Mathematical conventions

Spatial location sensors determine the parameters related to the degrees of freedom of a reference frame in a three-dimensional space. But some sensors, for technical reasons, or to limit costs or size, measure only three parameters (it's often simpler to measure rotations than translations). The most commonly used mathematical formalism breaks down the degrees of freedom as follows:

• three translational coordinates of the object relative to the reference ;

• three object rotation coordinates relative to the reference.

Generally speaking, the mathematical notation of "homogeneous coordinates" in matrix form is used to manipulate these parameters. This matrix, known as the "transition matrix" or "base change matrix", is a 4 x 4 matrix. The matrix corresponds to the mathematical...