Now look at a demonstration of the "gyaku zuki" (reverse punch) from Japanese Karate in the YouTube-video below:
Japanese Karate's "gyaku zuki" works differently from ITF Taekwon-Do's reverse punch. The rotation does not start from pivoting the foot, but starts from the hip. In fact, the rear foot pivots because of the extreme force working on it from above -- from the the big hip and torso rotation. Unlike the kinetic chaining in ITF Taekwon-Do where different parts of the body rotates, each adding to the momentum of the next in a sling shot fashion, the rotation in Japanese Karate does not seem to be sequential. If you look at the video again, notice that the hip, torso and arm rotates at the same time.
ITF Taekwon-Do has moved away from its Shotokan roots and has more in common, I believe, with some of the internal style Chinese martial arts and their concept of "fa jin."
Look at the video below of Tai-Chi Ch'uan Master Chen Xiaowang demonstrating "fa jin." Notice the alternation between relaxation and then sudden acceleration. This is known among the internal or soft style Chinese martial arts as "fa jin." This type of relaxation flowing into explosive acceleration using kinetic chaining is in fact the same thing we do in ITF Taekwon-Do. If you do not recognise the similarity then it probably means that you are focussing to much on vertical sine wave in your technique and too little on horizontal wave, i.e. kinetic chaining.
As far as horizontal body rotation is concerned, I believe that power generation in ITF Taekwon-Do is closer to Tai-Chi Ch'uan than Japanese Karate. Historically Taekwon-Do movements were very linear, resembling its Shotokan Karate roots. We can still see it in old style Taekwon-Do -- those schools that went independent of the ITF before the 1980s. Current ITF Taekwon-Do focus a lot on relaxation and various circular movements. For instance, when punching in Taekwon-Do the arm is not pulled to the hip, momentarily resting there, and then thrust again straight to the target. Instead, the arm is pulled back, but instead of stopping it does a small elliptical motion before thrusting out to the target. These ellipsis and circles that have become part of ITF Taekwon-Do has its cause in at least two maxims we adhere to in ITF Taekwon-Do:
1. The limbs should stay slightly bend (i.e. relaxed) through out its motion until it reaches its target.
2. The movement should never stop, until it reaches its target. (No jerky motions. No pulling back, stopping, then striking.)
The (sine) wave principle is one way we use to implement these maxims and create kinetic chaining. The wave helps us to stay relaxed and, if done correctly, prevents jerky (saw tooth type) movements.