--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/python/extrapolation.py	Fri Jul 13 17:08:31 2012 -0400
@@ -0,0 +1,173 @@
+##########
+# Extrapolation Hypothesis
+##########
+
+import sys
+
+sys.path.append("G:/0-phdstart/Code/traffic-intelligence1/python")
+
+import moving 
+
+#Default values
+FPS= 25  # No. of frame per second (FPS) 
+vLimit= 25/FPS	#assume limit speed is 90km/hr = 25 m/sec
+deltaT= FPS*5	# extrapolatation time Horizon = 5 second	
+			
+def ExtrapolationPosition (movingObject1, instant,deltaT):
+	''' extrapolation hypothesis: constant velocity'''
+	return movingObject1.getPositionAtInstant(instant) + movingObject1.getVelocityAtInstant(instant). multiply(deltaT)
+	
+def motion (position, velocity, acceleration):
+	''' extrapolation hypothesis: constant acceleration'''
+	from math import atan2,cos,sin
+	vInit= velocity
+	vInitial= velocity.norm2()
+	theta= atan2(velocity.y,velocity.x)
+	vFinal= vInitial+acceleration
+	
+	if acceleration<= 0:
+		v= max(0,vFinal)
+		velocity= moving.Point(v* cos(theta),v* sin(theta))
+		position= position+ (velocity+vInit). multiply(0.5)
+	else:
+		v= min(vLimit,vFinal)
+		velocity= moving.Point(v* cos(theta),v* sin(theta))
+		position= position+ (velocity+vInit). multiply(0.5)
+	return(position,velocity)	
+
+def motionPET (position, velocity, acceleration, deltaT):
+	''' extrapolation hypothesis: constant acceleration for calculating pPET '''
+	from math import atan2,cos,sin,fabs
+	vInit= velocity
+	vInitial= velocity.norm2()
+	theta= atan2(velocity.y,velocity.x)
+	vFinal= vInitial+acceleration * deltaT
+	if acceleration< 0:
+		if vFinal> 0:	
+			velocity= moving.Point(vFinal* cos(theta),vFinal* sin(theta))
+			position= position+ (vInit+ velocity). multiply(0.5*deltaT)
+		else:
+			T= fabs(vInitial/acceleration)
+			position= position + vInit. multiply(0.5*T)
+	elif acceleration> 0 :
+		if vFinal<= vLimit:
+			velocity= moving.Point(vFinal* cos(theta),vFinal* sin(theta))
+			position= position+ (vInit+ velocity). multiply(0.5*deltaT)
+		else:
+			time1= fabs((vLimit-vInitial)/acceleration)
+			velocity= moving.Point(vLimit* cos(theta),vLimit* sin(theta))
+			position= (position+ (velocity+vInit). multiply(0.5*time1)) + (velocity.multiply (deltaT-time1))
+	elif acceleration == 0:
+		position= position + velocity. multiply(deltaT)
+	
+	return position
+
+def timePET (position, velocity, acceleration, intersectedPoint ):
+	''' extrapolation hypothesis: constant acceleration for calculating pPET '''
+	from math import atan2,cos,sin,fabs
+	vInit= velocity
+	vInitial= velocity.norm2()
+	theta= atan2(velocity.y,velocity.x)
+	vFinal= vInitial+acceleration * deltaT
+	if acceleration< 0:
+		if vFinal> 0:	
+			velocity= moving.Point(vFinal* cos(theta),vFinal* sin(theta))
+			time= fabs((intersectedPoint.x-position.x)/(0.5*(vInit.x+ velocity.x)))
+		else:
+			time= fabs((intersectedPoint.x-position.x)/(0.5*(vInit.x)))
+	elif acceleration> 0 :
+		if vFinal<= vLimit:
+			velocity= moving.Point(vFinal* cos(theta),vFinal* sin(theta))
+			time= fabs((intersectedPoint.x-position.x)/(0.5*(vInit.x+ velocity.x)))
+		else:
+			time1= fabs((vLimit-vInitial)/acceleration) 
+			velocity= moving.Point(vLimit* cos(theta),vLimit* sin(theta))
+			time2= fabs((intersectedPoint.x-position.x)/(0.5*(vInit.x+ velocity.x)))
+			if time2<=time1:
+				time= time2
+			else:
+				position2= (position+ (velocity+vInit). multiply(0.5*time1)) 
+				time= time1+fabs((intersectedPoint.x-position2.x)/( velocity.x))
+	elif acceleration == 0:
+		time= fabs((intersectedPoint.x-position.x)/(velocity.x))
+	
+	return time
+	
+def motionSteering (position, velocity, deltaTheta, deltaT ):
+	''' extrapolation hypothesis: steering with deltaTheta'''
+	from math import atan2,cos,sin
+	vInitial= velocity.norm2()
+	theta= atan2(velocity.y,velocity.x)
+	newTheta= theta + deltaTheta
+	velocity= moving.Point(vInitial* cos(newTheta),vInitial* sin(newTheta))
+	position= position+ (velocity). multiply(deltaT)
+	return position	
+	
+def MonteCarlo(movingObject1,movingObject2, instant):
+	''' Monte Carlo Simulation :  estimate the probability of collision'''
+	from random import uniform
+	from math import pow, sqrt, sin, cos,atan2		
+	N=1000
+	ProbOfCollision = 0
+	for n in range (1, N):
+		# acceleration limit	
+		acc1 = uniform(-0.040444,0)
+		acc2 = uniform(-0.040444,0)	
+		p1= movingObject1.getPositionAtInstant(instant)
+		p2= movingObject2.getPositionAtInstant(instant)
+		v1= movingObject1.getVelocityAtInstant(instant)
+		v2= movingObject2.getVelocityAtInstant(instant)
+		distance= (p1-p2).norm2()
+		distanceThreshold= 1.8	
+		t=1				
+		while distance > distanceThreshold and t <= deltaT:
+			# Extrapolation position
+			(p1,v1) = motion(p1,v1,acc1)
+			(p2,v2) = motion(p2,v2,acc2)
+			distance= (p1-p2).norm2()
+			if distance <=distanceThreshold:
+				ProbOfCollision= ProbOfCollision+1
+			t+=1
+	POC= float(ProbOfCollision)/N
+	return POC
+	
+def velocitySteering(velocity,steering):
+	from math import atan2,cos,sin
+	vInitial= velocity.norm2()
+	theta= atan2(velocity.y,velocity.x)
+	newTheta= theta + steering
+	v= moving.Point(vInitial* cos(newTheta),vInitial* sin(newTheta))
+	return v
+
+def MonteCarloSteering(movingObject1,movingObject2, instant,steering1,steering2):
+	''' Monte Carlo Simulation :  estimate the probability of collision in case of steering'''
+	from random import uniform
+	from math import pow, sqrt, sin, cos,atan2		
+	N=1000
+	L= 2.4
+	ProbOfCollision = 0
+	for n in range (1, N):
+		# acceleration limit	
+		acc1 = uniform(-0.040444,0)
+		acc2 = uniform(-0.040444,0)	
+		p1= movingObject1.getPositionAtInstant(instant)
+		p2= movingObject2.getPositionAtInstant(instant)
+		vInit1= movingObject1.getVelocityAtInstant(instant)
+		v1= velocitySteering (vInit1,steering1)
+		vInit2= movingObject2.getVelocityAtInstant(instant)
+		v2= velocitySteering (vInit2,steering2)
+		distance= (p1-p2).norm2()
+		distanceThreshold= 1.8	
+		t=1				
+		while distance > distanceThreshold and t <= deltaT:
+			# Extrapolation position
+			(p1,v1) = motion(p1,v1,acc1)
+			(p2,v2) = motion(p2,v2,acc2)
+			distance= (p1-p2).norm2()
+			if distance <=distanceThreshold:
+				ProbOfCollision= ProbOfCollision+1
+			t+=1
+	POC= float(ProbOfCollision)/N
+	return POC
+
+