## 6 Experimental Results and Discussions
### Data Analysis  
After setting the world coordinate system, it starts the 3D reconstruction experiment of live fish: capturing the video of fish with 8 cameras simultaneously and reconstructing the markers attached to the fish body based on the image information with homemade motion capture software. The reconstruction result is shown in Figure 20. It displays the spatial positions of markers after 3D reconstruction taken from 0 to 700 frames with 100 frames separated, and the corresponding frame numbers by camera 6 with appropriate angle, where all markers are covered, is chosen as the comparison.  
According to the previous experimental data, we can get the motion trail of fish, which is shown in Figure 21, it can be seen from the picture that the tracks of marker 1 to 3 are relatively stable, while the tracks of markers 4 to 9 swing with a certain degree, and this is consistent with the swimming model of the Carangidae that the propulsion force is mainly caused by tail swing.  
Because fish swimming is a dynamic process, we take the relative movement between markers on the fish tail and markers on the front part of fish as a study object and select the motion direction of markers 1 to 3 as the motion direction of the fish. Then, the relative motion direction of each marker can be obtained, that is adjusting the overall fish swimming to the swimming along the \(X\) axis and observing the position of marker relative to it. As shown in Figure 22, the position \(P_{0}\) and velocity direction can be determined by the marker 1 to 3. The position of each marker in the relative speed direction is the shortest distance from the axis of \(P_{1}\) to \(P_{0}\).  
Figure 23 shows the distances between each marker and the axis, it can be seen that the markers of 5, 7, and 8 are similar in motion, all of which belong to the same side. Near the 50 th frame, the motion direction of these three markers is opposite to that of the other four markers, which is because  
Figure 21: Marker movement trajectory.  
Figure 20: D reconstruction results in software and pictures captured by camera.  
the axis is in the middle of the two markers sets; the markers on one side are away from the axis and the markers on other side must be close to the axis. At the same time we can see that when the fish is suspended in the water at 500 th frame, the markers of 5, 7 and 8 are farthest from the axis, this because the markers of 1 to 3 are chosen as the basic markers, which leads to the result that the axis will be tilted to this side and the markers of the other side are farthest from the axis. Observing the data from 0 to 200 frames, it can be seen that the movement of the fish tail is similar to the sinusoidal motion, which also conforms to the tail swing of the carangid in Formula (21).  
Because of the limitation of the experimental conditions, the system errors in our experiment are obtained by comparing the relative distances of calibrated markers which are arranged as in Figure 17. In order to achieve accurate results, both the motion of translation and rotation are analyzed, and the results are shown in Figure 24. The maximum error in translational motion is 3.84 mm, and the maximum error during rotation is 3.22 mm, which indicates that the error between the measured value and actual value is small.  
Figure 24: The system errors analysis of the relative distances of calibrated markers.  
Figure 23: Distance between the markers and the axis.  
Figure 22: Fish swimming diagram.