15.2. Technical Description
15.2.1. Nominal Instrument Orientation
The imaging instrument is mounted on the platform such that the nominal pointing direction of the instrument is looking "down" along the -Z axis (see Figure 15-1). To point the instrument in a direction other than this down-looking geometry, the platform can be oriented using axis rotation transforms.
15.2.2. Instrument Rotation Transforms
This section describes the axis rotation transform matrices that are used to perform the platform orientation rotations. The dimension of the vectors and matrices is 4 to also support translation operations through basic vector/matrix algebra operations. The matrix transforms are applied to the nominal pointing direction of the imaging system (see Figure 15-1):
The individual matrix transforms are defined using right-handed angles about the primary coordinate axes as follows:
To perform a series of rotations, the transforms are combined using basic vector/matrix algebra operations. For example, if the platform is to be rotated about the Z axis, then the Y axis and then the X axis, then the following operation would be performed:
