import matplotlib.pyplot as plt

#Les fonctions------------------------------------------------------

def calcul_vitesses(abscisses,ordonnees,temps):
    v_x=[]
    v_y=[]
    for n in range(len(abscisses)-1):
        v_x.append((abscisses[n+1]-abscisses[n])/(temps[n+1]-temps[n]))
        v_y.append((ordonnees[n+1]-ordonnees[n])/(temps[n+1]-temps[n]))
    temps=temps[:-1]
    return v_x,v_y,temps

def representation_graphique(abscisses,ordonnees,v_x,v_y):
    plt.figure(figsize=(10,3))
    plt.subplots_adjust(left=0.06, bottom=0.16, right=0.99, top=0.92,
                wspace=0.2, hspace=None)
    #------------------------------
    plt.subplot(1,3,1)
    plt.scatter(abscisses,ordonnees,marker='+')
    plt.title('Vecteur vitesse instantanne')
    plt.xlabel('x en (m)')
    plt.ylabel('Altitude z en (m)')
    plt.xlim(0.8*min(abscisses),1.2*max(abscisses))
    for i in range(0,len(v_x),1):
        V=plt.quiver(abscisses[i], ordonnees[i] ,v_x[i] , v_y[i],
         scale_units='xy',angles='xy', scale=12)
    #------------------------------
    plt.subplot(1,3,2)
    plt.scatter(abscisses,ordonnees,marker='+')
    plt.title('Variation du vecteur vitesse')
    plt.xlabel('x en (m)')
    plt.ylabel('Altitude z en (m)')
    plt.xlim(0.8*min(abscisses),1.2*max(abscisses))
    for i in range(1,len(v_x),1):
        DV=plt.quiver(abscisses[i],ordonnees[i],v_x[i]-v_x[i-1],v_y[i]-v_y[i-1],
        scale_units='xy',angles='xy', scale=2, color='red')
    #-------------------------------
    plt.subplot(1,3,3)
    plt.scatter(abscisses,ordonnees,marker='+')
    plt.title('Somme des forces exterieures')
    plt.xlabel('x en (m)')
    plt.ylabel('Altitude z en (m)')
    plt.xlim(0.8*min(abscisses),1.2*max(abscisses))
    for i in range(1,len(v_x),1):
        F=plt.quiver(abscisses[i],ordonnees[i],0,-0.06*9.8,
        scale_units='xy',angles='xy', scale=1, color='g')
    #-------------------------------
    plt.show()

#Le programme principal--------------------------------------------

x=[0.00,0.50,1.00,1.50,2.00,2.50,3.00,3.50,4.00,4.50,5.00]
z=[5.00,4.95,4.80,4.56,4.22,3.77,3.23,2.60,1.86,1.03,0.09]
t=[0.00,0.10,0.20,0.30,0.40,0.50,0.60,0.70,0.80,0.90,1.00]

v_x,v_y,temps_v=calcul_vitesses(x,z,t)
representation_graphique(x,z,v_x,v_y)