## simulate a coin flip -
from visual import *
scene.autoscale = 0


# updates position, velocity, angle, spin rate of coin (first arg.)
# falling in a gravitational field (vector, 2nd argument), over a
# time dt (number, 3rd argument), with damping (air resistance, 4th
# argument).
def coinspinfall(obj, g, dt, damping):
    obj.pos += obj.vel * dt
    obj.vel += g * dt
    obj.theta += obj.omega * dt
    obj.rotate(angle=obj.omega*dt, axis = (0,0,1))
    # very simple model for air resistance, if needed
    obj.omega -= damping * dt * obj.omega
    obj.vel -= dt * abs(cos(obj.theta)) * damping * obj.vel

# computes new velocity and spin rate, when coin bounces
# takes 2 arguments.
def coinbounce(coin, damp):
    # conserve energy, act with vertical force.
    # change in angular momentum is - r * cos(theta) * impulse
    # energy = 0.5 I om^2 + 0.5 m v^2
    # delta(omega) = +/- impulse/I * cos(theta)
    # delta(v) = impulse/m
    # take I = 0.3, m = 1
    # delta(E) = 0.5 I (+/-2 om * impulse *cos+ impulse^2*cos*cos) + 0.5 (2*v * impulse + impulse^2)
    # 2 delta(E) = impulse * (+/- 2 (om*I*cos)+(2*v) + (I*cos^2+1)*impulse)
    # set equal to zero, get impulse = -2*(+/- I*om*cos + v)/(I*cos^2+1)
    I = 0.3  ## moment of inertia, in units of m * r**2
    # debug E = 0.5 * I * coin.omega*coin.omega + 0.5 * coin.vel.y * coin.vel.y
    co = cos(coin.theta) ## handy variable to have
    # debug print coin.y,coin.vel.y,coin.omega,cos(coin.theta),E
    if coin.y+sin(coin.theta) < 0:
        impulse = -2.0 * (coin.omega * co + coin.vel.y)/(co*co/I+1)
        coin.vel.y += impulse
        coin.omega += impulse/I * co
        coin.y = -sin(coin.theta)+0.0001
    else:
        impulse = -2.0 * (-coin.omega * co + coin.vel.y)/(co*co/I+1)
        coin.vel.y += impulse
        coin.omega += -impulse/I* co
        coin.y = sin(coin.theta)+0.0001
    # simple model for loss of energy during bounce
    coin.omega -= coin.omega * damp
    coin.vel -= coin.vel * damp
    #E = 0.5 * I * coin.omega*coin.omega + 0.5 * coin.vel.y * coin.vel.y
    #print impulse,cos(coin.theta),E
    #coinreport(coin)

# Updates coin (1st arg) over time dt (third arg),
# with fractional loss of speed each bounce
# given by the 2nd argument.
# Using zero air resistance, magnitude of gravity = 1.
def coinupdate(coin, loss, dt):
    if coin.y+sin(coin.theta) > 0 and coin.y-sin(coin.theta)>0:
        damping = 0.0
        coinspinfall(coin, vector(0,-1, 0), dt, damping)
    else:
        coinbounce(coin, loss)
        #print coin.vel.y, coin.omega, coin.y

# makes a coin at position initialx along the x-axis and rotated
# by an initial angle initialtheta (first and second arguments)
def makecoin(initialx, initialtheta):
    coin = frame(pos=(initialx,10,0))
    coin.vel = vector(0,0,0)
    coin.theta = initialtheta
    coin.rotate(axis=(0,0,1),angle=coin.theta)
    coin.omega = 0.0
    cyl1 = cylinder(frame=coin,axis=(0,0.1,0),color=color.green)
    cyl2 = cylinder(frame=coin,axis=(0,-0.1,0),color=color.red)
    return coin

# returns true if the coin is still moving; if very slow, returns false.
def coinmoving(coin):
    return abs(coin.vel.y) > 0.1 or abs(coin.y) > 0.02

# reports which side is facing up
def coinreport(coin):
    print "Report on coin at position",coin.x,
    if cos(coin.theta) >0:
        print " Facing green up - Heads"
    else:
        print " Facing red up - Tails"