Can you clarify how the curved school works? . . .
Gladly Warren:
The Curved NT (my mentors' term) derives from the specs of the 1-2 and 4-5 steps of the Natural Turn.
It is somewhat complicated but I'll try to do it justice here.
Note that this explanation is from the perspective of the gentleman.
The lady's approach would be similar but still commands some differences...
The basis of the Curved Movement for NT or other figure is the foot position of the dancer relative to the partner; the RF of my partner is to the right of my RF—an extreme position, and how far apart will depend on skill level.
This position is not a requirement; certainly, Curved NT can be performed in the traditional (read: tighter) position where the RF of my partner is slightly to the left of my RF.
More often than not, however, it is the couple's alignment that demands its use.
Given this extreme position, the only way I can step forward inline, say towards DW, without having to bump into my partner's right leg or having to go OP is to rotate my (and partner's) feet 45deg. CCW, or to the left, effectively pointing them down LOD, and then taking the RF step.
In effect, this changes the first step of the NT from FWD to Diag Fwd and necessitates the crucial point, that my left side should be delayed so I can get past my partner's right leg on step 1; thus, creating a Late or Delayed CBM situation. This is the same on steps 4-5 too. This is the first bit.
Understanding the preceding, we can then, at the beginning of the figure, rotate further CCW so that now I am facing between DC and LOD.
I then take the first step D.Fwd. towards BETWEEN LOD and slightly to DW. The second step is taken LF in CBMP and ended toe TIGHTLY turned-in. The lady must shorten her 2nd step.
The curve happens over two steps, and the CBM is delayed so much that it can be argued that it is now a right-side lead (for the g.).
This is the situation where the lady HAS to toe-in (LF) heavily in order to a) not peel her hip off from the gentleman, and b) make the second step possible.
The technique requires good Body Flight on the prior step to swing the body and comfortably leave the left side behind on the first step—hence, the need for a good prep step.
This is the basic structure. There is an entire effect>cause>effect cascade involving customizations/skills.
m