Added description of TF calculation and publishing mechanism

docs/en/source/4_application_guide/coordinate_systems.md

@@ -11,3 +11,143 @@
 * All data published in our wrapper topics is optical data taken directly from our camera sensors.
 * static and dynamic TF topics publish optical CS and ROS CS to give the user the ability to move from one CS to other CS.
 
+### Using ROS2 TF Tools
+
+#### Viewing the TF Tree Structure
+
+You can use the following ROS2 commands to print and visualize the TF tree published by the camera package:
+
+**Print all TF relationships:**
+
+```bash
+ros2 run tf2_tools view_frames
+```
+
+This command generates a `frames.pdf` file that displays the hierarchical relationships between all frames.
+
+![image-20251027111351870](../image/application_guide/image4.png)
+
+**View all currently published TF information:**
+
+```bash
+ros2 topic echo /tf_static
+```
+
+#### Visualizing TF Tree with rviz2
+
+You can use rviz2 to visualize the TF tree structure and relative positions of coordinate systems in real-time:
+
+```bash
+rviz2
+```
+
+In rviz2:
+
+- Add the `TF` display plugin
+- Configure the Fixed Frame to `camera_link` or `camera_depth_optical_frame`
+- Select the TF frames to display
+
+![image-20251027140652727](../image/application_guide/image5.png)
+
+### Camera TF Calculation and Publishing Mechanism
+
+#### Core Function: `OBCameraNode::calcAndPublishStaticTransform()`
+
+The camera node calculates and publishes static transformation relationships between all sensors through this function. Below is a detailed explanation of the code:
+
+#### Quaternion Initialization and Coordinate System Transformation
+
+```cpp
+tf2::Quaternion quaternion_optical, zero_rot;
+zero_rot.setRPY(0.0, 0.0, 0.0);
+quaternion_optical.setRPY(-M_PI / 2, 0.0, -M_PI / 2);
+```
+
+**Explanation:**
+
+- `quaternion_optical`: Defines the rotation transformation from the optical coordinate system to the ROS standard coordinate system (90-degree rotation)
+- This rotation converts the camera optical coordinate system (X right, Y down, Z forward) to the ROS standard coordinate system (X forward, Y left, Z up)
+
+#### Obtaining Device Information and Base Stream
+
+```cpp
+auto base_stream_profile = stream_profile_[base_stream_];
+auto device_info = device_->getDeviceInfo();
+// The base stream is typically the DEPTH stream
+```
+
+**Explanation:**
+
+- A base stream (typically the depth stream) is selected, and all other sensor transformations are calculated relative to this base stream
+
+#### Iterating Through All Streams and Calculating Relative Transformations
+
+```cpp
+for (const auto &item : stream_profile_) {
+    auto stream_index = item.first;
+    auto stream_profile = item.second;
+
+    // Get the extrinsics of this stream relative to the base stream
+    OBExtrinsic ex;
+    ex = stream_profile->getExtrinsicTo(base_stream_profile);
+
+    // Convert rotation matrix to quaternion
+    auto Q = rotationMatrixToQuaternion(ex.rot);
+
+    // Apply optical coordinate system transformation: Q_new = quaternion_optical * Q * quaternion_optical.inverse()
+    Q = quaternion_optical * Q * quaternion_optical.inverse();
+
+    tf2::Vector3 trans(ex.trans[0], ex.trans[1], ex.trans[2]);
+```
+
+**Explanation:**
+
+- `OBExtrinsic` contains the rotation matrix (`rot`) and translation vector (`trans`) between two sensors
+- Quaternion multiplication applies the optical coordinate system transformation to each sensor's rotation relationship
+- This transformation converts the camera's native optical coordinate system to the ROS standard coordinate system
+
+#### Publishing TF Transformations
+
+```cpp
+// Publish the transformation from sensor to base stream (in ROS coordinate system)
+publishStaticTF(timestamp, trans, Q, frame_id_[base_stream_], frame_id_[stream_index]);
+
+// Publish the transformation from physical frame to its optical frame
+publishStaticTF(timestamp, zero_trans, quaternion_optical, frame_id_[stream_index],
+                optical_frame_id_[stream_index]);
+```
+
+**Explanation:**
+
+- First `publishStaticTF`: Publishes the transformation from the base stream to the current sensor (translation + rotation)
+- Second `publishStaticTF`: Publishes the transformation from physical frame to optical frame (pure rotation, no translation)
+- `frame_id_[stream_index]`: Physical coordinate system frame name (e.g., `camera_depth_frame`)
+- `optical_frame_id_[stream_index]`: Optical coordinate system frame name (e.g., `camera_depth_optical_frame`)
+
+#### Special Handling for Left and Right IR Cameras
+
+```cpp
+if (stream_index.first == OB_STREAM_IR_RIGHT && base_stream_.first == OB_STREAM_DEPTH) {
+    trans[0] = std::abs(trans[0]);
+}
+```
+
+**Explanation:**
+
+- Left and right IR cameras are symmetric about the center plane in the device coordinate system
+- Using `abs()` ensures the X-axis offset is positive, maintaining geometric consistency
+
+#### Publishing Extrinsics from Depth to Other Sensors
+
+```cpp
+if (enable_stream_[DEPTH] && enable_stream_[COLOR] && enable_publish_extrinsic_) {
+    OBExtrinsic ex = base_stream_profile->getExtrinsicTo(stream_profile_[COLOR]);
+    auto ex_msg = obExtrinsicsToMsg(ex, "depth_to_color_extrinsics");
+    depth_to_other_extrinsics_publishers_[COLOR]->publish(ex_msg);
+}
+```
+
+**Explanation:**
+
+- In addition to publishing transformation relationships through TF, raw extrinsic parameters are also published through custom topics
+- This allows users to directly access the camera's intrinsic and extrinsic parameters for high-precision point cloud alignment and depth-color registration