece for shape A (trapezium)"""
th_nom = np.radians(self.fiber_angle)
# Step 1: Define origin line L0
origin_point = Point2D(self.starting_position, 0.0)
L0 = Line2D.from_point_angle(origin_point, th_nom)
# Step 2: Define line L2, perpendicular to L0, tangent to circle s4
tangent_point = Point2D.from_polar(self.cg.s4, th_nom)
L2 = Line2D.from_point_angle(tangent_point, th_nom + np.pi / 2)
P0 = L0.intersection_line(L2)
# Step 3: Position P2 and P3 based on max_width and eccentricity
P2_dist = self.max_width * self.eccentricity
P3_dist = self.max_width * (1 - self.eccentricity)
P2 = P0 + Point2D.from_polar(P2_dist, L2.angle())
P3 = P0 + Point2D.from_polar(P3_dist, L2.angle() + np.pi)
# Step 4: Calculate the spanned angle (both deltas should be >= 0)
T2 = L0.intersection_circle_near(P2.norm(), P0)
T3 = L0.intersection_circle_near(P3.norm(), P0)
delta_phi_1 = fraction * (P2.angle() - T2.angle())
delta_phi_2 = fraction * (T3.angle() - P3.angle())
# Step 5: Calculate the side lines L1 and L3
L1 = L0.rotate(delta_phi_1)
L3 = L0.rotate(-delta_phi_2)
near_pt = Point2D(self.cg.s1, 0)
P1a = L1.intersection_circle_near(self.cg.s1, near_pt)
P4a = L3.intersection_circle_near(self.cg.s1, near_pt)
# Redefine P2 and P3 if needed (for rest pieces)
if fraction != 1.0:
P2 = L2.intersection_line(L1)
P3 = L2.intersection_line(L3)
# Step 6: Construct L4, parallel to L2, through either P1a or P4a,
# whichever is furthest from L2
if L2.distance_point(P1a) > L2.distance_point(P4a):
L4_through_point = P1a
else:
L4_through_point = P4a
L4 = Line2D.from_point_angle(L4_through_point, L2.angle())
# now redefine P1 and P4 as the intersection points:
P1b = L4.intersection_line(L1)
P4b = L4.intersection_line(L3)
ip_L1_L3 = L1.intersection_line(L3)
if L2.distance_point(ip_L1_L3) < L2.distance_point(P4b):
# Line segments L1 and L3 intersect within the polygon, so we have
# a 'hourglass' shape. Move P1 and P4 to the intersection point,
# effectively forming a triangle. We could just drop P4, if not
# for some other code expeccting 4-point polygons.
P1, P4 = ip_L1_L3, ip_L1_L3
else:
P1, P4 = P1b, P4b
# Step 7: Return the final ply piece
return PlyPiece(Polygon2D((P1, P2, P3, P4)), 0.0, -delta_phi_2,
delta_phi_1)
def construct_single_ply_piece(self, fraction=1.0):
"""Construct a ply piece for shape A (trapezium)"""
th_nom = np.radians(self.fiber_angle)
# Step 1: Define origin line L0
origin_point = Point2D(self.starting_position, 0.0)
L0 = Line2D.from_point_angle(origin_point, th_nom)
# Step 2: Define line L2, perpendicular to L0, tangent to circle s4
tangent_point = Point2D.from_polar(self.cg.s4, th_nom)
L2 = Line2D.from_point_angle(tangent_point, th_nom + np.pi/2)
P0 = L0.intersection_line(L2)
# Step 3: Position P2 and P3 based on max_width and eccentricity
P2_dist = self.max_width * self.eccentricity
P3_dist = self.max_width * (1 - self.eccentricity)
P2 = P0 + Point2D.from_polar(P2_dist, L2.angle())
P3 = P0 + Point2D.from_polar(P3_dist, L2.angle() + np.pi)
# Step 4: Calculate the spanned angle (both deltas should be >= 0)
T2 = L0.intersection_circle_near(P2.norm(), P0)
T3 = L0.intersection_circle_near(P3.norm(), P0)
delta_phi_1 = fraction*(P2.angle() - T2.angle())
delta_phi_2 = fraction*(T3.angle() - P3.angle())
# Step 5: Calculate the side lines L1 and L3
L1 = L0.rotate(delta_phi_1)
L3 = L0.rotate(-delta_phi_2)
near_pt = Point2D(self.cg.s1, 0)
P1a = L1.intersection_circle_near(self.cg.s1, near_pt)
P4a = L3.intersection_circle_near(self.cg.s1, near_pt)
# Redefine P2 and P3 if needed (for rest pieces)
if fraction != 1.0:
P2 = L2.intersection_line(L1)
P3 = L2.intersection_line(L3)
# Step 6: Construct L4, parallel to L2, through either P1a or P4a,
# whichever is furthest from L2
if L2.distance_point(P1a) > L2.distance_point(P4a):
L4_through_point = P1a
else:
L4_through_point = P4a
L4 = Line2D.from_point_angle(L4_through_point, L2.angle())
# now redefine P1 and P4 as the intersection points:
P1b = L4.intersection_line(L1)
P4b = L4.intersection_line(L3)
ip_L1_L3 = L1.intersection_line(L3)
if L2.distance_point(ip_L1_L3) < L2.distance_point(P4b):
# Line segments L1 and L3 intersect within the polygon, so we have
# a 'hourglass' shape. Move P1 and P4 to the intersection point,
# effectively forming a triangle. We could just drop P4, if not
# for some other code expeccting 4-point polygons.
P1, P4 = ip_L1_L3, ip_L1_L3
else:
P1, P4 = P1b, P4b
# Step 7: Return the final ply piece
return PlyPiece(Polygon2D((P1, P2, P3, P4)), 0.0, -delta_phi_2, delta_phi_1)
def construct_single_ply_piece(self, fraction=1.0):
"""Construct a ply piece for shape C (rectangle)"""
th_nom = np.radians(self.fiber_angle)
# Define origin line L0
origin_point = Point2D(self.starting_position, 0.0)
L0 = Line2D.from_point_angle(origin_point, th_nom)
# Define line L4
L4 = Line2D.from_point_angle(Point2D(0.0, 0.0), th_nom + np.pi / 2)
ip_L0_L4 = L0.intersection_line(L4)
# Construct P1 and P4
P1_dist = self.max_width * self.eccentricity
P4_dist = self.max_width * (1 - self.eccentricity)
P1 = ip_L0_L4 + Point2D.from_polar(P1_dist, L4.angle())
P4 = ip_L0_L4 + Point2D.from_polar(P4_dist, L4.angle() + np.pi)
# Construct side lines L1, L3, parallel to L0
L1 = Line2D.from_point_angle(P1, L0.angle())
L3 = Line2D.from_point_angle(P4, L0.angle())
# Intersection points L0, L1, L3 with circle
P0 = L0.intersection_circle_near(self.cg.s4, origin_point)
P2 = L1.intersection_circle_near(self.cg.s4, P0)
P3 = L3.intersection_circle_near(self.cg.s4, P0)
# Handle creation of rest pieces, with fraction < 1.0
delta_phi_1 = (P2.angle() - P0.angle())
delta_phi_2 = (P0.angle() - P3.angle())
if fraction != 1.0:
P2 = P2.rotate((fraction - 1.0) * delta_phi_1)
P3 = P3.rotate((1.0 - fraction) * delta_phi_2)
L1 = Line2D.from_point_angle(P2, L1.angle())
L3 = Line2D.from_point_angle(P3, L3.angle())
P1 = L4.intersection_line(L1)
P4 = L4.intersection_line(L3)
delta_phi_1 *= fraction
delta_phi_2 *= fraction
# Construct L2 through P2 or P3, whichever is furthest from L4
# Adjust the other point
if L4.distance_point(P2) > L4.distance_point(P3):
L2 = Line2D.from_point_angle(P2, L4.angle())
P3 = L2.intersection_line(L3)
else:
L2 = Line2D.from_point_angle(P3, L4.angle())
P2 = L2.intersection_line(L1)
# Return the final ply piece
return PlyPiece(Polygon2D((P1, P2, P3, P4)), 0.0, -delta_phi_2,
delta_phi_1)
def construct_single_ply_piece(self, fraction=1.0):
"""Construct a ply piece for shape C (rectangle)"""
th_nom = np.radians(self.fiber_angle)
# Define origin line L0
origin_point = Point2D(self.starting_position, 0.0)
L0 = Line2D.from_point_angle(origin_point, th_nom)
# Define line L4
L4 = Line2D.from_point_angle(Point2D(0.0, 0.0), th_nom + np.pi/2)
ip_L0_L4 = L0.intersection_line(L4)
# Construct P1 and P4
P1_dist = self.max_width * self.eccentricity
P4_dist = self.max_width * (1 - self.eccentricity)
P1 = ip_L0_L4 + Point2D.from_polar(P1_dist, L4.angle())
P4 = ip_L0_L4 + Point2D.from_polar(P4_dist, L4.angle() + np.pi)
# Construct side lines L1, L3, parallel to L0
L1 = Line2D.from_point_angle(P1, L0.angle())
L3 = Line2D.from_point_angle(P4, L0.angle())
# Intersection points L0, L1, L3 with circle
P0 = L0.intersection_circle_near(self.cg.s4, origin_point)
P2 = L1.intersection_circle_near(self.cg.s4, P0)
P3 = L3.intersection_circle_near(self.cg.s4, P0)
# Handle creation of rest pieces, with fraction < 1.0
delta_phi_1 = (P2.angle() - P0.angle())
delta_phi_2 = (P0.angle() - P3.angle())
if fraction != 1.0:
P2 = P2.rotate((fraction - 1.0) * delta_phi_1)
P3 = P3.rotate((1.0 - fraction) * delta_phi_2)
L1 = Line2D.from_point_angle(P2, L1.angle())
L3 = Line2D.from_point_angle(P3, L3.angle())
P1 = L4.intersection_line(L1)
P4 = L4.intersection_line(L3)
delta_phi_1 *= fraction
delta_phi_2 *= fraction
# Construct L2 through P2 or P3, whichever is furthest from L4
# Adjust the other point
if L4.distance_point(P2) > L4.distance_point(P3):
L2 = Line2D.from_point_angle(P2, L4.angle())
P3 = L2.intersection_line(L3)
else:
L2 = Line2D.from_point_angle(P3, L4.angle())
P2 = L2.intersection_line(L1)
# Return the final ply piece
return PlyPiece(Polygon2D((P1, P2, P3, P4)), 0.0, -delta_phi_2, delta_phi_1)
def construct_single_ply_piece(self, fraction=1.0):
"""Construct a ply piece for shape A (trapezium)"""
th_nom = np.radians(self.fiber_angle)
# Step 1: Define origin line L0
origin_point = Point2D(self.starting_position, 0.0)
L0 = Line2D.from_point_angle(origin_point, th_nom )
# Step 2: Define line L2, perpendicular to L0, tangent to circle s4
tangent_point = Point2D.from_polar(self.cg.s4, th_nom)
L2 = Line2D.from_point_angle(tangent_point, th_nom + np.pi/2)
P0 = L0.intersection_line(L2)
# Step 3: Position P2 and P3 based on max_width and eccentricity
P2_dist = self.max_width * self.eccentricity
P3_dist = self.max_width * (1 - self.eccentricity)
P2 = P0 + Point2D.from_polar(P2_dist, L2.angle())
P3 = P0 + Point2D.from_polar(P3_dist, L2.angle() + np.pi)
# Step 4: Calculate a rough estimate of the spanned angle
delta_phi_1 = (P2.angle() - P0.angle())
delta_phi_2 = (P0.angle() - P3.angle())
ip_L0_s2 = L0.intersection_circle_near(self.cg.s2, origin_point)
ip_L0_s4 = L0.intersection_circle_near(self.cg.s4, origin_point)
ratio = 0.0
REQ_RATIO = 2.0
# Step 5: Iterate until the ratio of spanned angles on s4 and s2 is (nearly) correct
while abs(ratio - REQ_RATIO) > TOL:
delta_phi_on_s2 = REQ_RATIO * (delta_phi_1 + delta_phi_2)
ip_L1_s2 = ip_L0_s2.rotate(REQ_RATIO * delta_phi_1)
ip_L3_s2 = ip_L0_s2.rotate(-REQ_RATIO * delta_phi_2)
L1 = Line2D.from_points(ip_L1_s2, P2)
L3 = Line2D.from_points(ip_L3_s2, P3)
ip_L1_s4 = L1.intersection_circle_near(self.cg.s4, P0)
ip_L3_s4 = L3.intersection_circle_near(self.cg.s4, P0)
delta_phi_1 = ip_L1_s4.angle() - ip_L0_s4.angle()
delta_phi_2 = ip_L0_s4.angle() - ip_L3_s4.angle()
delta_phi_on_s4 = delta_phi_1 + delta_phi_2
ratio = delta_phi_on_s2 / delta_phi_on_s4
# Redefine P2 and P3 if needed (for rest pieces)
if fraction != 1.0:
ip_L1_s2 = ip_L1_s2.rotate((fraction - 1.0) * delta_phi_1)
ip_L3_s2 = ip_L3_s2.rotate((1.0 - fraction) * delta_phi_2)
# Apply an additional rotation to avoid having more than one overlap
ip_L3_s2 = ip_L3_s2.rotate(delta_phi_1 + delta_phi_2)
ip_L1_s4 = ip_L1_s4.rotate((fraction - 1.0) * delta_phi_1)
ip_L3_s4 = ip_L3_s4.rotate((1.0 - fraction) * delta_phi_2)
L1 = Line2D.from_points(ip_L1_s2, ip_L1_s4)
L3 = Line2D.from_points(ip_L3_s2, ip_L3_s4)
delta_phi_1 *= fraction
delta_phi_2 *= fraction
# Step 6: redefine P1 to P4 as the intersection points
L4 = Line2D.from_point_angle(Point2D(0.0, 0.0), L2.angle())
P1 = L1.intersection_line(L4)
P2 = L2.intersection_line(L1)
P3 = L3.intersection_line(L2)
P4 = L4.intersection_line(L3)
# Step 7: Return the final ply piece
return PlyPiece(Polygon2D((P1, P2, P3, P4)), 0.0, -delta_phi_2, delta_phi_1)
def make_intersection(L, s):
return L.intersection_circle_near(s, Point2D.from_polar(s, phi_nom))
def construct_single_ply_piece(self, fraction=1.0):
"""Construct a ply piece for shape A (trapezium)"""
th_nom = np.radians(self.fiber_angle)
# Step 1: Define origin line L0
origin_point = Point2D(self.starting_position, 0.0)
L0 = Line2D.from_point_angle(origin_point, th_nom)
# Step 2: Define line L2, perpendicular to L0, tangent to circle s4
tangent_point = Point2D.from_polar(self.cg.s4, th_nom)
L2 = Line2D.from_point_angle(tangent_point, th_nom + np.pi / 2)
P0 = L0.intersection_line(L2)
# Step 3: Position P2 and P3 based on max_width and eccentricity
P2_dist = self.max_width * self.eccentricity
P3_dist = self.max_width * (1 - self.eccentricity)
P2 = P0 + Point2D.from_polar(P2_dist, L2.angle())
P3 = P0 + Point2D.from_polar(P3_dist, L2.angle() + np.pi)
# Step 4: Calculate a rough estimate of the spanned angle
delta_phi_1 = (P2.angle() - P0.angle())
delta_phi_2 = (P0.angle() - P3.angle())
ip_L0_s2 = L0.intersection_circle_near(self.cg.s2, origin_point)
ip_L0_s4 = L0.intersection_circle_near(self.cg.s4, origin_point)
ratio = 0.0
REQ_RATIO = 2.0
# Step 5: Iterate until the ratio of spanned angles on s4 and s2 is (nearly) correct
while abs(ratio - REQ_RATIO) > TOL:
delta_phi_on_s2 = REQ_RATIO * (delta_phi_1 + delta_phi_2)
ip_L1_s2 = ip_L0_s2.rotate(REQ_RATIO * delta_phi_1)
ip_L3_s2 = ip_L0_s2.rotate(-REQ_RATIO * delta_phi_2)
L1 = Line2D.from_points(ip_L1_s2, P2)
L3 = Line2D.from_points(ip_L3_s2, P3)
ip_L1_s4 = L1.intersection_circle_near(self.cg.s4, P0)
ip_L3_s4 = L3.intersection_circle_near(self.cg.s4, P0)
delta_phi_1 = ip_L1_s4.angle() - ip_L0_s4.angle()
delta_phi_2 = ip_L0_s4.angle() - ip_L3_s4.angle()
delta_phi_on_s4 = delta_phi_1 + delta_phi_2
ratio = delta_phi_on_s2 / delta_phi_on_s4
# Redefine P2 and P3 if needed (for rest pieces)
if fraction != 1.0:
ip_L1_s2 = ip_L1_s2.rotate((fraction - 1.0) * delta_phi_1)
ip_L3_s2 = ip_L3_s2.rotate((1.0 - fraction) * delta_phi_2)
# Apply an additional rotation to avoid having more than one overlap
ip_L3_s2 = ip_L3_s2.rotate(delta_phi_1 + delta_phi_2)
ip_L1_s4 = ip_L1_s4.rotate((fraction - 1.0) * delta_phi_1)
ip_L3_s4 = ip_L3_s4.rotate((1.0 - fraction) * delta_phi_2)
L1 = Line2D.from_points(ip_L1_s2, ip_L1_s4)
L3 = Line2D.from_points(ip_L3_s2, ip_L3_s4)
delta_phi_1 *= fraction
delta_phi_2 *= fraction
# Step 6: redefine P1 to P4 as the intersection points
L4 = Line2D.from_point_angle(Point2D(0.0, 0.0), L2.angle())
P1 = L1.intersection_line(L4)
P2 = L2.intersection_line(L1)
P3 = L3.intersection_line(L2)
P4 = L4.intersection_line(L3)
# Step 7: Return the final ply piece
return PlyPiece(Polygon2D((P1, P2, P3, P4)), 0.0, -delta_phi_2,
delta_phi_1)
def make_intersection(L, s):
return L.intersection_circle_near(s,
Point2D.from_polar(s, phi_nom))
