好的，这并不难，下面是代码：
import math
# visualisation
import matplotlib.pyplot as plt
import matplotlib.lines as lines
# visualisation
def Sum_points(P1, P2):
x1, y1 = P1
x2, y2 = P2
return x1+x2, y1+y2
def Multiply_point(multiplier, P):
x, y = P
return float(x)*float(multiplier), float(y)*float(multiplier)
def Check_if_object_is_polygon(Cartesian_coords_list):
if Cartesian_coords_list[0] == Cartesian_coords_list[len(Cartesian_coords_list)-1]:
return True
else:
return False
class Object():
def __init__(self, Cartesian_coords_list):
self.Cartesian_coords_list = Cartesian_coords_list
def Find_Q_point_position(self, P1, P2):
Summand1 = Multiply_point(float(3)/float(4), P1)
Summand2 = Multiply_point(float(1)/float(4), P2)
Q = Sum_points(Summand1, Summand2)
return Q
def Find_R_point_position(self, P1, P2):
Summand1 = Multiply_point(float(1)/float(4), P1)
Summand2 = Multiply_point(float(3)/float(4), P2)
R = Sum_points(Summand1, Summand2)
return R
def Smooth_by_Chaikin(self, number_of_refinements):
refinement = 1
copy_first_coord = Check_if_object_is_polygon(self.Cartesian_coords_list)
while refinement <= number_of_refinements:
self.New_cartesian_coords_list = []
for num, tuple in enumerate(self.Cartesian_coords_list):
if num+1 == len(self.Cartesian_coords_list):
pass
else:
P1, P2 = (tuple, self.Cartesian_coords_list[num+1])
Q = obj.Find_Q_point_position(P1, P2)
R = obj.Find_R_point_position(P1, P2)
self.New_cartesian_coords_list.append(Q)
self.New_cartesian_coords_list.append(R)
if copy_first_coord:
self.New_cartesian_coords_list.append(self.New_cartesian_coords_list[0])
self.Cartesian_coords_list = self.New_cartesian_coords_list
refinement += 1
return self.Cartesian_coords_list
if __name__ == "__main__":
Cartesian_coords_list = [(1,1),
(1,3),
(4,5),
(5,1),
(2,0.5),
(1,1),
]
obj = Object(Cartesian_coords_list)
Smoothed_obj = obj.Smooth_by_Chaikin(number_of_refinements = 5)
# visualisation
x1 = [i for i,j in Smoothed_obj]
y1 = [j for i,j in Smoothed_obj]
x2 = [i for i,j in Cartesian_coords_list]
y2 = [j for i,j in Cartesian_coords_list]
plt.plot(range(7),range(7),'w', alpha=0.7)
myline = lines.Line2D(x1,y1,color='r')
mynewline = lines.Line2D(x2,y2,color='b')
plt.gca().add_artist(myline)
plt.gca().add_artist(mynewline)
plt.show()
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