Basic rules

1. Extrinsic rotations (fixed axes)-rotate around fixed axis

• Yaw: rotate around original z-axis
• Pitch: rotate around original y-axis
• Roll: rotate around original x-axis

2. Intrinsic rotations (moving axes)-rotate each axes moved

• Yaw: rotate around original z-axis
• Pitch: rotate around new y-axis(after Yaw has been applied)
• Roll: rotate around new x-axis(after Yaw and Pitch has been applied)

Intrinsic cases using HelixToolkit

1. creating transformation

   
   using System.Windows.Media.Media3D;
   using HelixToolkit.Wpf;
   public Matrix3D CalculateAttitudeMatrix(double yaw, double pitch, double roll)
   {
       // Convert angles to radians
       double yawRad = yaw * Math.PI / 180.0;
       double pitchRad = pitch * Math.PI / 180.0;
       double rollRad = roll * Math.PI / 180.0;
   
       // Create rotation matrices
       var yawRotation = new RotateTransform3D(new AxisAngleRotation3D(new Vector3D(0, 0, 1), yaw)).Value;
       var pitchRotation = new RotateTransform3D(new AxisAngleRotation3D(new Vector3D(0, 1, 0), pitch)).Value;
       var rollRotation = new RotateTransform3D(new AxisAngleRotation3D(new Vector3D(1, 0, 0), roll)).Value;
   
       // Combine rotations (order matters: first yaw, then pitch, then roll)
       return rollRotation * pitchRotation * yawRotation;
   }
     

2. applying

   Matrix3D attitudeMatrix = CalculateAttitudeMatrix(yaw, pitch, roll);
   // Apply the transformation to your model
   yourModel.Transform = new MatrixTransform3D(attitudeMatrix);