What I find lacking in these geometrical methodologies is that they rarely focus on movements in the vertical direction. I struggled a lot with the pattern-oriented, geometric-centric, mostly because the emphasis of the teachers I had at the beginning was on "OK, so let's explore what can we do after this step". They'd give us several options, and in my naive tango beginner mind, I would categorize these as different sequences, that my little bird brain could not grasp. Building a catalog of theoretical possibilities is an interesting goal, but I think a more direct and attainable goal is to focus on how to make a particular step/sequence easier for both the leader and the follower. My dancing only really took off when I started focusing on getting my partner to move with me in harmony with the music. This led me directly to the importance of controlling the up and down movements (i.e. getting closer to the floor or further, depending on the desired effect). Now I think of my dancing in very small building blocks with the most emphasis being on the vertical dimension. When my students ask me what to do after a particular step that we've been working on in class (using the principle of movements of your entire body in all 3 dimensions), I just tell them to walk forward out of it.