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

In section Geometry basics: coordinate systems, points, vectors, and transforms, we learned about the homogeneous transform, which is a 4x4 matrix that defines the position and orientation of a coordinate system with 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 transform.

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 transforms from one coordinate system to another.