# this version of the Euler-Cromer code should look quite like the 1-D version
# except that acceleration, velocity, and position are all defined to be 3-D
# vectors.  You'll notice in the line "funct1.plot(pos=(r.x,r.y))" that when you
# just want the x or y component of a vector, you call for it by appending
# ".x" or ".y" to the vector name.

from __future__ import division
from visual import *
from visual.graph import *

# set up for the graph
graph1 = gdisplay(title="y vs. x",xtitle="x", ytitle="y")
funct1 = gcurve(gdisplay=graph1, color=color.cyan)

# constant
gmag=9.8 #the magnitude of the acceleration due to gravity
g = vector(0,-gmag,0) #the vector for acceleration due to gravity

# set initial conditions & time step
t=0
dt=0.002
r = vector(0,0,0)   #initiallizing position vector
v = vector(15,15,0) #initializing velocity vector

# plot initial position
funct1.plot(pos=(r.x,r.y))

# apply the Euler-Cromer method to each component
while r.y >= 0: #continue the calculation until the projectile lands
    a = g       #set accleration to always be that due to gravity
    v = v + a*dt #use this acceleration to update velocity
    r = r + v*dt #use this velocity to update position
    t=t+dt
    funct1.plot(pos=(r.x,r.y)) # add the new point to the graph