# The Method of Multi-Camera Layout in Motion Capture System for Diverse Small Animals
## 2 The Parameters of Multi-Camera System
### The Intersecting Volume of Multi-Camera System  
A successful motion capture begins when the capture object is photographed by at least 2 cameras which require the object to be within the range of the visual field of this two cameras [16]. The intersection area of the multi-camera is cut by the moving plane of the target. The size of the working field of the camera is determined according to the size of the working distance (_WD_), focal length (_f_) and the chip size (_v_ and _h_). By calculating the intersecting volume in the typical layout (shown support file S4 for details), it is known that: (1) the variation range of the intersection volume of multiple cameras in the half-annular layout is the largest and the intersection volume of the arch layout is always larger than the annular layout; (2) the intersection volume of the three kinds of layout increases with the increase of the focal length (_f_) and the intersecting volume of the annular and half-annular layout decreases with the increase of the pitch angle (\(\alpha\)). (3) When the angle between the cameras (\(\theta\)) is closer to 23.33 degrees, the greater the intersecting volume of the half-annular layout; (4) when \(\theta\) is greater than 40 degrees, the intersecting volume of the half-annular layout is smaller than the other two types within the definition domain of \(f\) and \(\alpha\). Therefore, if we want to get a larger intersecting volume than the rest of the two forms using the half-annular layout, we need to make sure that \(\theta\) is within the range of 25 to 40 degrees and \(\alpha\) is within 21.33 to 90 degrees. Small animals of different shapes can be abstracted as the smallest outer enveloping cuboids (length--_l_, width--_w_, height--_h_) that can completely capture the animals' body and the intersecting volume of a multi-camera is an irregular space volume which can abstract the inner enveloping cuboids (length--_L_, width--_W_, height--_H_), that can be completely covered by the intersection volume. It is an important precondition to ensure that the object is successfully captured because the overall shape of the captured object is within the inner enveloping cuboid of the multi-camera. Therefore, the study of the coordination between the two is the first step to determine an appropriate camera layout for different kinds of small animal motion capture. Based on theoretical calculations (Support File S4 for details), the dimensions and proportions of the inner enveloping cuboids of different multi-camera layouts were obtained. The ratio of the width to the length and the ratio of the height to the length of the smallest outer enveloping cuboids of the small animal (see Figure 1) are used to determine the inner enveloping cuboids of the intersecting volume of the multi-camera, in the selection of an appropriate camera layout. It is known that the inner enveloping cuboids of the arch layout tend to be flat, the ratio of the width to the length (_W/L_) was about 0.593 and the ratio of the height to the length (_H/L_) was about 0.296 (Figure 3). When the length (_L_) of the intersection volume of the three layouts were the same, the volume of the inner enveloping cuboids of the half-annular layout was obviously larger than that of the other two forms. Moreover, the ratio of the width to length was about 4.79 and the ratio of the height to length was about 1.97. The inner enveloping cuboids of the annular layout was near the cube, the ratio of the width to length was about 1 and the ratio of the height to length was about 1.114.