--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/trafficintelligence/objectsmoothing.py	Fri Jun 15 11:19:10 2018 -0400
@@ -0,0 +1,246 @@
+from trafficintelligence import storage, moving, utils
+
+from math import atan2, degrees, sin, cos, pi
+from numpy import median
+
+import matplotlib.pyplot as plt
+
+def findNearest(feat, featureSet,t,reverse=True):
+    dist={}
+    for f in featureSet:
+        if reverse:
+            dist[f]= moving.Point.distanceNorm2(feat.getPositionAtInstant(t+1),f.getPositionAtInstant(t))
+        else:
+            dist[f]= moving.Point.distanceNorm2(feat.getPositionAtInstant(t-1),f.getPositionAtInstant(t))
+    return min(dist, key=dist.get) # = utils.argmaxDict(dist)
+    
+def getFeatures(obj, featureID):
+    currentFeature = obj.getFeature(featureID)
+    first = currentFeature.getFirstInstant()
+    last = currentFeature.getLastInstant()
+    featureList=[[currentFeature,first,last,moving.Point(0,0)]]
+    # find the features to fill in the beginning of the object existence
+    while first != obj.getFirstInstant():
+        delta=featureList[-1][3]
+        featureSet = [f for f in obj.getFeatures() if f.existsAtInstant(first-1)]
+        feat = findNearest(currentFeature,featureSet,first-1,reverse=True)
+        if feat.existsAtInstant(first):
+            featureList.append([feat,feat.getFirstInstant(),first-1,(currentFeature.getPositionAtInstant(first)-feat.getPositionAtInstant(first))+delta])
+        else:
+            featureList.append([feat,feat.getFirstInstant(),first-1,(currentFeature.getPositionAtInstant(first)-feat.getPositionAtInstant(first-1))+delta])
+        currentFeature = feat
+        first= feat.getFirstInstant()
+    # find the features to fill in the end of the object existence
+    delta=moving.Point(0,0)
+    currentFeature = obj.getFeature(featureID) # need to reinitialize
+    while last!= obj.getLastInstant():
+        featureSet = [f for f in obj.getFeatures() if f.existsAtInstant(last+1)]
+        feat = findNearest(currentFeature,featureSet,last+1,reverse=False)
+        if feat.existsAtInstant(last):
+            featureList.append([feat,last+1,feat.getLastInstant(),(currentFeature.getPositionAtInstant(last)-feat.getPositionAtInstant(last))+delta])
+        else:
+            featureList.append([feat,last+1,feat.getLastInstant(),(currentFeature.getPositionAtInstant(last)-feat.getPositionAtInstant(last+1))+delta])
+        currentFeature = feat
+        last= feat.getLastInstant()
+        delta=featureList[-1][3]
+    return featureList
+    
+def buildFeature(obj, featureID, num = 1):
+    featureList= getFeatures(obj, featureID)
+    tmp={}
+    delta={}
+    for i in featureList:
+        for t in range(i[1],i[2]+1):
+            tmp[t]=[i[0],i[3]]
+    newTraj = moving.Trajectory()
+    
+    for instant in obj.getTimeInterval():
+        newTraj.addPosition(tmp[instant][0].getPositionAtInstant(instant)+tmp[instant][1])
+    newFeature= moving.MovingObject(num,timeInterval=obj.getTimeInterval(),positions=newTraj)
+    return newFeature
+
+def getBearing(p1,p2,p3):
+    angle = degrees(atan2(p3.y -p1.y, p3.x -p1.x))
+    bearing1 = (90 - angle) % 360
+    angle2 = degrees(atan2(p2.y -p1.y, p2.x -p1.x))
+    bearing2 = (90 - angle2) % 360    
+    dist= moving.Point.distanceNorm2(p1, p2)
+    return [dist,bearing1,bearing2,bearing2-bearing1]
+
+#Quantitative analysis "CSJ" functions    
+def computeVelocities(obj, smoothing=True, halfWidth=3):  #compute velocities from positions
+    velocities={}
+    for i in list(obj.timeInterval)[:-1]:
+        p1= obj.getPositionAtInstant(i)
+        p2= obj.getPositionAtInstant(i+1)
+        velocities[i]=p2-p1        
+    velocities[obj.getLastInstant()]= velocities[obj.getLastInstant()-1]  # duplicate last point
+    if smoothing:
+        velX= [velocities[y].aslist()[0] for y in sorted(velocities.keys())]
+        velY= [velocities[y].aslist()[1] for y in sorted(velocities.keys())]
+        v1= list(utils.filterMovingWindow(velX, halfWidth))
+        v2= list(utils.filterMovingWindow(velY, halfWidth))
+        smoothedVelocity={}
+        for t,i in enumerate(sorted(velocities.keys())):
+            smoothedVelocity[i]=moving.Point(v1[t], v2[t])
+        velocities=smoothedVelocity
+    return velocities
+    
+def computeAcceleration(obj,fromPosition=True):
+    acceleration={}
+    if fromPosition:
+        velocities=computeVelocities(obj,False,1)
+        for i in sorted(velocities.keys()):
+            if i != sorted(velocities.keys())[-1]:
+                acceleration[i]= velocities[i+1]-velocities[i]
+    else:
+        for i in list(obj.timeInterval)[:-1]:
+            v1= obj.getVelocityAtInstant(i)
+            v2= obj.getVelocityAtInstant(i+1)
+            acceleration[i]= v2-v1
+    return acceleration
+    
+def computeJerk(obj,fromPosition=True):
+    jerk={}
+    acceleration=computeAcceleration(obj,fromPosition=fromPosition)
+    for i in sorted(acceleration.keys()):
+        if i != sorted(acceleration.keys())[-1]:
+            jerk[i] = (acceleration[i+1]-acceleration[i]).norm2()
+    return jerk
+    
+def sumSquaredJerk(obj,fromPosition=True):
+    jerk= computeJerk(obj,fromPosition=fromPosition)
+    t=0
+    for i in sorted(jerk.keys()):
+        t+= jerk[i]* jerk[i]
+    return t
+    
+def smoothObjectTrajectory(obj, featureID,newNum,smoothing=False,halfWidth=3,create=False):
+    results=[]    
+    bearing={}
+    if create:
+        feature = buildFeature(obj, featureID , num=1) # why num=1
+    else:
+        feature = obj.getFeature(featureID)
+    for t in feature.getTimeInterval():
+        p1= feature.getPositionAtInstant(t)
+        p2= obj.getPositionAtInstant(t)
+        if t!=feature.getLastInstant():
+            p3= feature.getPositionAtInstant(t+1)
+        else:
+            p1= feature.getPositionAtInstant(t-1)
+            p3= feature.getPositionAtInstant(t)
+        bearing[t]= getBearing(p1,p2,p3)[1]        
+        results.append(getBearing(p1,p2,p3))
+    
+    medianResults=median(results,0)
+    dist= medianResults[0]
+    angle= medianResults[3]
+    
+    for i in sorted(bearing.keys()):
+        bearing[i]= bearing[i]+angle
+
+    if smoothing:
+        bearingInput=[]
+        for i in sorted(bearing.keys()):
+            bearingInput.append(bearing[i])
+        import utils
+        bearingOut=utils.filterMovingWindow(bearingInput, halfWidth)
+        for t,i in enumerate(sorted(bearing.keys())):
+            bearing[i]=bearingOut[t]
+        
+        #solve a smoothing problem in case of big drop in computing bearing (0,360)    
+        for t,i in enumerate(sorted(bearing.keys())):
+            if i!= max(bearing.keys()) and abs(bearingInput[t] - bearingInput[t+1])>=340:
+                for x in range(max(i-halfWidth,min(bearing.keys())),min(i+halfWidth,max(bearing.keys()))+1):
+                    bearing[x]=bearingInput[t-i+x]
+
+    translated = moving.Trajectory()
+    for t in feature.getTimeInterval():
+        p1= feature.getPositionAtInstant(t)
+        p1.x = p1.x + dist*sin(bearing[t]*pi/180)
+        p1.y = p1.y + dist*cos(bearing[t]*pi/180)
+        translated.addPosition(p1)
+        
+    #modify first and last un-smoothed positions (half width)
+    if smoothing:
+        d1= translated[halfWidth]- feature.positions[halfWidth]
+        d2= translated[-halfWidth-1]- feature.positions[-halfWidth-1]
+        for i in range(halfWidth):
+            p1= feature.getPositionAt(i)+d1
+            p2= feature.getPositionAt(-i-1)+d2
+            translated.setPosition(i,p1)
+            translated.setPosition(-i-1,p2)
+        
+    newObj= moving.MovingObject(newNum,timeInterval=feature.getTimeInterval(),positions=translated)
+    return newObj
+    
+def smoothObject(obj, newNum, minLengthParam = 0.7, smoothing = False, plotResults = True, halfWidth = 3, _computeVelocities = True, optimize = True, create = False):
+    '''Computes a smoother trajectory for the object
+    and optionnally smoother velocities
+    
+    The object should have its features in obj.features
+    TODO: check whether features are necessary'''
+    if not obj.hasFeatures():
+        print('Object {} has an empty list of features: please load and add them using obj.setFeatures(features)'.format(obj.getNum()))
+        from sys import exit
+        exit()
+
+    featureList=[i for i,f in enumerate(obj.getFeatures()) if f.length() >= minLengthParam*obj.length()]
+    if featureList==[]:
+        featureList.append(utils.argmaxDict({i:f.length() for i,f in enumerate(obj.getFeatures())}))
+        create = True
+    newObjects = []
+    for featureID in featureList: # featureID should be the index in the list of obj.features
+        newObjects.append(smoothObjectTrajectory(obj, featureID, newNum, smoothing = smoothing, halfWidth = halfWidth, create = create))
+
+    newTranslated = moving.Trajectory()
+    newInterval = []
+    for t in obj.getTimeInterval():
+        xCoord=[]
+        yCoord=[]
+        for i in newObjects:
+            if i.existsAtInstant(t):
+                p1= i.getPositionAtInstant(t)
+                xCoord.append(p1.x)
+                yCoord.append(p1.y)
+        if xCoord != []:
+            tmp= moving.Point(median(xCoord), median(yCoord))
+            newInterval.append(t)
+            newTranslated.addPosition(tmp)
+    
+    newObj= moving.MovingObject(newNum, timeInterval = moving.TimeInterval(min(newInterval),max(newInterval)),positions=newTranslated)
+        
+    if _computeVelocities:
+        tmpTraj = moving.Trajectory()
+        velocities= computeVelocities(newObj,True,5)
+        for i in sorted(velocities.keys()):
+            tmpTraj.addPosition(velocities[i])
+        newObj.velocities=tmpTraj
+    else:
+        newObj.velocities=obj.velocities
+    
+    if optimize:
+        csj1= sumSquaredJerk(obj,fromPosition=True)
+        csj2= sumSquaredJerk(newObj,fromPosition=True)
+        if csj1<csj2:
+            newObj=obj
+            newObj.velocities=obj.velocities
+        if _computeVelocities and csj1>=csj2:
+            csj3= sumSquaredJerk(obj,fromPosition=False)
+            csj4= sumSquaredJerk(newObj,fromPosition=False)
+            if csj4<=csj3:
+                newObj.velocities= obj.velocities
+
+    newObj.featureNumbers=obj.featureNumbers
+    newObj.features=obj.getFeatures()
+    newObj.userType=obj.userType
+
+    if plotResults:
+        plt.figure()
+        plt.title('objects_id = {}'.format(obj.num))
+        for i in featureList:
+            obj.getFeature(i).plot('cx-')
+        obj.plot('rx-')
+        newObj.plot('gx-')        
+    return newObj