Moving Platform Simulation - Async Sensors

Moving_Platform_Simulation_-_Async_Sensors.ipynb

{
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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# Multi-Sensor Moving Platform Simulation Example - Async Modification\n",
    "This example looks at how multiple sensors can be mounted on a single moving platform and exploiting a defined moving\n",
    "platform as a sensor target.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Building a Simulated Multi-Sensor Moving Platform\n",
    "The focus of this example is to show how to setup and configure a simulation environment in order to provide a\n",
    "multi-sensor moving platform, as such the application of a tracker will not be covered in detail. For more information\n",
    "about trackers and how to configure them review of the tutorials and demonstrations is recommended.\n",
    "\n",
    "This example makes use of Stone Soup :class:`~.MovingPlatform`, :class:`~.MultiTransitionMovingPlatform` and\n",
    ":class:`~.Sensor` objects.\n",
    "\n",
    "In order to configure platforms, sensors and the simulation we will need to import some specific Stone Soup objects.\n",
    "As these have been introduced in previous tutorials they are imported upfront. New functionality within this example\n",
    "will be imported at the relevant point in order to draw attention to the new features.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Some general imports and set up\n",
    "from datetime import datetime\n",
    "from datetime import timedelta\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "# Stone Soup imports:\n",
    "from stonesoup.types.state import State, GaussianState\n",
    "from stonesoup.types.array import StateVector\n",
    "from stonesoup.types.array import CovarianceMatrix\n",
    "from stonesoup.models.transition.linear import (\n",
    "    CombinedLinearGaussianTransitionModel, ConstantVelocity)\n",
    "from stonesoup.predictor.particle import ParticlePredictor\n",
    "from stonesoup.resampler.particle import SystematicResampler\n",
    "from stonesoup.updater.particle import ParticleUpdater\n",
    "from stonesoup.measures import Mahalanobis\n",
    "from stonesoup.hypothesiser.distance import DistanceHypothesiser\n",
    "from stonesoup.dataassociator.neighbour import GNNWith2DAssignment\n",
    "from stonesoup.tracker.simple import SingleTargetTracker\n",
    "\n",
    "# Define the simulation start time\n",
    "start_time = datetime.now()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create a multi-sensor platform\n",
    "We have previously demonstrated how to create a :class:`~.FixedPlatform` which exploited a\n",
    ":class:`~.RadarRangeBearingElevation` *Sensor* in order to detect and track targets generated within a\n",
    ":class:`~.MultiTargetGroundTruthSimulator`.\n",
    "\n",
    "In this example we are going to create a moving platform which will be mounted with a pair of sensors and moves within\n",
    "a 6 dimensional state space according to the following $\\mathbf{x}$.\n",
    "\n",
    "\\begin{align}\\mathbf{x} = \\begin{bmatrix}\n",
    "                         x\\\\ \\dot{x}\\\\ y\\\\ \\dot{y}\\\\ z\\\\ \\dot{z} \\end{bmatrix}\n",
    "                     = \\begin{bmatrix}\n",
    "                         0\\\\ 0\\\\ 0\\\\ 50\\\\ 8000\\\\ 0 \\end{bmatrix}\\end{align}\n",
    "\n",
    "The platform will be initiated with a near constant velocity model which has been parameterised to have zero noise.\n",
    "Therefore the platform location at time $k$ is given by $F_{k}x_{k-1}$ where $F_{k}$ is given by:\n",
    "\n",
    "\\begin{align}F_{k} = \\begin{bmatrix}\n",
    "           1 & \\triangle k & 0 & 0 & 0 & 0\\\\\n",
    "           0 & 1 & 0 & 0 & 0 & 0\\\\\n",
    "           0 & 0 & 1 & \\triangle k & 0 & 0\\\\\n",
    "           0 & 0 & 0 & 1 & 0 & 0\\\\\n",
    "           0 & 0 & 0 & 0 & 1 & \\triangle k \\\\\n",
    "           0 & 0 & 0 & 0 & 0 & 1\\\\\n",
    "             \\end{bmatrix}\\end{align}\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# First import the Moving platform\n",
    "from stonesoup.platform.base import MovingPlatform\n",
    "\n",
    "# Define the initial platform position, in this case the origin\n",
    "initial_loc = StateVector([[0], [0], [0], [50], [8000], [0]])\n",
    "initial_state = State(initial_loc, start_time)\n",
    "\n",
    "# Define transition model and position for 3D platform\n",
    "transition_model = CombinedLinearGaussianTransitionModel(\n",
    "    [ConstantVelocity(0.), ConstantVelocity(0.), ConstantVelocity(0.)])\n",
    "\n",
    "# create our fixed platform\n",
    "sensor_platform = MovingPlatform(states=initial_state,\n",
    "                                 position_mapping=(0, 2, 4),\n",
    "                                 velocity_mapping=(1, 3, 5),\n",
    "                                 transition_model=transition_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With our platform generated we now need to build a set of sensors which will be mounted onto the platform. In this\n",
    "case we will exploit a :class:`~.RadarElevationBearingRangeRate` and a :class:`~.PassiveElevationBearing` sensor\n",
    "(e.g. an optical sensor, which has no capability to directly measure range).\n",
    "\n",
    "First we will create a radar which is capable of measuring bearing ($\\phi$), elevation ($\\theta$), range\n",
    "($r$) and range-rate ($\\dot{r}$) of the target platform.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---------------------------\n",
    "\n",
    "\n",
    "Modification for Async\n",
    "=================="
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from stonesoup.base import Base, Property\n",
    "\n",
    "class AsyncSensorMixin(Base):\n",
    "    time_between_detections: timedelta = Property(doc=\"Minimum time between sensor generating detections\")\n",
    "        \n",
    "    def __init__(self, *args, **kwargs):\n",
    "        super().__init__(*args, **kwargs)\n",
    "        self._previous_time = None\n",
    "    \n",
    "    def measure(self, *args, **kwargs):\n",
    "        detections = super().measure(*args, **kwargs)\n",
    "        \n",
    "        if self._previous_time is None and detections:  # Handle initialisation of previous timestamp\n",
    "            detection = next(iter(detections))\n",
    "            self._previous_time = detection.timestamp\n",
    "        elif detections:\n",
    "            detection = next(iter(detections))\n",
    "            if detection.timestamp >= self._previous_time + self.time_between_detections:\n",
    "                self._previous_time = detection.timestamp\n",
    "            else:\n",
    "                detections = set()\n",
    "        return detections"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---------------------------"
   ]
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   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import a range rate bearing elevation capable radar\n",
    "from stonesoup.sensor.radar.radar import RadarElevationBearingRangeRate\n",
    "\n",
    "# Create a radar sensor\n",
    "radar_noise_covar = CovarianceMatrix(np.diag(\n",
    "    np.array([np.deg2rad(3),  # Elevation\n",
    "              np.deg2rad(3),  # Bearing\n",
    "              100.,  # Range\n",
    "              25.])))  # Range Rate\n",
    "\n",
    "class RadarElevationBearingRangeRateAsync(AsyncSensorMixin, RadarElevationBearingRangeRate):\n",
    "    pass\n",
    "\n",
    "radar = RadarElevationBearingRangeRateAsync(ndim_state=6,\n",
    "                                           position_mapping=(0, 2, 4),\n",
    "                                           velocity_mapping=(1, 3, 5),\n",
    "                                           noise_covar=radar_noise_covar,\n",
    "                                           time_between_detections=timedelta(seconds=2))\n",
    "\n",
    "# radar mountings\n",
    "radar_mounting_offsets = StateVector([10, 0, 0])  # e.g. nose cone\n",
    "radar_rotation_offsets = StateVector([0, 0, 0])\n",
    "\n",
    "# Mount the radar onto the platform\n",
    "sensor_platform.add_sensor(radar,\n",
    "                           mounting_offset=radar_mounting_offsets,\n",
    "                           rotation_offset=radar_rotation_offsets)"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our second sensor is a passive sensor, capable of measuring the bearing ($\\phi$) and elevation ($\\theta$)\n",
    "of the target platform. For the purposes of this example we will assume that the passive sensor is an imager.\n",
    "The imager sensor model is described by the following equations:\n",
    "\n",
    "\\begin{align}\\mathbf{z}_k = h(\\mathbf{x}_k, \\dot{\\mathbf{x}}_k)\\end{align}\n",
    "\n",
    "where:\n",
    "\n",
    "* $\\mathbf{z}_k$ is a measurement vector of the form:\n",
    "\n",
    "\\begin{align}\\mathbf{z}_k = \\begin{bmatrix} \\theta \\\\ \\phi \\end{bmatrix}\\end{align}\n",
    "\n",
    "* $h$ is a non - linear model function of the form:\n",
    "\n",
    "\\begin{align}h(\\mathbf{x}_k,\\dot{\\mathbf{x}}_k) = \\begin{bmatrix}\n",
    "              \\arcsin(\\mathcal{z} /\\sqrt{\\mathcal{x} ^ 2 + \\mathcal{y} ^ 2 +\\mathcal{z} ^ 2}) \\\\\n",
    "              \\arctan(\\mathcal{y},\\mathcal{x}) \\ \\\n",
    "              \\end{bmatrix} + \\dot{\\mathbf{x}}_k\\end{align}\n",
    "\n",
    "* $\\mathbf{z}_k$ is Gaussian distributed with covariance $R$, i.e.:\n",
    "\n",
    "\\begin{align}\\mathbf{z}_k  \\sim \\mathcal{N}(0, R)\\end{align}\n",
    "\n",
    "\\begin{align}R = \\begin{bmatrix}\n",
    "            \\sigma_{\\theta}^2 & 0 \\\\\n",
    "            0 & \\sigma_{\\phi}^2  \\\\\n",
    "            \\end{bmatrix}\\end{align}\n",
    "\n"
   ]
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  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import a passive sensor capability\n",
    "from stonesoup.sensor.passive import PassiveElevationBearing\n",
    "\n",
    "imager_noise_covar = CovarianceMatrix(np.diag(np.array([np.deg2rad(0.05),  # Elevation\n",
    "                                                        np.deg2rad(0.05)])))  # Bearing\n",
    "\n",
    "class PassiveElevationBearingAsync(AsyncSensorMixin, PassiveElevationBearing):\n",
    "    pass\n",
    "\n",
    "imager = PassiveElevationBearingAsync(ndim_state=6,\n",
    "                                      mapping=(0, 2, 4),\n",
    "                                      noise_covar=imager_noise_covar,\n",
    "                                      time_between_detections=timedelta(seconds=3))\n",
    "\n",
    "# imager mounting offset\n",
    "imager_mounting_offsets = StateVector([0, 8, -1])  # e.g. wing mounted imaging pod\n",
    "imager_rotation_offsets = StateVector([0, 0, 0])\n",
    "\n",
    "# Mount the imager onto the platform\n",
    "sensor_platform.add_sensor(imager,\n",
    "                           mounting_offset=imager_mounting_offsets,\n",
    "                           rotation_offset=imager_rotation_offsets)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that we have added sensors to specific locations on the aircraft, defined by the mounting_offset parameter.\n",
    "The values in this array are defined in the platforms local coordinate frame of reference. So in this case an offset\n",
    "of $[0, 8, -1]$ means the sensor is located 8 meters to the right and 1 meter below the center point of the\n",
    "platform.\n",
    "\n",
    "Now that we have mounted the two sensors we can see that the platform object has both associated with it:\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(RadarElevationBearingRangeRateAsync(position_mapping=(0, 2, 4), noise_covar=CovarianceMatrix([[5.23598776e-02, 0.00000000e+00, 0.00000000e+00,\n",
       "                    0.00000000e+00],\n",
       "                   [0.00000000e+00, 5.23598776e-02, 0.00000000e+00,\n",
       "                    0.00000000e+00],\n",
       "                   [0.00000000e+00, 0.00000000e+00, 1.00000000e+02,\n",
       "                    0.00000000e+00],\n",
       "                   [0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n",
       "                    2.50000000e+01]]), time_between_detections=datetime.timedelta(seconds=2), ndim_state=6, velocity_mapping=(1, 3, 5)),\n",
       " PassiveElevationBearingAsync(ndim_state=6, mapping=(0, 2, 4), noise_covar=CovarianceMatrix([[0.00087266, 0.        ],\n",
       "                   [0.        , 0.00087266]]), time_between_detections=datetime.timedelta(seconds=3)))"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sensor_platform.sensors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create a Target Platform\n",
    "There are two ways of generating a target in Stone Soup. Firstly, we can use the inbuilt ground-truth generator\n",
    "functionality within Stone Soup, which we demonstrated in the previous example, and creates a random target based on\n",
    "our selected parameters. The second method provides a means to generate a target which will perform specific\n",
    "behaviours, this is the approach we will take here.\n",
    "\n",
    "In order to create a target which moves in pre-defined sequences we exploit the fact that platforms can be used as\n",
    "sensor targets within a simulation, coupled with the :class:`~.MultiTransitionMovingPlatform` which enables a platform\n",
    "to be provided with a pre-defined list of transition models and transition times. The platform will continue to loop\n",
    "over the transition sequence provided until the simulation ends.\n",
    "\n",
    "When simulating sensor platforms it is important to note that within the simulation Stone Soup treats all platforms as\n",
    "potential targets. Therefore if we created multiple sensor platforms they would each *sense* all other platforms\n",
    "within the simulation (sensor-target geometry dependant).\n",
    "\n",
    "For this example we will create an air target which will fly a sequence of straight and level followed by a\n",
    "coordinated turn in the $x-y$ plane. This is configured such that the target will perform each manoeuvre for 8\n",
    "seconds, and it will turn through 45 degrees over the course of the turn manoeuvre.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import a Constant Turn model to enable target to perform basic manoeuvre\n",
    "from stonesoup.models.transition.linear import ConstantTurn\n",
    "\n",
    "straight_level = CombinedLinearGaussianTransitionModel(\n",
    "    [ConstantVelocity(0.), ConstantVelocity(0.), ConstantVelocity(0.)])\n",
    "\n",
    "# Configure the aircraft turn behaviour\n",
    "turn_noise_diff_coeffs = np.array([0., 0.])\n",
    "\n",
    "turn_rate = np.pi/32  # specified in radians per seconds...\n",
    "\n",
    "turn_model = ConstantTurn(turn_noise_diff_coeffs=turn_noise_diff_coeffs, turn_rate=turn_rate)\n",
    "\n",
    "# Configure turn model to maintain current altitude\n",
    "turning = CombinedLinearGaussianTransitionModel(\n",
    "    [turn_model, ConstantVelocity(0.)])\n",
    "\n",
    "manoeuvre_list = [straight_level, turning]\n",
    "manoeuvre_times = [timedelta(seconds=8),\n",
    "                   timedelta(seconds=8)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have created a list of manoeuvre behaviours and durations we can build our multi-transition moving\n",
    "platform. Because we intend for this platform to be a target we do not need to attach any sensors to it.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import a multi-transition moving platform\n",
    "from stonesoup.platform.base import MultiTransitionMovingPlatform\n",
    "\n",
    "initial_target_location = StateVector([[0], [-40], [1800], [0], [8000], [0]])\n",
    "initial_target_state = State(initial_target_location, start_time)\n",
    "target = MultiTransitionMovingPlatform(transition_models=manoeuvre_list,\n",
    "                                       transition_times=manoeuvre_times,\n",
    "                                       states=initial_target_state,\n",
    "                                       position_mapping=(0, 2, 4),\n",
    "                                       velocity_mapping=(1, 3, 5),\n",
    "                                       sensors=None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating the simulator\n",
    "Now that we have build our sensor platform and a target platform we need to wrap them in a simulator. Because we do\n",
    "not want any additional ground truth objects, which is how most simulators work in Stone Soup, we need to use a\n",
    ":class:`~.DummyGroundTruthSimulator` which returns a set of empty ground truth paths with timestamps. These are then\n",
    "feed into a :class:`~.PlatformDetectionSimulator` with the two platforms we have already built.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import the required simulators\n",
    "from stonesoup.simulator.simple import DummyGroundTruthSimulator\n",
    "from stonesoup.simulator.platform import PlatformDetectionSimulator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now need to create an array of timestamps which starts at *datetime.now()* and enable the simulator to run for\n",
    "25 seconds.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "times = np.arange(0, 24, 1)  # 25 seconds\n",
    "\n",
    "timestamps = [start_time + timedelta(seconds=float(elapsed_time)) for elapsed_time in times]\n",
    "\n",
    "truths = DummyGroundTruthSimulator(times=timestamps)\n",
    "sim = PlatformDetectionSimulator(groundtruth=truths, platforms=[sensor_platform, target])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create a Tracker\n",
    "Now that we have setup our sensor platform, target and simulation we need to create a tracker. For this example we\n",
    "will use a Particle Filter as this enables us to handle the non-linear nature of the imaging sensor. In this example\n",
    "we will use an inflated constant noise model to account for target motion uncertainty.\n",
    "\n",
    "Note that we don't add a measurement model to the updater, this is because each sensor adds their measurement model to\n",
    "each detection they generate. The tracker handles this internally by checking for a measurement model with each\n",
    "detection it receives and applying only the relevant measurement model.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "target_transition_model = CombinedLinearGaussianTransitionModel(\n",
    "    [ConstantVelocity(5), ConstantVelocity(5), ConstantVelocity(1)])\n",
    "\n",
    "# First add a Particle Predictor\n",
    "predictor = ParticlePredictor(target_transition_model)\n",
    "\n",
    "# Now create a resampler and particle updater\n",
    "resampler = SystematicResampler()\n",
    "updater = ParticleUpdater(measurement_model=None,\n",
    "                          resampler=resampler)\n",
    "\n",
    "# Create a particle initiator\n",
    "from stonesoup.initiator.simple import GaussianParticleInitiator, SinglePointInitiator\n",
    "single_point_initiator = SinglePointInitiator(\n",
    "    GaussianState([[0], [-40], [2000], [0], [8000], [0]], np.diag([10000, 1000, 10000, 1000, 10000, 1000])),\n",
    "    None)\n",
    "\n",
    "initiator = GaussianParticleInitiator(number_particles=500,\n",
    "                                      initiator=single_point_initiator)\n",
    "\n",
    "hypothesiser = DistanceHypothesiser(predictor, updater, measure=Mahalanobis(), missed_distance=np.inf)\n",
    "data_associator = GNNWith2DAssignment(hypothesiser)\n",
    "\n",
    "from stonesoup.deleter.time import UpdateTimeStepsDeleter\n",
    "deleter = UpdateTimeStepsDeleter(time_steps_since_update=10)\n",
    "\n",
    "# Create a Kalman single-target tracker\n",
    "tracker = SingleTargetTracker(\n",
    "    initiator=initiator,\n",
    "    deleter=deleter,\n",
    "    detector=sim,\n",
    "    data_associator=data_associator,\n",
    "    updater=updater\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The final step is to iterate our tracker over the simulation and plot out the results. Because we have a bearing\n",
    "only sensor it does not make sense to plot out the detections without animating the resulting plot. This\n",
    "animation shows the sensor platform (blue) moving towards the true target position (red). The estimated target\n",
    "position is shown in black, radar detections are shown in yellow while the bearing only imager detections are\n",
    "coloured green.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
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       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_img72bf1ac142da4931b2758424d65b291c\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider72bf1ac142da4931b2758424d65b291c\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim72bf1ac142da4931b2758424d65b291c.set_frame(parseInt(this.value));\"></input>\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button onclick=\"anim72bf1ac142da4931b2758424d65b291c.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
       "      <button onclick=\"anim72bf1ac142da4931b2758424d65b291c.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
       "          </i></button>\n",
       "      <button onclick=\"anim72bf1ac142da4931b2758424d65b291c.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button onclick=\"anim72bf1ac142da4931b2758424d65b291c.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button onclick=\"anim72bf1ac142da4931b2758424d65b291c.pause_animation()\"><i class=\"fa fa-pause\">\n",
       "          </i></button>\n",
       "      <button onclick=\"anim72bf1ac142da4931b2758424d65b291c.play_animation()\"><i class=\"fa fa-play\"></i>\n",
       "          </button>\n",
       "      <button onclick=\"anim72bf1ac142da4931b2758424d65b291c.next_frame()\"><i class=\"fa fa-step-forward\">\n",
       "          </i></button>\n",
       "      <button onclick=\"anim72bf1ac142da4931b2758424d65b291c.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
       "          </i></button>\n",
       "      <button onclick=\"anim72bf1ac142da4931b2758424d65b291c.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form action=\"#n\" name=\"_anim_loop_select72bf1ac142da4931b2758424d65b291c\" class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_72bf1ac142da4931b2758424d65b291c\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_72bf1ac142da4931b2758424d65b291c\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_72bf1ac142da4931b2758424d65b291c\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_72bf1ac142da4931b2758424d65b291c\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_72bf1ac142da4931b2758424d65b291c\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_72bf1ac142da4931b2758424d65b291c\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_img72bf1ac142da4931b2758424d65b291c\";\n",
       "    var slider_id = \"_anim_slider72bf1ac142da4931b2758424d65b291c\";\n",
       "    var loop_select_id = \"_anim_loop_select72bf1ac142da4931b2758424d65b291c\";\n",
       "    var frames = new Array(48);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtAAAAGwCAYAAACAS1JbAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
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