In [1]:
from math import *
from matplotlib.pyplot import *
from matplotlib import animation
from IPython.display import HTML
from random import choice
In [2]:
def doubleEpicycloide(data, a=0, b=2*pi, nb_planche=100) :
#découpage temporelle
T=[a+(b-a)*k/nb_planche for k in range(nb_planche)]
#Création de la figure
fig = figure(figsize=(7,7))
#taille
xmin=-25
xmax=25
#Bornes graphiques
xlim((xmin, xmax))
ylim((xmin, xmax))
#Titre
title("Epicycloïde a double gravitation")
def doubleInit():
return ()
centreXx=1/2*xmax
centreXy=1/2*xmax
centreYx=1/2*xmin
centreYy=1/2*xmin
def constructionDoubleEpicycloide(i):
centreXx=1/2*xmax
centreXy=1/2*xmax
centreYx=1/2*xmin
centreYy=1/2*xmin
print("\rPlanche "+str(round((i+1)/nb_planche*100, 2))+"%", end='')
if(i==nb_planche-1) : print("\rCalculs terminés")
n=nb_planche-1
S=[a+(b-a)*k/n for k in range(n+1)]
T=S[:(i+1)]
epiXx=[centreXx for t in T]
epiXy=[centreXy for t in T]
epiYx=[centreYx for t in T]
epiYy=[centreYy for t in T]
for num_cercle in range(len(data)) :
v=data[num_cercle]["V"]
RX=data[num_cercle]["X"][0]
pX=data[num_cercle]["X"][1]
xX=RX*cos(v*T[-1]+pX)
yX=RX*sin(v*T[-1]+pX)
RY=data[num_cercle]["Y"][0]
pY=data[num_cercle]["Y"][1]
xY=RY*cos(v*T[-1]+pY)
yY=RY*sin(v*T[-1]+pY)
cerclesX[num_cercle].set_data([centreXx+RX*cos(v*s+pX) for s in S], [centreXy+RX*sin(v*s+pX) for s in S])
cerclesY[num_cercle].set_data([centreYx+RY*cos(v*s+pY) for s in S], [centreYy+RY*sin(v*s+pY) for s in S])
centreXx+=xX
centreXy+=yX
centreYx+=xY
centreYy+=yY
for k in range(i+1) :
epiXx[k]+=RX*cos(v*T[k]+pX)
epiXy[k]+=RX*sin(v*T[k]+pX)
epiYx[k]+=RY*cos(v*T[k]+pY)
epiYy[k]+=RY*sin(v*T[k]+pY)
epiX.set_data(epiXx, epiXy)
epiY.set_data(epiYx, epiYy)
axe1X.set_data([epiXx[i], epiXx[i]],[epiXy[i], xmin])
axe1Y.set_data([epiYx[i], xmax],[epiYy[i], epiYy[i]])
Dessin1.set_data(epiXx, epiYy)
return ()
#Initialisations
cerclesX=[]
cerclesY=[]
for num_cercle in range(len(data)) :
v=data[num_cercle]["V"]
RX=data[num_cercle]["X"][0]
pX=data[num_cercle]["X"][1]
RY=data[num_cercle]["Y"][0]
pY=data[num_cercle]["Y"][1]
cercleX, =plot([], [], lw=1)
cerclesX.append(cercleX)
cercleY, =plot([], [], lw=1)
cerclesY.append(cercleY)
#epicycloïde
epiX, =plot([], [], lw=3)
epiY, =plot([], [], lw=3)
#Axe
axe1X, =plot([], [], 'r', lw=1)
axe1Y, =plot([], [], 'r', lw=1)
#Dessin
Dessin1, =plot([], [], 'r')
print("Calculs en cours")
return animation.FuncAnimation(fig, constructionDoubleEpicycloide, init_func=doubleInit,frames=nb_planche, interval=50, blit=True)
In [3]:
#V:vitesse, X:[rayonX, phaseX], Y:[rayonY, phaseY]
data=[
{'V':1, 'X':[6,0], 'Y':[6,0]},
{'V':2, 'X':[3,-pi/3], 'Y':[3,2*pi/3]},
{'V':4, 'X':[2,0], 'Y':[2,0]}
]
HandSpineroide=doubleEpicycloide(data)
HTML(HandSpineroide.to_jshtml())
Out[3]:
In [4]:
def epicycloide(data, a=0, b=2*pi, nb_planche=100) :
nb_cercle=len(data)
#Correctif
for num_cercle in range(nb_cercle) :
try : phase=data[num_cercle]['P']
except : data[num_cercle]['P']=0
try : couleur=data[num_cercle]['C']
except : data[num_cercle]['P']=choice(['r', 'g', 'b', 'c', 'm', 'k'])
#Création de la figure
fig = figure(figsize=(7,7))
xmax=1
for num_cercle in range(nb_cercle) : xmax+=abs(data[num_cercle]['R'])
xmin=-xmax
#Bornes graphiques
xlim((xmin, xmax))
ylim((xmin, xmax))
#Titre
title("Epicycloïde")
def init():
return ()
def constructionEpicycloide(i):
print("\rPlanche "+str(round((i+1)/nb_planche*100, 2))+"%", end='')
if(i==nb_planche-1) : print("\rCalculs terminés")
n=nb_planche-1
centreX=0
centreY=0
S=[a+(b-a)*k/n for k in range(n+1)]
T=S[:(i+1)]
epiX=[0 for t in T]
epiY=[0 for t in T]
for num_cercle in range(nb_cercle) :
R=data[num_cercle]['R']
v=data[num_cercle]['V']
p=data[num_cercle]['P']
c=data[num_cercle]['C']
X=[centreX+R*cos(v*t+p)/5 for t in T]
Y=[centreY+R*sin(v*t+p)/5 for t in T]
x=R*cos(v*T[-1]+p)
y=R*sin(v*T[-1]+p)
points[num_cercle].set_data([centreX+x], [centreY+y])
arcs[num_cercle].set_data(X, Y)
angles[num_cercle].set_data([centreX+R*cos(v*T[0]+p), centreX, centreX+x], [centreY+R*sin(v*T[0]+p), centreY, centreY+y])
cercles[num_cercle].set_data([centreX+R*cos(v*s+p) for s in S], [centreY+R*sin(v*s+p) for s in S])
centreX+=x
centreY+=y
for k in range(i+1) :
epiX[k]+=R*cos(v*T[k]+p)
epiY[k]+=R*sin(v*T[k]+p)
epi.set_data(epiX, epiY)
return ()
#Initialisations
points=[]
arcs=[]
angles=[]
cercles=[]
for num_cercle in range(nb_cercle) :
R=data[num_cercle]['R']
v=data[num_cercle]['V']
c=data[num_cercle]['C']
p=data[num_cercle]['P']
point, =plot([], [], c+'o', lw=2)
points.append(point)
arc, =plot([], [], c, lw=0.79)
arcs.append(arc)
angle, =plot([], [], c, lw=1, label="Cercle "+str(num_cercle+1)+" : $R="+str(R)+"$,\t $\\omega="+str(v)+"$,\t $\\varphi="+str(round(p, 2))+"$")
angles.append(angle)
cercle, =plot([], [], c, lw=1)
cercles.append(cercle)
#epicycloïde
c=data[-1]['C']
epi, =plot([], [], c, lw=3)
#Affichage des label
legend(loc="upper left", bbox_to_anchor=(0, 0))
print("Calculs en cours")
return animation.FuncAnimation(fig, constructionEpicycloide, init_func=init,frames=nb_planche, interval=50, blit=True)
In [5]:
#V= vitesse, R=rayon, P=phase, C=couleur (optionelle)
data=[
{'V':1, 'R':6, 'P':0, 'C':'b'},
{'V':-2, 'R':3, 'P':pi/3, 'C':'m'},
{'V':4, 'R':2, 'P':0, 'C':'r'},
]
HandSpineroide=epicycloide(data)
HTML(HandSpineroide.to_jshtml())
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