9.3. The homogeneous transform: mapping coordinates to other coordinate systems

In section Coordinates: points, vectors and frames, we learned the frame, which is a 4x4 matrix that defines the position and orientation of a coordinate system, in respect to a reference coordinate system.

In section The homogeneous transform: mapping coordinates to other coordinate systems, we learned that the same 4x4 matrix can also be defined as a translation and rotation of a point, vector, or frame.

In this new section, we will use both definitions to see the third and last role of the homogeneous transform, which is remapping points, vectors and frames from a given coordinate system to another coordinate system.