예제 #1
0
        private void ReadFrame(object sender, EventArgs arg)//捕获摄像头画面的事件
        {
            DateTime TimeStart = DateTime.Now;

            // VideoCapture捕获一帧图像
            try
            {
                capture.Retrieve(mat, 0);
            }
            catch { }

            // 创建Tensor作为网络输入
            TFTensor tensor = Mat2Tensor(mat);

            // 前向推理
            TFSession.Runner runner = session.GetRunner();
            runner.AddInput(graph["image_tensor"][0], tensor);
            runner.Fetch(graph["num_detections"][0]);
            runner.Fetch(graph["detection_scores"][0]);
            runner.Fetch(graph["detection_boxes"][0]);
            runner.Fetch(graph["detection_classes"][0]);
            TFTensor[] outputs = runner.Run();

            // 解析结果
            float num = ((float[])outputs[0].GetValue(jagged: true))[0];

            float[]   scores  = ((float[][])outputs[1].GetValue(jagged: true))[0];
            float[][] boxes   = ((float[][][])outputs[2].GetValue(jagged: true))[0];
            float[]   classes = ((float[][])outputs[3].GetValue(jagged: true))[0];

            // 显示检测框和类别
            for (int i = 0; i < (int)num; i++)
            {
                if (scores[i] > 0.8)
                {
                    int left   = (int)(boxes[i][1] * frameWidth);
                    int top    = (int)(boxes[i][0] * frameHeight);
                    int right  = (int)(boxes[i][3] * frameWidth);
                    int bottom = (int)(boxes[i][2] * frameHeight);
                    CvInvoke.PutText(mat, labels[(int)classes[i]] + ": " + scores[i].ToString("0.00"), new Point(left, top), FontFace.HersheyDuplex, (right - left) / 200, colorGreen);
                    CvInvoke.Rectangle(mat, new Rectangle(left, top, right - left, bottom - top), colorRed, 2);
                }
            }

            // 在imageBox上显示经过缩放的图像
            Mat dst = new Mat();

            CvInvoke.Resize(mat, dst, new Size(imageBox.Width, imageBox.Height));
            imageBox.Image = cameraFlag ? dst : null;
            TimeSpan TimeCount = DateTime.Now - TimeStart;

            textFPS.Text = (1000 / TimeCount.TotalMilliseconds).ToString("0.00");
        }
    public PolicyValue PolicyValueFn(Board board)
    {
        HashSet <int> legalMoves = new HashSet <int>(board.GetAvailableMoves());

        float[,,,] currentState = (float[, , , ])board.CurrentState();

        TFSession.Runner runner = session.GetRunner();
        runner.AddInput(graph["input_states"][0], currentState);
        runner.Fetch(graph["action_fc/LogSoftmax"][0], graph["evaluation_fc2/Tanh"][0]);
        TFTensor[] output = runner.Run();

        float evaluation = ((float[, ])(output[1].GetValue()))[0, 0];

        float[,] action_fc = ((float[, ])(output[0].GetValue()));
        List <ActionP> actionPs = new List <ActionP>();

        for (int i = 0; i < width * width; i++)
        {
            if (legalMoves.Contains(i))
            {
                actionPs.Add(new ActionP(i, Mathf.Exp(action_fc[0, i])));
            }
        }

        return(new PolicyValue(actionPs, evaluation));
    }
예제 #3
0
    public void Update(Texture2D resizedTexture, float jointDistanceLimit, float jointThreshold, Color colorThreshold, bool useLabeling)
    {
        Color32[] pixels      = resizedTexture.GetPixels32();
        TFTensor  inputTensor = CreateShapes(pixels, colorThreshold);

        TFSession.Runner runner = session.GetRunner();
        runner.AddInput(graph["Placeholder"][0], inputTensor);
        runner.Fetch(graph["split_2"][0], graph["split_2"][1], graph["split_2"][2], graph["split_2"][3]);

        TFTensor[] outputTensor = runner.Run();
        nnOutputPtr   = outputTensor[0].Data;
        nnOutputPtrX  = outputTensor[1].Data;
        nnOutputPtrY  = outputTensor[2].Data;
        nnOutputPtrZ  = outputTensor[3].Data;
        heatmapWidth  = (int)outputTensor[0].Shape[1];
        heatmapHeight = (int)outputTensor[0].Shape[2];

        if (heatmapBuff == null)
        {
            heatmapBuff = new float[heatmapHeight, heatmapWidth, NN_JOINT_COUNT, (int)HEATMAP_TYPE.Length];
        }
        else
        {
            Array.Clear(heatmapBuff, 0, heatmapBuff.Length);
        }
        ExtractHeatmaps(nnOutputPtr, nnOutputPtrX, nnOutputPtrY, nnOutputPtrZ);
        Extract2DJoint(jointDistanceLimit, jointThreshold, useLabeling);
        Extract3DJoint();
    }
예제 #4
0
        static void Main(string[] args)
        {
            using (TFGraph graph = new TFGraph())
            {
                graph.Import(File.ReadAllBytes(@"C:\Users\Ben\Desktop\frozen.pb"));

                TFSession        session = new TFSession(graph);
                TFSession.Runner runner  = session.GetRunner();

                float[] x1 = new float[] { 239, 958, 8, 34, 239 };
                float[] x2 = new float[] { 239, 958, 8, 34, 239 };
                float[] x3 = new float[] { 239, 958, 8, 34, 239 };

                TFTensor x = new TFTensor(new float[][] { x1, x2, x3 });

                runner.AddInput(graph["Placeholder"][0], x);
                runner.Fetch(graph["add"][0]);

                var output = runner.Run();

                TFTensor result = output[0];

                var v = result.GetValue();

                return;
            }
        }
예제 #5
0
        public ReadOnlyCollection <Prediction> Run()
        {
            string libsBath = ConfigurationManager.AppSettings["LibsPath"];
            string setsPath = ConfigurationManager.AppSettings["SetsPath"];

            string image = $@"{setsPath}\sample_flower.jpg";

            byte[]   model  = File.ReadAllBytes($@"{setsPath}\output_graph.pb");
            string[] labels = File.ReadAllLines($@"{setsPath}\output_labels.txt");

            using (var graph = new TFGraph())
            {
                graph.Import(new TFBuffer(model));

                using (var session = new TFSession(graph))
                {
                    TFTensor tensor = ImageUtil.CreateTensorFromImageFile(image);

                    TFSession.Runner runner = session.GetRunner();

                    if (runner == null || tensor == null)
                    {
                        Console.WriteLine("Runner or Tensor is null!?");
                        Environment.Exit(1);
                    }

                    runner.AddInput(graph["DecodeJpeg/contents"][0], tensor);
                    runner.Fetch(graph["final_result"][0]);

                    try
                    {
                        TFTensor[] output = runner.Run();

                        float[,] scores = (float[, ])output[0].GetValue();

                        var predictions = new List <Prediction>();

                        for (int i = 0; i < scores.Length; i++)
                        {
                            float  score = scores[0, i];
                            string label = labels[i];

                            predictions.Add(new Prediction(label, score));
                        }

                        return(predictions
                               .OrderByDescending(p => p.Score)
                               .ToList()
                               .AsReadOnly());
                    }
                    catch (TFException e)
                    {
                        Console.WriteLine(e.ToString());
                    }
                }
            }

            return(new List <Prediction>().AsReadOnly());
        }
예제 #6
0
 public int RunClassifier(float[] input)
 {
     TFSession.Runner runner = session.GetRunner();
     runner.AddInput(graph[input_name][0], input);
     runner.Fetch(graph[output_name][0]);
     float[,] result = runner.Run()[0].GetValue() as float[, ];
     return(ArgMax(result, 0));
 }
예제 #7
0
            public TFTensor [] Run(params int [] inputValues)
            {
                Assert(inputValues.Length == inputs.Length);

                session = new TFSession(graph);
                runner  = session.GetRunner();

                for (int i = 0; i < inputs.Length; i++)
                {
                    runner.AddInput(inputs [i], (TFTensor)inputValues [i]);
                }
                runner.Fetch(outputs);
                return(runner.Run());
            }
예제 #8
0
 public override void AdjustPose()
 {
     TFSession.Runner runner = session.GetRunner();
     runner.AddInput(graph ["input_1"] [0], new float[, ] {
         { head.rotation.x, head.rotation.y, head.rotation.z, head.rotation.w, head.position.x * scalingFactor, head.position.y * scalingFactor, head.position.z * scalingFactor,
           hand_left.rotation.x, hand_left.rotation.y, hand_left.rotation.z, hand_left.rotation.w, hand_left.position.x * scalingFactor, hand_left.position.y * scalingFactor, hand_left.position.z * scalingFactor,
           hand_right.rotation.x, hand_right.rotation.y, hand_right.rotation.z, hand_right.rotation.w, hand_right.position.x * scalingFactor, hand_right.position.y * scalingFactor, hand_right.position.z * scalingFactor }
     });
     runner.Fetch(graph["dense_2/BiasAdd"][0]);
     float[,] output_tensor = runner.Run() [0].GetValue() as float[, ];
     bodyTransform.rotation = new Quaternion(output_tensor [0, 0], output_tensor [0, 1], output_tensor [0, 2], output_tensor [0, 3]);
     bodyTransform.position = new Vector3(output_tensor [0, 4] / scalingFactor, output_tensor [0, 5] / scalingFactor, output_tensor [0, 6] / scalingFactor);
     Debug.Log(output_tensor [0, 0] + " " + output_tensor [0, 1] + " " + output_tensor [0, 2] + " " + output_tensor [0, 3] + " " + output_tensor [0, 4] + " " + output_tensor [0, 5] + " " + output_tensor [0, 6]);
 }
        /// <summary>
        /// Receive a frame from camera.
        /// </summary>
        /// <param name="sender"></param>
        /// <param name="e"></param>
        private void Camera_ImageGrabbed(object sender, EventArgs e)
        {
            if (camera.Retrieve(frame))
            {
                CvInvoke.Flip(frame, frame, Emgu.CV.CvEnum.FlipType.Horizontal);
                CvInvoke.Resize(frame, resizedFrame, new System.Drawing.Size(detectionSize, detectionSize), 0, 0);

                TFTensor         tensor = TransformInput(resizedFrame.Bitmap);
                TFSession.Runner runner = session.GetRunner();

                runner.AddInput(graph["image"][0], tensor);
                runner.Fetch(
                    graph["heatmap"][0],
                    graph["offset_2"][0],
                    graph["displacement_fwd_2"][0],
                    graph["displacement_bwd_2"][0]
                    );

                var result           = runner.Run();
                var heatmap          = (float[, , , ])result[0].GetValue(jagged: false);
                var offsets          = (float[, , , ])result[1].GetValue(jagged: false);
                var displacementsFwd = (float[, , , ])result[2].GetValue(jagged: false);
                var displacementsBwd = (float[, , , ])result[3].GetValue(jagged: false);

                Pose[] poses = posenet.DecodeMultiplePoses(
                    heatmap, offsets,
                    displacementsFwd,
                    displacementsBwd,
                    outputStride: 16, maxPoseDetections: 100,
                    scoreThreshold: 0.5f, nmsRadius: 20);

                Drawing(frame, poses);

                Dispatcher.Invoke(new Action(() =>
                {
                    img.Source = frame.Bitmap.BitmapToBitmapSource();
                }));
            }
        }
    private IList ParseYOLO(TFSession.Runner runner, float threshold, int numResultsPerClass)
    {
        runner.Fetch(graph["output"][0]);
        var outputs = runner.Run();
        var output  = outputs[0].GetValue() as float[, , , ];

        foreach (var o in outputs)
        {
            o.Dispose();
        }

        var gridSize   = _inputWidth / _blockSize;
        int numClasses = labels.Length;

        var list = new List <Dictionary <string, object> >();

        for (int y = 0; y < gridSize; y++)
        {
            for (int x = 0; x < gridSize; x++)
            {
                for (int b = 0; b < _numBoxesPerBlock; b++)
                {
                    int offset = (numClasses + 5) * b;

                    float confidence = expit(output[0, y, x, offset + 4]);

                    float[] classes = new float[numClasses];
                    for (int c = 0; c < numClasses; c++)
                    {
                        classes[c] = output[0, y, x, offset + 5 + c];
                    }
                    softmax(classes);

                    int   detectedClass = -1;
                    float maxClass      = 0;
                    for (int c = 0; c < numClasses; ++c)
                    {
                        if (classes[c] > maxClass)
                        {
                            detectedClass = c;
                            maxClass      = classes[c];
                        }
                    }

                    float confidenceInClass = maxClass * confidence;

                    if (confidenceInClass > threshold)
                    {
                        float xPos = (x + expit(output[0, y, x, offset + 0])) * _blockSize;
                        float yPos = (y + expit(output[0, y, x, offset + 1])) * _blockSize;

                        float w = (float)((Math.Exp(output[0, y, x, offset + 2]) * _anchors[2 * b + 0]) * _blockSize);
                        float h = (float)(Math.Exp(output[0, y, x, offset + 3]) * _anchors[2 * b + 1]) * _blockSize;

                        float xmin = Math.Max(0, (xPos - w / 2) / _inputWidth);
                        float ymin = Math.Max(0, (yPos - h / 2) / _inputHeight);

                        var rect = new Dictionary <string, float>
                        {
                            { "x", xmin },
                            { "y", ymin },
                            { "w", Math.Min(1 - xmin, w / _inputWidth) },
                            { "h", Math.Min(1 - ymin, h / _inputHeight) }
                        };

                        var result = new Dictionary <string, object>
                        {
                            { "rect", rect },
                            { "confidenceInClass", confidenceInClass },
                            { "detectedClass", labels[detectedClass] }
                        };

                        list.Add(result);
                    }
                }
            }
        }

        var sortedList = list.OrderByDescending(i => i["confidenceInClass"]).ToList();

        var results  = new List <Dictionary <string, object> >();
        var counters = new Dictionary <string, int>();

        sortedList.ForEach(i =>
        {
            String detectedClass = (string)i["detectedClass"];

            if (counters.ContainsKey(detectedClass))
            {
                if (counters[detectedClass] >= numResultsPerClass)
                {
                    return;
                }
                counters[detectedClass] += 1;
            }
            else
            {
                counters.Add(detectedClass, 1);
            }

            results.Add(i);
        });

        //Utils.Log(results);

        return(results);
    }
    private IList ParseSSD(TFSession.Runner runner, float threshold, int numResultsPerClass)
    {
        runner.Fetch(graph["detection_boxes"][0],
                     graph["detection_classes"][0],
                     graph["detection_scores"][0],
                     graph["num_detections"][0]);

        var outputs = runner.Run();

        var boxes          = outputs[0].GetValue() as float[, , ];
        var classes        = outputs[1].GetValue() as float[, ];
        var scores         = outputs[2].GetValue() as float[, ];
        var num_detections = outputs[3].GetValue() as float[];

        foreach (var o in outputs)
        {
            o.Dispose();
        }

        var results  = new List <Dictionary <string, object> >();
        var counters = new Dictionary <string, int>();

        for (int i = 0; i < (int)num_detections[0]; i++)
        {
            if (scores[0, i] < threshold)
            {
                continue;
            }

            string detectedClass = labels[(int)classes[0, i]];

            if (counters.ContainsKey(detectedClass))
            {
                if (counters[detectedClass] >= numResultsPerClass)
                {
                    continue;
                }
                counters[detectedClass] += 1;
            }
            else
            {
                counters.Add(detectedClass, 1);
            }

            float ymin = Math.Max(0, boxes[0, i, 0]);
            float xmin = Math.Max(0, boxes[0, i, 1]);
            float ymax = boxes[0, i, 2];
            float xmax = boxes[0, i, 3];

            var rect = new Dictionary <string, float>
            {
                { "x", xmin },
                { "y", ymin },
                { "w", Math.Min(1 - xmin, xmax - xmin) },
                { "h", Math.Min(1 - ymin, ymax - ymin) }
            };

            var result = new Dictionary <string, object>
            {
                { "rect", rect },
                { "confidenceInClass", scores[0, i] },
                { "detectedClass", detectedClass }
            };

            results.Add(result);
        }

        //Utils.Log(results);

        return(results);
    }
예제 #12
0
        public override IObservable <Pose> Process(IObservable <IplImage> source)
        {
            return(Observable.Defer(() =>
            {
                TFSessionOptions options = new TFSessionOptions();
                unsafe
                {
                    byte[] GPUConfig = new byte[] { 0x32, 0x02, 0x20, 0x01 };
                    fixed(void *ptr = &GPUConfig[0])
                    {
                        options.SetConfig(new IntPtr(ptr), GPUConfig.Length);
                    }
                }

                var graph = new TFGraph();
                var session = new TFSession(graph, options, null);
                var bytes = File.ReadAllBytes(ModelFileName);
                graph.Import(bytes);

                IplImage temp = null;
                TFTensor tensor = null;
                TFSession.Runner runner = null;
                var config = ConfigHelper.PoseConfig(PoseConfigFileName);
                return source.Select(input =>
                {
                    var poseScale = 1.0;
                    const int TensorChannels = 3;
                    var frameSize = input.Size;
                    var scaleFactor = ScaleFactor;
                    if (scaleFactor.HasValue)
                    {
                        poseScale = scaleFactor.Value;
                        frameSize.Width = (int)(frameSize.Width * poseScale);
                        frameSize.Height = (int)(frameSize.Height * poseScale);
                        poseScale = 1.0 / poseScale;
                    }

                    if (tensor == null || tensor.GetTensorDimension(1) != frameSize.Height || tensor.GetTensorDimension(2) != frameSize.Width)
                    {
                        tensor = new TFTensor(
                            TFDataType.Float,
                            new long[] { 1, frameSize.Height, frameSize.Width, TensorChannels },
                            frameSize.Width * frameSize.Height * TensorChannels * sizeof(float));
                        runner = session.GetRunner();
                        runner.AddInput(graph["Placeholder"][0], tensor);
                        runner.Fetch(graph["concat_1"][0]);
                    }

                    var frame = input;
                    if (frameSize != input.Size)
                    {
                        if (temp == null || temp.Size != frameSize)
                        {
                            temp = new IplImage(frameSize, input.Depth, input.Channels);
                        }

                        CV.Resize(input, temp);
                        frame = temp;
                    }

                    using (var image = new IplImage(frameSize, IplDepth.F32, TensorChannels, tensor.Data))
                    {
                        CV.Convert(frame, image);
                    }

                    // Run the model
                    var output = runner.Run();

                    // Fetch the results from output:
                    var poseTensor = output[0];
                    var pose = new Mat((int)poseTensor.Shape[0], (int)poseTensor.Shape[1], Depth.F32, 1, poseTensor.Data);
                    var result = new Pose(input);
                    var threshold = MinConfidence;
                    for (int i = 0; i < pose.Rows; i++)
                    {
                        BodyPart bodyPart;
                        bodyPart.Name = config[i];
                        bodyPart.Confidence = (float)pose.GetReal(i, 2);
                        if (bodyPart.Confidence < threshold)
                        {
                            bodyPart.Position = new Point2f(float.NaN, float.NaN);
                        }
                        else
                        {
                            bodyPart.Position.X = (float)(pose.GetReal(i, 1) * poseScale);
                            bodyPart.Position.Y = (float)(pose.GetReal(i, 0) * poseScale);
                        }
                        result.Add(bodyPart);
                    }
                    return result;
                });
            }));
        }
예제 #13
0
        public int ExecuteGraph(IEnumerable <Tensor> inputs_it, IEnumerable <Tensor> outputs_it)
        {
            Profiler.BeginSample("TFSharpInferenceComponent.ExecuteGraph");
            Tensor[] inputs  = inputs_it.ToArray();
            Tensor[] outputs = outputs_it.ToArray();

            // TODO: Can/should we pre-allocate that?
            TFSession.Runner runner = m_session.GetRunner();

            inputs.ToList().ForEach((Tensor input) =>
            {
                if (input.Shape.Length == 0)
                {
                    var data = input.Data.GetValue(0);
                    if (input.DataType == typeof(int))
                    {
                        runner.AddInput(m_graph[input.Name][0], (int)data);
                    }
                    else
                    {
                        runner.AddInput(m_graph[input.Name][0], (float)data);
                    }
                }
                else
                {
                    runner.AddInput(m_graph[input.Name][0], input.Data);
                }
            });

            // TODO: better way to pre-allocate this?
            outputs.ToList().ForEach(s => runner.Fetch(s.Name));

            TFStatus status = new TFStatus();

            Profiler.BeginSample("TFSharpInferenceComponent.ExecuteGraph.RunnerRun");
            var out_tensors = runner.Run(status);

            Profiler.EndSample();

            if (!status.Ok)
            {
                Debug.LogError(status.StatusMessage);
                return(-1);
            }

            Debug.Assert(outputs.Length == out_tensors.Length);

            for (var i = 0; i < outputs.Length; ++i)
            {
                if (outputs[i].Shape.Length == 0)
                {
                    // Handle scalars
                    outputs[i].Data = Array.CreateInstance(outputs[i].DataType, new long[1] {
                        1
                    });
                    outputs[i].Data.SetValue(out_tensors[i].GetValue(), 0);
                }
                else
                {
                    outputs[i].Data = out_tensors[i].GetValue() as Array;
                }
            }

            Profiler.EndSample();
            // TODO: create error codes
            return(0);
        }
    public override void AdjustPose()
    {
        TFSession.Runner runner = session.GetRunner();

        //Assume model is trained with body x and z positions and y rotation normalized to that of the head
        //Assume model is trained with right hand coordinate system

        //Pivot the head and hands in the y-axis around the head such that the head's y rotation is 0
        Vector3 rotationPoint  = head.position;
        float   headRotation   = head.rotation.eulerAngles.y;
        float   rotationAmount = headRotation;

        TransformInfo pivotedHead      = Math3D.PivotY(head, rotationPoint, rotationAmount);
        TransformInfo pivotedHandLeft  = Math3D.PivotY(hand_left, rotationPoint, rotationAmount);
        TransformInfo pivotedHandRight = Math3D.PivotY(hand_right, rotationPoint, rotationAmount);

        //pivoted_head.position = pivotedHead.position;
        //pivoted_head.rotation = pivotedHead.rotation;

        //pivoted_left.position = pivotedHandLeft.position;
        //pivoted_left.rotation = pivotedHandLeft.rotation;

        //pivoted_right.position = pivotedHandRight.position;
        //pivoted_right.rotation = pivotedHandRight.rotation;

        //Convert rotations to right hand coordinate system
        //Quaternion convertedHeadRotation = Math3D.RightToLeftHand (pivotedHead.rotation.x, pivotedHead.rotation.y, pivotedHead.rotation.z, pivotedHead.rotation.w);
        //Quaternion convertedLeftHandRotation = Math3D.RightToLeftHand (pivotedHead.rotation.x, pivotedHead.rotation.y, pivotedHead.rotation.z, pivotedHead.rotation.w);
        //Quaternion convertedRightHandRotation = Math3D.RightToLeftHand (pivotedHead.rotation.x, pivotedHead.rotation.y, pivotedHead.rotation.z, pivotedHead.rotation.w);
        Quaternion pivotedHeadRotation      = pivotedHead.rotation;
        Quaternion pivotedLeftHandRotation  = pivotedHandLeft.rotation;
        Quaternion pivotedRightHandRotation = pivotedHandRight.rotation;

        float[,] inputs = new float[, ] {
            {
                pivotedHeadRotation.x,
                pivotedHeadRotation.y,
                pivotedHeadRotation.z,
                pivotedHeadRotation.w,
                0,
                pivotedHead.position.y *scalingFactor,
                0,
                pivotedLeftHandRotation.x,
                pivotedLeftHandRotation.y,
                pivotedLeftHandRotation.z,
                pivotedLeftHandRotation.w,
                pivotedHandLeft.position.x *scalingFactor,
                pivotedHandLeft.position.y *scalingFactor,
                pivotedHandLeft.position.z *scalingFactor,
                pivotedRightHandRotation.x,
                pivotedRightHandRotation.y,
                pivotedRightHandRotation.z,
                pivotedRightHandRotation.w,
                pivotedHandRight.position.x *scalingFactor,
                pivotedHandRight.position.y *scalingFactor,
                pivotedHandRight.position.z *scalingFactor
            }
        };

        runner.AddInput(graph [inputLayer] [0], inputs);
        runner.Fetch(graph[outputLayer][0]);
        float[,] output_tensor = runner.Run() [0].GetValue() as float[, ];
        float x = output_tensor [0, 0];
        float y = output_tensor [0, 1];
        float z = output_tensor [0, 2];
        float w = 1 - x * x - y * y - z * z;

        if (w < 0)
        {
            bodyTransform.position = head.position + positionOffset;
            Quaternion newRotation = Quaternion.Euler(new Vector3(0, head.rotation.eulerAngles.y));
            bodyTransform.rotation = newRotation;
            return;
        }
        w = Mathf.Sqrt(w);

        bodyTransform.rotation = Math3D.RightToLeftHand(x, y, z, w);
        bodyTransform.Rotate(new Vector3(0, headRotation));
        // position the body such that the base of the neck is right under the head
        bodyTransform.position = bodyTransform.position + head.position - neck.position + positionOffset;
    }