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import math
import matplotlib
import matplotlib.pyplot as plt
from matplotlib.pyplot import *
def combinaison_lineaire(A,B,u,v):
return [A[0]*u+B[0]*v,A[1]*u+B[1]*v]
def interpolation_lineaire(A,B,t):
return combinaison_lineaire(A,B,t,1-t)
def vecteur_unitaire(P1,P2):
Ux = P2[0]-P1[0]
Uy = P2[1]-P1[1]
norme = math.sqrt(Ux*Ux+Uy*Uy)
if norme!=0:
return [Ux/norme,Uy/norme]
else:
return False
def test_alignement_4pts(points,epsilon):
U1 = vecteur_unitaire(points[0],points[1])
U2 = vecteur_unitaire(points[1],points[2])
U3 = vecteur_unitaire(points[2],points[3])
if U2:
x = 2.0-(U1[0]*U2[0]+U1[1]*U2[1]+U2[0]*U3[0]+U2[1]*U3[1])
else:
x = 1.0-(U1[0]*U3[0]+U1[1]*U3[1])
if abs(x) < epsilon:
return True
else:
return False
def division_courbe_bezier_3(points_control):
P01 = interpolation_lineaire(points_control[0],points_control[1],0.5)
P12 = interpolation_lineaire(points_control[1],points_control[2],0.5)
P23 = interpolation_lineaire(points_control[2],points_control[3],0.5)
P01_12 = interpolation_lineaire(P01,P12,0.5)
P12_23 = interpolation_lineaire(P12,P23,0.5)
Q = interpolation_lineaire(P01_12,P12_23,0.5)
return ([points_control[0],P01,P01_12,Q],[Q,P12_23,P23,points_control[3]])
def courbe_bezier_3_recursif(points_control,epsilon,pile_points_courbe):
if test_alignement_4pts(points_control,epsilon):
pile_points_courbe.append(points_control[0])
else:
(points_1,points_2) = division_courbe_bezier_3(points_control)
courbe_bezier_3_recursif(points_1,epsilon,pile_points_courbe)
courbe_bezier_3_recursif(points_2,epsilon,pile_points_courbe)
def courbe_bezier_3_recursif_init(points_control,epsilon):
pile_points_courbe = []
courbe_bezier_3_recursif(points_control,epsilon,pile_points_courbe)
pile_points_courbe.append(points_control[-1])
return pile_points_courbe
def plot_points(points_courbe,style='-'):
x = []
y = []
for p in points_courbe:
x.append(p[0])
y.append(p[1])
plot(x,y,style)
class Courbe:
def __init__(self,P0,P1,P2,P3,epsilon):
self.points_courbe = []
self.epsilon = epsilon
self.bezier_3_recursif_init([P0,P1,P2,P3])
self.points_control = [P0,P1,P2,P3]
def bezier_3_recursif_init(self,points_control):
courbe_bezier_3_recursif(points_control,self.epsilon,self.points_courbe)
self.P2 = points_control[2]
self.P3 = points_control[3]
def ajouter(self,P2,P3):
P0 = self.P3
P1 = [P0[0]+P0[0]-self.P2[0],P0[1]+P0[1]-self.P2[1]]
self.bezier_3_recursif_init([P0,P1,P2,P3])
self.points_control.append(P1)
self.points_control.append(P2)
self.points_control.append(P3)
self.dernier_point = P3
def liste_points(self):
self.points_courbe.append(self.dernier_point)
return self.points_courbe
def liste_points_control(self):
self.points_control.append(self.dernier_point)
return self.points_control
courbe = Courbe([0,0],[0,1],[1,1],[1,0],5e-3)
courbe.ajouter([2,0],[3,0])
courbe.ajouter([3,1],[2,1.5])
courbe.ajouter([3,3],[4,2])
points = courbe.liste_points()
points_control = courbe.liste_points_control()
matplotlib.pyplot.figure()
plot_points(points,style='.')
plot_points(points,style='r-')
plot_points(points_control,'o')
axis([0,5,-4,4])
grid()
plt.show() |
