好的，这并不难，下面是代码：
import math# visualisationimport matplotlib.pyplot as pltimport matplotlib.lines as lines# visualisationdef Sum_points(P1, P2): x1, y1 = P1 x2, y2 = P2 return x1+x2, y1+y2def 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 Falseclass 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_listif __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()
