Working space of Kinects in ambulance

Since the 3D scan of patient body happens in ambulance, a study of how to position Kinect to achieve best filed of view of body is necessary. The Kinect should be placed neither too far away from nor too close to patient due to the operational range of the Kinect mentioned in the last post. The basic geometry and triangulation will be used to derive the interval equation of the configuration in which the best field of view can be guaranteed and the overlays between two Kinects are optimized. As the exact model of ambulance is undefined yet, the calculation will use symbols to represent parameters of the configuration.

Figure 1 Schematic diagram of the ambulance

As shown in the figure 1, the ambulance has internal size of W by H (only transverse plane is shown). The patient will lie on the bed which is height of h(bed). Here we assume that the bed is placed at the centre of ambulance. The Kinect camera is placed on the wall with height of (h(bed)+Δh). The middle line of Kinect should point to the middle of the bed to get more completed view of the patient.
Based on simple triangulation, the best angle between the central view line and the wall is:

then the lower bound of the field of view is:

and the upper bound would be:

In order to satisfy the operational range (near field mode), both lower and upper bound should have:

Given the internal width of the ambulance and the relative vertical distance between Kinect and the bed, the best angle to place the Kinect can be calculated. The bounds of the filed of view are then checked to ensure the patient is in the best operational range.
For the other Kinect on the another side, it can be placed at the same pose since they are symmetrical in this case.