You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
148 lines
3.6 KiB
148 lines
3.6 KiB
import matplotlib.pyplot as plt
|
|
import numpy as np
|
|
import time
|
|
# import shape
|
|
|
|
# On active le "mode interactif" de pyplot. Ainsi, les plt.show() ne sont plus nécessaires.
|
|
plt.ion()
|
|
|
|
# --------------------------------------------------------------------------------------
|
|
# Fonction de "fin temporaire" pendant l'avancée du TP. Attend une frappe Entrée, puis quitte le script.
|
|
|
|
def stop_ici():
|
|
plt.pause(0.1) # nécessaire pour que matplotlib ait le temps d'afficher les figures
|
|
input()
|
|
exit()
|
|
|
|
# Exercice 1
|
|
|
|
# Question 1
|
|
#! F(A,B,C,t) = (1-t)**2*A + 2*t*(1 - t)*B + t**2*C
|
|
|
|
def formuleBezier2(t,A,B,C):
|
|
return (1-t)**2*A + 2*t*(1 - t)*B + t**2*C
|
|
|
|
A, B, C = np.array([0,1]),np.array([3,3]),np.array([5,0])
|
|
allt = np.linspace(0,1,100)
|
|
allFt = np.zeros((len(allt),2))
|
|
for i in range(len(allt)):
|
|
allFt[i] = formuleBezier2(allt[i],A,B,C)
|
|
plt.figure()
|
|
plt.plot(allFt[:,0],allFt[:,1])
|
|
|
|
# Exercice 2
|
|
|
|
# Question 1
|
|
#! F(A,B,C,D,t) = (1-t)**3*A + 3*t*(1 - t)**2*B + 3*t**2*(1 - t)*C + t**3*D
|
|
|
|
def formuleBezier3(t,A,B,C,D):
|
|
return (1-t)**3*A + 3*t*(1 - t)**2*B + 3*t**2*(1 - t)*C + t**3*D
|
|
|
|
A, B, C, D = np.array([0,1]),np.array([3,3]),np.array([5,0]),np.array([7,1])
|
|
allt = np.linspace(0,1,100)
|
|
allFt = np.zeros((len(allt),2))
|
|
for i in range(len(allt)):
|
|
allFt[i] = formuleBezier3(allt[i],A,B,C,D)
|
|
plt.figure()
|
|
plt.plot(allFt[:,0],allFt[:,1])
|
|
|
|
# Exercice 3
|
|
|
|
# Question 1
|
|
def binom(N,k):
|
|
return np.math.factorial(N)/(np.math.factorial(k)*np.math.factorial(N-k))
|
|
|
|
# Question 2
|
|
|
|
def formuleBezierGenerale(t,P):
|
|
Ft = np.zeros(2)
|
|
for k in range(len(P)):
|
|
Ft += P[k]*np.math.factorial(len(P)-1)/(np.math.factorial(k)*np.math.factorial(len(P)-1-k))*t**k*(1-t)**(len(P)-1-k)
|
|
return Ft
|
|
|
|
P = [np.array([0,1]),np.array([3,3]),np.array([5,0]),np.array([7,1])]
|
|
allt = np.linspace(0,1,100)
|
|
allFt = np.zeros((len(allt),2))
|
|
for i in range(len(allt)):
|
|
allFt[i] = formuleBezierGenerale(allt[i],P)
|
|
plt.figure()
|
|
plt.plot(allFt[:,0],allFt[:,1])
|
|
|
|
|
|
# Exercice 4
|
|
|
|
A,B = np.array([0,1]),np.array([3,3])
|
|
allt = np.linspace(0,1,100)
|
|
|
|
|
|
#! /* version non vectorisée */
|
|
#* allFt = np.zeros((len(allt),2))
|
|
#* for i in range(len(allt)):
|
|
#* t = allt[i]
|
|
#* allFt[i] = (1-t)*A + t*B
|
|
|
|
#! /* version vectorisée */
|
|
#* allFt = (1-allt[:,None])*As[None,:] + allt[:,None]*B[None,:]
|
|
|
|
|
|
# Question 1
|
|
|
|
from time import time
|
|
debut = time()
|
|
allFt = np.zeros((len(allt),2))
|
|
for i in range(len(allt)):
|
|
t = allt[i]
|
|
allFt[i] = (1-t)*A + t*B
|
|
fin = time()
|
|
duree = fin - debut
|
|
print("Durée de la boucle for pour la non-vectorisé : ",duree)
|
|
|
|
debut = time()
|
|
allFt = (1-allt[:,None])*A[None,:] + allt[:,None]*B[None,:]
|
|
fin = time()
|
|
duree = fin - debut
|
|
print("Durée de la boucle for pour la vectorisé : ",duree)
|
|
|
|
# c'est environ 26 fois plus rapide
|
|
|
|
# Question 2
|
|
|
|
# Question a
|
|
# shape = shape(allt)
|
|
# shape2 = (len(allt[:None]),2)
|
|
# shape3 = (len(B),2)
|
|
# shape4 = (len(B[None,:]),2)
|
|
# shape5 = (len(allt[:,None]*B[None,:]),2)
|
|
|
|
# print(shape(allt))
|
|
# print("shape2 = ",shape2)
|
|
# print("shape3 = ",shape3)
|
|
# print("shape4 = ",shape4)
|
|
# print("shape5 = ",shape5)
|
|
|
|
|
|
# Question b
|
|
# allFt = (1-allt)*A + allt*B
|
|
|
|
# Question 3
|
|
# def formuleBezierVectorisee(allt, P):
|
|
# allFt = np.zeros((len(allt),2))
|
|
# for k in range(len(P)):
|
|
# allFt += P[k]*np.math.factorial(len(P)-1)/(np.math.factorial(k)*np.math.factorial(len(P)-1-k))*allt**k*(1-allt)**(len(P)-1-k)
|
|
# return allFt
|
|
|
|
# P = [np.array([0,1]),np.array([3,3]),np.array([5,0]),np.array([7,1])]
|
|
# allt = np.linspace(0,1,100)
|
|
|
|
# debut = time()
|
|
# allFt = formuleBezierVectorisee(allt,P)
|
|
# fin = time()
|
|
# duree = fin - debut
|
|
# print("Durée de la formule vectorisée : ",duree)
|
|
|
|
|
|
|
|
|
|
|
|
stop_ici() # pour arrêter le script ici
|