Beispiel #1
0
    def drawToAnimation(self):
        """ Draw. Assuming that the human is standing.
        
        Parameters
        ----------
        
        
        """

        listPlanes = []
        if self.chair and self.table:
            listPlanes.append(self.chair.getPartition(Ps=1))
            listPlanes.append(self.table.getPartition(Ps=1))
        listPlanes = list(flatten(listPlanes))

        alphas = [1 for plane in listPlanes]

        fig, ax = draw(xlim=[0, self.room.L],
                       ylim=[0, self.room.W],
                       zlim=[0, self.room.H],
                       planes=listPlanes,
                       enablevect=False,
                       alphas=alphas)

        fig, ax = draw(figure=fig, axes=ax, vectors=[self.led], colors='blue')

        return fig, ax
    def draw(self, displayRoom=False, displayReflectivity=False):
        """ Draw.
        
        Parameters
        ----------
        displayRoom: bool
        displayReflectivity: bool
        
        
        """

        if displayRoom:
            if displayReflectivity:
                alphas = [
                    0.5 * plane.reflectivity for plane in self.listPlanes
                ]
            else:
                alphas = [1 for plane in self.listPlanes]

            fig, ax = draw(xlim=[0, self.room.L],
                           ylim=[0, self.room.W],
                           zlim=[0, self.room.H],
                           planes=self.listPlanes,
                           vectors=Vector(coord=self.human.normalVect,
                                          refPoint=self.human.ctrPoint,
                                          which='cartesian'),
                           enablevect=False,
                           alphas=alphas)
        else:
            listPlanes = []
            listPlanes.append(self.human.listPlanes)
            if self.chair and self.table:
                listPlanes.append(self.chair.getPartition(Ps=1))
                listPlanes.append(self.table.getPartition(Ps=1))
            listPlanes = list(flatten(listPlanes))

            if displayReflectivity:
                alphas = [0.5 * plane.reflectivity for plane in listPlanes]
            else:
                alphas = [1 for plane in listPlanes]

            fig, ax = draw(xlim=[0, self.room.L],
                           ylim=[0, self.room.W],
                           zlim=[0, self.room.H],
                           planes=listPlanes,
                           vectors=Vector(coord=self.human.normalVect,
                                          refPoint=self.human.ctrPoint,
                                          which='cartesian'),
                           enablevect=False,
                           alphas=alphas)

        fig, ax = draw(figure=fig,
                       axes=ax,
                       circles=[self.human.pd, self.pd],
                       scales=5e3,
                       vectors=[self.human.led, self.led])

        return fig, ax
Beispiel #3
0
    def getPartition(self, Ps=1, delta=None):

        planes = []
        if delta == None:
            planes.append(self.head.getPartition(Ps=Ps))
            planes.append(self.body.getPartition(Ps=Ps))
            planes.append(self.leg.getPartition(Ps=Ps))
        else:
            if delta > 0.15:
                delta = 0.15
            planes.append(self.head.getPartition(delta=delta))
            planes.append(self.body.getPartition(delta=delta))
            planes.append(self.leg.getPartition(delta=delta))

        planes = list(flatten(planes))
        return planes
    def getPartition(self, Ps=1, delta=None):
        """ Partition all objects.
        
        Parameters
        ----------
        Ps: list
            List of number of partition of each side. 
        delta: list
            Define the partition based on partition lengths

        Returns
        -------
        list:
            A list of partitioned planes. Each plane is an instant of 
            RectPlane_py.
        
        """

        planes = []
        if delta == None:
            planes.append(self.head.getPartition(Ps=Ps))
            planes.append(self.body.getPartition(Ps=Ps))
            if self.leg:
                planes.append(self.leg.getPartition(Ps=Ps))
            if self.chair:
                planes.append(self.chair.getPartition(Ps=Ps))
            if self.table:
                planes.append(self.table.getPartition(Ps=Ps))
        else:
            if delta > 0.15:
                delta = 0.15
            planes.append(self.head.getPartition(delta=delta))
            planes.append(self.body.getPartition(delta=delta))
            if self.leg:
                planes.append(self.leg.getPartition(delta=delta))
            if self.chair:
                planes.append(self.chair.getPartition(delta=delta))
            if self.table:
                planes.append(self.table.getPartition(delta=delta))

        planes = list(flatten(planes))
        return planes
Beispiel #5
0
    def calc(self,
             LEDs,
             PDs,
             blockingObj,
             reflectingObj,
             partitionDist=speed_of_light * 1e-9,
             numReflections=3,
             verbose=False):
        """ Calcute the CIR.
        
        Parameters
        ----------
        LEDs: list
            List of LEDs. But, currently supports 1 LED.
        PDs: list
            List of PDs. Currently supports 1 PD.
        blockingObj: list
            List of blocking objects. 
        reflectingObj: list
            List of reflecting objects, for example a room.
            The naming is due to we might need a genera case when
            we can do the assumptions of infinite room such that 
            what matters most are the ceiling and the floor.
            Note that the blockingObj will also be treated as a 
            relfecting object.
        partitionDist: double, optional
            Delta distance based on which we partition a plane 
            (the default value is 1ns * c, c: speed of light).
            The default value is c*timesampling, timesampling is 
            assumed to 1ns by default. See Schulze's paper. 
        numReflections: inf or integer, optional
            Denoting the number of reflections (the default is 3).


        """

        # Transform into list
        if not isinstance(LEDs, list):
            LEDs = [LEDs]

        if not isinstance(PDs, list):
            PDs = [PDs]

        if not isinstance(blockingObj, list):
            blockingObj = [blockingObj]

        if not isinstance(reflectingObj, list):
            reflectingObj = [reflectingObj]

        # Currently support 1 LED and 1 PD
        assert len(LEDs) == 1 and len(PDs) == 1

        # Partition assuming that all obj in reflectingObj
        # has the getPartition method
        reflectingPlanes = []
        for obj in reflectingObj:
            reflectingPlanes.append(obj.getPartition(delta=partitionDist))

        # don't forget to include blockingObj as reflecting objects
        for obj in blockingObj:
            reflectingPlanes.append(obj.getPartition(delta=partitionDist))

        # flatten the list
        reflectingPlanes = list(flatten(reflectingPlanes))

        # Partition blockingObj
        blockingPlanes = []
        for obj in blockingObj:
            # The number of partition on each side is one
            blockingPlanes.append(obj.getPartition(Ps=1))

        blockingPlanes = list(flatten(blockingPlanes))

        # Get simple planes
        simpleReflectingPlanes = [
            plane.getSimplePlane() for plane in reflectingPlanes
        ]
        simpleBlockingPlanes = [
            plane.getSimplePlane() for plane in blockingPlanes
        ]
        emitters = [led.getSimplePointSource() for led in LEDs]
        collectors = [pd.getSimpleBareDetector() for pd in PDs]

        # Get the farthest vertix from origin
        dummyPlanes = []
        for obj in reflectingObj:
            dummyPlanes.append(obj.getPartition(Ps=1))

        dummyPlanes = list(flatten(dummyPlanes))

        # Assuming each dummyPlane has the vertixes attributes
        # Collect all vertices
        verts = np.array(list(flatten([plane.verts for plane in dummyPlanes
                                       ]))).reshape(-1, 3)

        # Calculate norm relative to origin
        listOfNorm = list(map(lambda v: np.linalg.norm(v), verts))

        outerVert = verts[listOfNorm.index(max(listOfNorm))]

        if verbose:
            print("> Calculating CIR......(wait)")

        self.ht_los, self.ht_diff = calcCIRTimeDom(self.timeSampling,
                                                   numReflections, outerVert,
                                                   emitters[0], collectors[0],
                                                   simpleReflectingPlanes,
                                                   simpleBlockingPlanes)

        if verbose:
            print("> Finish calculating CIR :)")

        self.t = np.arange(self.ht_los.size) * self.timeSampling

        return self.ht_los, self.ht_diff
    def updateListPlanesAndCheckValidity(self):

        # Get all planes
        self.listPlanes = []
        self.listPlanes.append(self.human.listPlanes)
        self.listPlanes.append(self.room.listPlanes)
        if self.chair and self.table:
            self.listPlanes.append(self.chair.getPartition(Ps=1))
            self.listPlanes.append(self.table.getPartition(Ps=1))
        self.listPlanes = list(flatten(self.listPlanes))

        # Get blocking object
        self.blockingObj = []
        if self.chair:
            self.blockingObj.append(self.chair)
        if self.table:
            self.blockingObj.append(self.table)
        if self.human:
            self.blockingObj.append(self.human)

        # Validate whether a vertice is NOT out of bounds
        roomVerts = np.append(self.room.listPlanes[0].verts,
                              self.room.listPlanes[1].verts).reshape([-1, 3])

        delaunay = Delaunay(roomVerts)

        verts = np.array(
            list(flatten([plane.verts.tolist()
                          for plane in self.listPlanes]))).reshape([-1, 3])

        if self.human.led:
            verts = np.append(verts, self.human.led.loc).reshape([-1, 3])
        elif self.human.pd:
            verts = np.append(verts, self.human.pd.loc).reshape([-1, 3])

#         # Check feasibility of human
#         verts = np.array(list(flatten([plane.verts.tolist() for plane in self.human.listPlanes]))).reshape([-1,3])

#         # Check feasibility of chair
#         verts = np.array(list(flatten([plane.verts.tolist() for plane in self.chair.getPartition(Ps=1)]))).reshape([-1,3])

#         # Check feasibility of table
#         verts = np.array(list(flatten([plane.verts.tolist() for plane in self.table.getPartition(Ps=1)]))).reshape([-1,3])

#         # Check feasibility of LED
#         verts = self.human.led.loc

#         # Check feasibility of PD
#         verts = self.human.pd.loc

        self.isValid = np.alltrue(delaunay.find_simplex(verts) >= 0)

        # Check whether the human intersects with the furniture
        if self.chair and self.table:
            chairVerts = np.append(self.chair.listPlanes[0].verts,
                                   self.chair.listPlanes[1].verts).reshape(
                                       [-1, 3])
            tableVerts = np.append(
                self.tableAsCube.listPlanes[0].verts,
                self.tableAsCube.listPlanes[1].verts).reshape([-1, 3])

            verts = np.array(
                list(
                    flatten([
                        plane.verts.tolist() for plane in self.human.listPlanes
                    ]))).reshape([-1, 3])

            if self.human.led:
                verts = np.append(verts, self.human.led.loc).reshape([-1, 3])
            elif self.human.pd:
                verts = np.append(verts, self.human.pd.loc).reshape([-1, 3])

            self.isValid = np.alltrue(
                Delaunay(chairVerts).find_simplex(verts) < 0) and np.alltrue(
                    Delaunay(tableVerts).find_simplex(verts) < 0)
    def __init__(self,
                 roomDim,
                 humanLoc,
                 humanDirection,
                 chairLoc=None,
                 chairDirection=0,
                 mode='rx',
                 activity='calling',
                 position='standing'):

        # Assertion checks
        assert len(roomDim) == 3 and np.alltrue(np.array(roomDim) > 0)

        assert mode.lower() == 'tx' or mode.lower() == 'rx',\
            ("'mode' is not recognized! Should be either 'tx' or 'rx'")

        assert activity.lower() == 'calling' or activity.lower() == 'reading' or activity.lower() == 'usbdongle',\
            ("'activity' is not recognized! Should be either 'calling', 'reading' or 'usbdongle'")

        assert position.lower() == 'standing' or position.lower() == 'sitting',\
            ("'mode' is not recognized! Should be either 'standing' or 'sitting'")

        assert not(activity.lower() == 'usbdongle' and position.lower()=='standing'),\
            ("cannot choose the `usbdongle` aciticity and the `standing` position.")

        # Human and other elements
        self.human = Human(loc=humanLoc,
                           direction=humanDirection,
                           mode=mode,
                           activity=activity,
                           position=position)

        # Room
        # Reflectivities
        # Except the floor, which is modeled as a pinewood, other
        # parts are modeled with plasters
        rho_keys = ['b', 't', 's', 'n', 'e', 'w']

        if mode.lower() == 'tx':
            # IR-LED (uplink)
            rho_vals = [0.92, 0.83, 0.83, 0.83, 0.83, 0.83]
        elif mode.lower() == 'rx':
            # VL-LED (downlink)
            rho_vals = [0.54, 0.76, 0.76, 0.76, 0.76, 0.76]

        reflectivities = {
            rho_keys[i]: rho_vals[i]
            for i in range(len(rho_keys))
        }

        self.room = Room(dimensions=roomDim,
                         identity=1,
                         reflectivities=reflectivities)

        # A chair and a table
        self.chair, self.table, self.tableAsCube = None, None, None
        if chairLoc:
            self.chair = Cube(Vector(
                np.array([1, np.deg2rad(90), np.deg2rad(0)])),
                              ctrPoint=np.array([0, 0, 0.2]),
                              dimensions=[0.4, 0.4, 0.4],
                              reflectivities={
                                  'p0': 0.04,
                                  'p1': 0.04,
                                  'p2': 0.04,
                                  'p3': 0.04,
                                  'p4': 0.04,
                                  'p5': 0.04
                              })
            self.chair = self.chair.rotate(chairDirection, np.array([0, 0, 1]))
            self.chair = self.chair.translate(
                np.array([*chairLoc, 0]) + self.chair.ctrPoint)

            Rd = getRodriguesMtx(chairDirection, np.array([0, 0, 1]))
            shiftedVect = (
                Rd @ np.array([0.2, 0, 0]).reshape(3, 1)).reshape(-1)
            self.chair = self.chair.translate(shiftedVect +
                                              self.chair.ctrPoint)

            # The table's location is defined based on
            self.table = Cube(Vector(
                np.array([1, np.deg2rad(90), np.deg2rad(0)])),
                              ctrPoint=np.array([0, 0, 0.3]),
                              dimensions=[0.6, 1.2, 0.9],
                              reflectivities={
                                  'p0': 0.04,
                                  'p1': 0.04,
                                  'p2': 0.04,
                                  'p3': 0.04,
                                  'p4': 0.04,
                                  'p5': 0.04
                              })
            self.table = self.table.rotate(chairDirection, np.array([0, 0, 1]))
            self.table = self.table.translate(
                np.array([*chairLoc, 0]) + self.table.ctrPoint)

            Rd = getRodriguesMtx(chairDirection, np.array([0, 0, 1]))
            shiftedVect = (Rd @ np.array([1, 0, 0]).reshape(3, 1)).reshape(-1)
            self.table = self.table.translate(shiftedVect +
                                              self.table.ctrPoint)

            # The table is modeled a simple plane
            self.tableAsCube = self.table
            self.table = self.table.listPlanes[2]

        # LED or PD
        self.led, self.pd = None, None

        if mode.lower() == 'rx':
            self.led = PointSource(
                np.pi,
                0,
                np.array([self.room.L / 2, self.room.W / 2, self.room.H]),
                m=-np.log(2) / np.log(np.cos(np.deg2rad(40.))))
        elif mode.lower() == 'tx':
            self.pd = BareDetector(
                np.pi,
                0,
                np.array([self.room.L / 2, self.room.W / 2, self.room.H]),
                area=1e-4,
                FoV=np.deg2rad(85))

        # Get all planes
        self.listPlanes = []
        self.listPlanes.append(self.human.listPlanes)
        self.listPlanes.append(self.room.listPlanes)
        if self.chair and self.table:
            self.listPlanes.append(self.chair.getPartition(Ps=1))
            self.listPlanes.append(self.table.getPartition(Ps=1))
        self.listPlanes = list(flatten(self.listPlanes))

        # Get blocking object
        self.blockingObj = []
        if self.chair:
            self.blockingObj.append(self.chair)
        if self.table:
            self.blockingObj.append(self.table)
        if self.human:
            self.blockingObj.append(self.human)

        # Validate whether a vertice is NOT out of bounds
        roomVerts = np.append(self.room.listPlanes[0].verts,
                              self.room.listPlanes[1].verts).reshape([-1, 3])

        delaunay = Delaunay(roomVerts)

        verts = np.array(
            list(flatten([plane.verts.tolist()
                          for plane in self.listPlanes]))).reshape([-1, 3])

        if self.human.led:
            verts = np.append(verts, self.human.led.loc).reshape([-1, 3])
        elif self.human.pd:
            verts = np.append(verts, self.human.pd.loc).reshape([-1, 3])

#         # Check feasibility of human
#         verts = np.array(list(flatten([plane.verts.tolist() for plane in self.human.listPlanes]))).reshape([-1,3])

#         # Check feasibility of chair
#         verts = np.array(list(flatten([plane.verts.tolist() for plane in self.chair.getPartition(Ps=1)]))).reshape([-1,3])

#         # Check feasibility of table
#         verts = np.array(list(flatten([plane.verts.tolist() for plane in self.table.getPartition(Ps=1)]))).reshape([-1,3])

#         # Check feasibility of LED
#         verts = self.human.led.loc

#         # Check feasibility of PD
#         verts = self.human.pd.loc

        self.isValid = np.alltrue(delaunay.find_simplex(verts) >= 0)

        # Check whether the human intersects with the furniture
        if self.chair and self.table:
            chairVerts = np.append(self.chair.listPlanes[0].verts,
                                   self.chair.listPlanes[1].verts).reshape(
                                       [-1, 3])
            tableVerts = np.append(
                self.tableAsCube.listPlanes[0].verts,
                self.tableAsCube.listPlanes[1].verts).reshape([-1, 3])

            verts = np.array(
                list(
                    flatten([
                        plane.verts.tolist() for plane in self.human.listPlanes
                    ]))).reshape([-1, 3])

            if self.human.led:
                verts = np.append(verts, self.human.led.loc).reshape([-1, 3])
            elif self.human.pd:
                verts = np.append(verts, self.human.pd.loc).reshape([-1, 3])

            self.isValid = np.alltrue(
                Delaunay(chairVerts).find_simplex(verts) < 0) and np.alltrue(
                    Delaunay(tableVerts).find_simplex(verts) < 0)
Beispiel #8
0
    def calc(self,
             LEDs,
             PDs,
             blockingObj,
             reflectingObj,
             partitionDist=speed_of_light * 1e-9,
             numReflections=math.inf,
             verbose=False):
        """ Calcute the CIR.
        
        Parameters
        ----------
        LEDs: list
            List of LEDs. But, currently supports 1 LED.
        PDs: list
            List of PDs. Currently supports 1 PD.
        blockingObj: list
            List of blocking objects. 
        reflectingObj: list
            List of reflecting objects, for example a room.
            The naming is due to we might need a genera case when
            we can do the assumptions of infinite room such that 
            what matters most are the ceiling and the floor.
            Note that the blockingObj will also be treated as a 
            relfecting object.
        partitionDist: double (optional)
            Delta distance based on which we partition a plane.
            The default value is c*timesampling, timesampling is 
            assumed to 1ns by default. See Schulze's paper.
        numReflections: inf or integer (optional)
            Denoting the number of reflections.


        """

        # Transform into list
        if not isinstance(LEDs, list):
            LEDs = [LEDs]

        if not isinstance(PDs, list):
            PDs = [PDs]

        if not isinstance(blockingObj, list):
            blockingObj = [blockingObj]

        if not isinstance(reflectingObj, list):
            reflectingObj = [reflectingObj]

        # Currently support 1 LED and 1 PD
        assert len(LEDs) == 1 and len(PDs) == 1

        # Partition assuming that all obj in reflectingObj
        # has the getPartition method
        reflectingPlanes = []
        for obj in reflectingObj:
            reflectingPlanes.append(obj.getPartition(delta=partitionDist))

        # don't forget to include blockingObj as reflecting objects
        for obj in blockingObj:
            reflectingPlanes.append(obj.getPartition(delta=partitionDist))

        # flatten the list
        reflectingPlanes = list(flatten(reflectingPlanes))

        # Partition blockingObj
        blockingPlanes = []
        for obj in blockingObj:
            # The number of partition on each side is one
            blockingPlanes.append(obj.getPartition(Ps=1))

        blockingPlanes = list(flatten(blockingPlanes))

        # Get simple planes
        simpleReflectingPlanes = [
            plane.getSimplePlane() for plane in reflectingPlanes
        ]
        simpleBlockingPlanes = [
            plane.getSimplePlane() for plane in blockingPlanes
        ]
        emitters = [led.getSimplePointSource() for led in LEDs]
        collectors = [pd.getSimpleBareDetector() for pd in PDs]

        if verbose:
            print("> Calculating CIR......(wait)")

        if len(self.H_f) != 0:
            # self.Hf_los,self.Hf_diff = calcCIRFreqDom_fromMtx(self.f,
            #     emitters[0],collectors[0],simpleReflectingPlanes,
            #     self.H_f,self.t_f,self.r_f,self.H_los,blockingplanes=simpleBlockingPlanes)
            self.Hf_los, self.Hf_diff = calcCIRFreqDom_fromMtx(
                self.f, self.Nplanes, self.reflectivities, self.H_f, self.t_f,
                self.r_f, self.H_los)
        else:
            self.Hf_los, self.Hf_diff = calcCIRFreqDom(self.f, emitters[0],
                                                       collectors[0],
                                                       simpleReflectingPlanes,
                                                       simpleBlockingPlanes)

        if verbose:
            print("> Finish calculating CIR :)")

        return self.Hf_los, self.Hf_diff
Beispiel #9
0
def getArrayMobility(randomMobModel='rwp',
                     activity='walking',
                     dimensions=(0, 1),
                     velocityMinMax=(0.1, 1),
                     waitTimeMax=1.,
                     excludedArea=1.,
                     minSamples=30):
    """ Obtain arrays of locations, velocities, time instances, directions, and 
    changes of polar and azimuth angles of orientation of the UE.

    Parameters
    ----------
    randomMobModel: {'rwp','rd','lw'}
        'rwp': random waypoint
        'rd' : random direction
        'lw' : Levy-walk
    activity: {'sitting','standing','walking'}
        self-explanotory
    dimensions: tuple(2,)
        Areas of mobility of the human. 
        Ex: dimensions = (roomLength,roomWidth)
    velocityMinMax: tuple(2,)
        The minimum and maximum of velocities.
    waitTimeMax: double
        The maximum waiting time in seconds.
    excludedArea: double
        Area that will be excluded during simulation.
        Currently, it is as simple as a circle centered at the origin.
        Therefore, it is now only suitable for the simple office environment.
    minSamples: double
        The minimum number of generated samples. Default is 30.


    """

    assert randomMobModel.lower() in {'rwp', 'rd', 'lw'}
    assert activity.lower() in {'sitting', 'standing', 'walking'}
    assert len(dimensions) == len(velocityMinMax) == 2
    assert waitTimeMax >= 0
    assert excludedArea >= 0

    if activity.lower() == 'walking':
        if randomMobModel.lower() == 'rwp':
            rmm = RandomWaypoint(1,
                                 dimensions=dimensions,
                                 velocity=velocityMinMax,
                                 wt_max=waitTimeMax)
        elif randomMobModel.lower() == 'rd':
            rmm = RandomDirection(1,
                                  dimensions=dimensions,
                                  velocity=velocityMinMax,
                                  wt_max=waitTimeMax)
        elif randomMobModel.lower() == 'lw':
            rmm = TruncatedLevyWalk(1,
                                    dimensions=dimensions,
                                    WT_MAX=waitTimeMax)

        # Make an iterable object from rmm
        rmmIter = iter(rmm)

        while True:
            arrayLoc = []
            arrayVel = []
            arrayTime = [0]

            while True:
                loc = next(rmmIter)

                if np.linalg.norm(loc) < excludedArea:
                    break
                else:
                    arrayLoc.append(np.array(loc))
                    arrayVel.append(np.array(rmm.velocity))

            for i in range(len(arrayLoc) - 1):
                if arrayVel[i] == 0:
                    deltaTime = 0
                else:
                    deltaTime = np.linalg.norm(arrayLoc[i + 1] -
                                               arrayLoc[i]) / arrayVel[i]

                arrayTime.append(arrayTime[i] + deltaTime)

            arrayVel = np.array(list(flatten(arrayVel)))
            arrayTime = np.array(list(flatten(arrayTime)))
            arrayLoc = np.array(list(flatten(arrayLoc))).reshape((-1, 2))

            if arrayLoc.shape[0] >= minSamples:
                break

        arrayDir = []
        for i in range(arrayLoc.shape[0] - 1):
            arrayDir.append(getDirection(arrayLoc[i], arrayLoc[i + 1]))

        arrayDir.append(arrayDir[-1])
        arrayDir = np.array(arrayDir)

        ro = RandomOrientation('walking')
        arrayTheta0, arrayOmega0 = ro.genSamples(arrayTime)
    else:  # {'sitting','standing'}
        ro = RandomOrientation(activity)
        arrayTime = np.arange(minSamples) * 0.001
        # 1 ms resolution
        arrayTheta0, arrayOmega0 = ro.genSamples(arrayTime)

        arrayLoc, arrayVel, arrayDir = [], [], []

    return {
        'arrayLoc': arrayLoc,
        'arrayVel': arrayVel,
        'arrayTime': arrayTime,
        'arrayDir': arrayDir,
        'arrayTheta0': arrayTheta0,
        'arrayOmega0': arrayOmega0
    }