def start_points(self, axis):
#Define Start_Point for Propagation Algorithm
for i in range(self.Vectors.shape[0]):
for j in range(3):
if (New_Vectors[i][j][axis] == Zero_Point[axis]):
Start_Point = New_Vectors[i][j]
break
#End Point
End_Point = np.zeros(3)
for i in range(Cylinder_normals.shape[0]):
if (np.array_equal(Cylinder_normals[i], Winding_Direction)):
End_Point = Cylinder_vectors[i][0]
break
#Check for Direction Sanity
Dir_1 = np.cross(New_Normals[Start_Point_Index], Winding_Direction)
Dir_1 = Dir_1 / np.linalg.norm(Dir_1)
Dir_2 = np.subtract(Second_Point, Start_Point)
Dir_2 = Dir_2 / np.linalg.norm(Dir_2)
if (np.array_equal(Dir_1, Dir_2) == False):
Temp = Second_Point
Second_Point = Start_Point
Start_Point = Temp
Path_Points.append(Start_Point)
Path_Points.append(Second_Point)
#Third Point
Third_Point = np.zeros(3)
Third_Edge_1 = np.zeros(3)
Third_Point_Index_list = Point_Index_fun(New_Points, Second_Point)
Third_Point_Index_list.remove(Second_Point_Index)
for i in range(len(Third_Point_Index_list)):
for j in range(3):
if (np.array_equal(New_Vectors[Third_Point_Index_list[i]][j],
Second_Point) == False):
if (New_Vectors[Third_Point_Index_list[i]][j][axis] ==
Second_Point[axis]):
Third_Edge_1 = New_Vectors[
Third_Point_Index_list[i]][j]
Third_Point_Index = Third_Point_Index_list[i]
break
Third_Edge_2 = Third_Vertex_fun(Third_Edge_1, Second_Point,
Third_Point_Index, New_Vectors)
Vector_Third_Edge = Plane_Winding_Direction(
New_Normals[Third_Point_Index], Winding_Direction, 0.2)
Third_Point = Intersection_fun(Third_Edge_1, Third_Edge_2,
Second_Point, Vector_Third_Edge)
#print("I",Third_Edge_1,Third_Edge_2,Third_Point)
Path_Points.append(Third_Point)
Third_Point = np.zeros(3)
Third_Edge_1 = np.zeros(3)
Third_Point_Index_list = Point_Index_fun(New_Points, Second_Point)
Third_Point_Index_list.remove(Second_Point_Index)
for i in range(len(Third_Point_Index_list)):
for j in range(3):
if (np.array_equal(New_Vectors[Third_Point_Index_list[i]][j],
Second_Point) == False):
if (New_Vectors[Third_Point_Index_list[i]][j][axis] ==
Second_Point[axis]):
Third_Edge_1 = New_Vectors[Third_Point_Index_list[i]][j]
Third_Point_Index = Third_Point_Index_list[i]
break
Third_Edge_2 = Third_Vertex_fun(Third_Edge_1, Second_Point, Third_Point_Index,
New_Vectors)
Vector_Third_Edge = Plane_Winding_Direction(New_Normals[Third_Point_Index],
Winding_Direction, 0.3)
print("Vector_Third_Edge", Vector_Third_Edge)
print("Third_Edge_1", Third_Edge_1)
print("Third_Edge_2", Third_Edge_2)
Third_Point = Intersection_fun(Third_Edge_1, Third_Edge_2, Second_Point,
Vector_Third_Edge)
#print("I",Third_Edge_1,Third_Edge_2,Third_Point)
Path_Points.append(Third_Point)
#Start Propogation Tool
Fourth_point_Index = find_Index(Third_Edge_1, Third_Edge_2, Third_Point_Index,
New_Points)
Propagation_Array = np.zeros((6, 3))
Propagation_Array[0] = Second_Point
Propagation_Array[1] = Third_Point
Third_Point = np.zeros(3)
Third_Edge_1 = np.zeros(3)
Third_Point_Index_list = Point_Index_fun(New_Points, Second_Point)
Third_Point_Index_list.remove(Second_Point_Index)
for i in range(len(Third_Point_Index_list)):
for j in range(3):
if (np.array_equal(New_Vectors[Third_Point_Index_list[i]][j],
Second_Point) == False):
if (New_Vectors[Third_Point_Index_list[i]][j][axis] ==
Second_Point[axis]):
Third_Edge_1 = New_Vectors[Third_Point_Index_list[i]][j]
Third_Point_Index = Third_Point_Index_list[i]
break
Third_Edge_2 = Third_Vertex_fun_2(Third_Edge_1, Second_Point,
Third_Point_Index)
Vector_Third_Edge = Plane_Winding_Direction(New_Normals[Third_Point_Index],
Winding_Direction, 0.2)
Third_Point = Intersection_fun(Third_Edge_1, Third_Edge_2, Second_Point,
Vector_Third_Edge)
#print("I",Third_Edge_1,Third_Edge_2,Third_Point)
Path_Points.append(Third_Point)
def next_point_edge(Point_1, Point_2, Vertex_1, Vertex_2, Index_1, Index_2):
e = 0.01 #error
friction_coefficient = 0.2
#Defining egde Vector and Normals
#Normal of Previous Triangle
N1 = New_Normals[Index_1]
#print("N1",N1,Index_1)
def next_point_edge(Point_1, Point_2, Vertex_1, Vertex_2, Index_1, Index_2):
e = 0.01 #error
friction_coefficient = 0.2
#Defining egde Vector and Normals
#Normal of Previous Triangle
N1 = New_Normals[Index_1]
#print("N1",N1,Index_1)
#Normal of New_Triangle
N2 = New_Normals[Index_2]
#print("N2",N2,Index_2)
T1 = np.subtract(Point_2, Point_1)
T1 = T1 / np.linalg.norm(T1)
#print("T1",T1)
#Determining Intersection point(New Point P2, and new vertexes)
Third_Vertex = Third_Vertex_fun_2(Vertex_1, Vertex_2, Index_2)
#print("Vertex_1,Vertex_2",Vertex_1,Vertex_2,Third_Vertex)
#Make the points Counterclockwise
Vertex_1, Vertex_2 = counter_clockwise_check(Vertex_1, Vertex_2,
Third_Vertex, N2)
#print("Vertex_1,Vertex_2",Vertex_1,Vertex_2,Third_Vertex)
Edge_Vector = np.subtract(Vertex_2, Vertex_1)
Edge_Vector = Edge_Vector / np.linalg.norm(Edge_Vector)
#print("EV",Edge_Vector)
input_angle = math.acos(np.dot(T1, Edge_Vector))
Zero_degree_Vector = np.cross(N2, Edge_Vector)
Zero_degree_Vector = Zero_degree_Vector / np.linalg.norm(
Zero_degree_Vector)
Geodesic_Vector = np.add(
math.sin(input_angle) * Zero_degree_Vector,
math.cos(input_angle) * Edge_Vector)
#Normalising the vectors
Geodesic_Vector = Geodesic_Vector / np.linalg.norm(Geodesic_Vector)
#print("GV", Geodesic_Vector)
#Favored Direction
Favored_Dir = Plane_Winding_Direction(N2, Winding_Direction, Winding_angle)
#print("Favored_Dir",Favored_Dir)
#Calculating tangents to curve and normal to plane
Surface_normal = np.add(N1, N2)
Surface_normal = Surface_normal / np.linalg.norm(Surface_normal)
#print("Surface normal mod",np.linalg.norm(Surface_normal))
#print("Surface Normal",Surface_normal)
#print("#######")
#Storage Variable
Max = Favored_Dir
Min = Geodesic_Vector
Mid = np.add(Max, Min)
Mid = Mid / np.linalg.norm(Mid)
Curve_vector = np.add(Mid, -1 * T1)
Curve_vector = Curve_vector / np.linalg.norm(Curve_vector)
#Geodesic Slippage calculation
#Curve_Geodesic = np.subtract(Geodesic_Vector,T1)
#Curve_Geodesic = Curve_Geodesic/np.linalg.norm(Curve_Geodesic)
#print("Curve_Geodesic",Curve_Geodesic)
#print("Curve geo mod",np.linalg.norm(Curve_Geodesic))
#print(np.dot(Curve_Geodesic,-1*Surface_normal))
#print(math.acos(np.dot(Curve_Geodesic,-1*Surface_normal)))
#Slippage_Geodesic = math.tan(math.acos(np.dot(Curve_Geodesic,-1*Surface_normal)))
#print("Slippage Geodesic",Slippage_Geodesic)
Dot_product = np.dot(Curve_vector, -1 * Surface_normal)
if (Dot_product > 1):
Dot_product = 0.999
Slippage_tendency = math.tan(math.acos(Dot_product))
a = 0
while (((friction_coefficient - Slippage_tendency) > 0 and
(friction_coefficient - Slippage_tendency) < e) == False
and a < 20):
a = a + 1
if (friction_coefficient - Slippage_tendency) < 0:
Max = Mid
if (friction_coefficient - Slippage_tendency) > 0:
Min = Mid
Mid = np.add(Max, Min)
Mid = Mid / np.linalg.norm(Mid)
#print(Mid_1)
Curve_vector = np.add(Mid, -1 * T1)
Curve_vector = Curve_vector / np.linalg.norm(Curve_vector)
Dot_product = np.dot(Curve_vector, -1 * Surface_normal)
if (Dot_product > 1):
Dot_product = 0.999
Slippage_tendency = math.tan(math.acos(Dot_product))
#print(Slippage_tendency)
#Define the Propogtion Vector
Propogation_Vector = Mid
#print("Propogation_Vector",Propogation_Vector)
#Determining Intersection point(New Point P2, and new vertexes)
#print(Vertex_1, Vertex_2, Third_Vertex, Propogation_Vector, N2, Point_2)
Intersection_Point, New_Vertex_1 = new_point(Vertex_1, Vertex_2,
Third_Vertex,
Propogation_Vector, N2,
Point_2)
#print(Vertex_1,Vertex_2,Third_Vertex)
#print(New_Vertex_1)
#print("Intersection_Point",Intersection_Point)
New_Vertex_2 = Third_Vertex
#print(New_Vertex_2)
New_Index_1 = Index_2
#print(Index_2)
if (Intersection_Point[axis] < End_Point[axis]):
New_Index_2 = find_Index(New_Vertex_1, New_Vertex_2, Index_2)
else:
New_Index_2 = 0
Forward_Array = np.zeros((6, 3))
New_Point_1 = Point_2
New_Point_2 = Intersection_Point
Forward_Array[0] = New_Point_1
Forward_Array[1] = New_Point_2
Forward_Array[2] = New_Vertex_1
Forward_Array[3] = New_Vertex_2
Forward_Array[4][0] = New_Index_1
Forward_Array[5][0] = New_Index_2
#print("Forward Array",Forward_Array)
return Forward_Array
def next_point_edge(self, Point_1, Point_2, Vertex_1, Vertex_2, Index_1,
Index_2):
e = 0.01 #error
friction_coefficient = 0.7
#Defining egde Vector and Normals
#Normal of Previous Triangle
N1 = self.Normals[Index_1]
print("N1", N1, Index_1)
#Normal of New_Triangle
N2 = self.Normals[Index_2]
print("N2", N2, Index_2)
T1 = np.subtract(Point_2, Point_1)
T1 = T1 / np.linalg.norm(T1)
#print("T1",T1)
#Determining Intersection point(New Point P2, and new vertexes)
Third_Vertex = Third_Vertex_fun(Vertex_1, Vertex_2, Index_2,
self.Vectors)
#print("Vertex_1,Vertex_2",Vertex_1,Vertex_2,Third_Vertex)
#Make the points Counterclockwise
Vertex_1, Vertex_2 = counter_clockwise_check(Vertex_1, Vertex_2,
Third_Vertex, N2)
#print("Vertex_1,Vertex_2",Vertex_1,Vertex_2,Third_Vertex)
Edge_Vector = np.subtract(Vertex_2, Vertex_1)
Edge_Vector = Edge_Vector / np.linalg.norm(Edge_Vector)
#print("EV",Edge_Vector)
input_angle = math.acos(np.dot(T1, Edge_Vector))
Zero_degree_Vector = np.cross(N2, Edge_Vector)
Zero_degree_Vector = Zero_degree_Vector / np.linalg.norm(
Zero_degree_Vector)
Geodesic_Vector = np.add(
math.sin(input_angle) * Zero_degree_Vector,
math.cos(input_angle) * Edge_Vector)
#Normalising the vectors
Geodesic_Vector = Geodesic_Vector / np.linalg.norm(Geodesic_Vector)
print("Geodesic_vector", Geodesic_Vector)
#Favored Direction
Favored_Dir = Plane_Winding_Direction(N2, self.Winding_Direction,
self.Winding_angle)
print("Favored_Dir", Favored_Dir)
#Calculating tangents to curve and normal to plane
Surface_normal = np.add(N1, N2)
Surface_normal = Surface_normal / np.linalg.norm(Surface_normal)
#print("Surface normal mod",np.linalg.norm(Surface_normal))
#print("Surface Normal",Surface_normal)
#Storage Variable
Max = Favored_Dir
Min = Geodesic_Vector
Mid = np.add(Max, Min)
Mid = Mid / np.linalg.norm(Mid)
Curve_vector = np.add(Max, -1 * T1)
#Curve_vector = Curve_vector/np.linalg.norm(Curve_vector)
#Geodesic Slippage calculation
#Curve_Geodesic = np.subtract(Geodesic_Vector,T1)
#Curve_Geodesic = Curve_Geodesic/np.linalg.norm(Curve_Geodesic)
#print("Curve_Geodesic",Curve_Geodesic)
#Slippage_Geodesic = math.tan(math.acos(np.dot(Curve_Geodesic,-1*Surface_normal)))
#print("Slippage Geodesic",Slippage_Geodesic)
Dot_product = np.dot(Curve_vector, -1 * Surface_normal)
if (Dot_product > 1):
Dot_product = 0.999
if (Dot_product < -1):
Dot_product = -0.999
Slippage_tendency = abs(math.tan(math.acos(Dot_product)))
#print("Dot product",Dot_product)
#print(math.tan(math.acos(Dot_product)))
a = 0
if (Slippage_tendency < friction_coefficient):
Propogation_Vector = Max
else:
while (abs(friction_coefficient - Slippage_tendency) >
e) and a < 40:
if (friction_coefficient < Slippage_tendency):
Max = Mid
if (friction_coefficient > Slippage_tendency):
Min = Mid
Mid = np.add(Max, Min)
Mid = Mid / np.linalg.norm(Mid)
#print(Mid_1)
Curve_vector = np.add(Mid, -1 * T1)
#Curve_vector = Curve_vector/np.linalg.norm(Curve_vector)
Dot_product = np.dot(Curve_vector, -1 * Surface_normal)
print("Dot_product", Dot_product)
if (Dot_product > 1):
Dot_product = 0.999
if (Dot_product < -1):
Dot_product = -0.999
Slippage_tendency = abs(math.tan(math.acos(Dot_product)))
a = a + 1
#print("Max",Max)
#print("Min",Min)
#print("Mid",Mid)
#print("Slippage_tendency",abs(Slippage_tendency))
#Define the Propogtion Vector
Propogation_Vector = Mid
print("Propogation Vector", Propogation_Vector)
Intersection_Point, New_Vertex_1 = new_point(Vertex_1, Vertex_2,
Third_Vertex,
Propogation_Vector, N2,
Point_2)
New_Vertex_2 = Third_Vertex
angle_axis = Plane_Direction(N2, self.Winding_Direction)
local_angle = math.acos(
math.cos(math.pi / 6) *
math.cos(math.asin(np.dot(angle_axis, Propogation_Vector))))
#print("New_Vertex_1",New_Vertex_1)
#print("New_Vertex_2",New_Vertex_2)
print("Intersection_Point", Intersection_Point)
#print(bool(Intersection_Point[self.axis]*self.Winding_Direction[self.axis]<self.End_Point[self.axis]*self.Winding_Direction[self.axis]))
New_Index_1 = Index_2
#print(self.Winding_Direction[self.axis])
#print("End_Point",self.End_Point)
#print(Index_2)
if (Intersection_Point[self.axis] * self.Winding_Direction[self.axis] <
self.End_Point[self.axis] * self.Winding_Direction[self.axis]):
New_Index_2 = find_Index(New_Vertex_1, New_Vertex_2, Index_2,
self.Points)
else:
New_Index_2 = 0
Forward_Array = np.zeros((6, 3))
New_Point_1 = Point_2
New_Point_2 = Intersection_Point
#print("New_Index_1",New_Index_1)
#print(self.Vectors[New_Index_1])
#print("New_Index_2",New_Index_2)
#print(self.Vectors[New_Index_2])
Forward_Array[0] = New_Point_1
Forward_Array[1] = New_Point_2
Forward_Array[2] = New_Vertex_1
Forward_Array[3] = New_Vertex_2
Forward_Array[4][0] = New_Index_1
Forward_Array[5][0] = New_Index_2
#print("Forward Array",Forward_Array)
#print("####")
return Forward_Array, local_angle