Inverse tang

[Peter Blomberg]

I've long struggled with parts that have two curved edges close to each other, but not having the same point of origin. The task is to fill in the area between the curves.

If the curves are far enough apart, I can use tndis and chords. However, if they are close, then I'd have to rotate chords and tndises, which isn't ideal.

Luckily, we have tang for the inside (in yellow). This eliminates the need to rotate ndises, but effectively doubles the number of points. If the inside and the outside of an area to be filled have significantly different number of points, then the result is a large amount of extremely narrow triangles, so this is to be avoided.

What if we had an inverse tang (in black) to be used for the outside? With an equal number of points, it is easy to fill the light gray area with quads.

   

[Philippe Hurbain]

Could be interesting indeed...
- thin rings can often be done with properly scaled ring primitives, even though it is sometimes required to slightly adjust inner and/or outer diameter 
- rotated prims is too be avoided if possible, but their use is sometimes mandatory, and the resulting vertex mismatch is generally quite small. 
-  if the ntang prim family is to be created, how should the middle vertex be mathematically defined ? As a mirror of tang middle vertex?

[Peter Blomberg]

-  if the ntang prim family is to be created, how should the middle vertex be mathematically defined ? As a mirror of tang middle vertex?

That's one way. However, it might be easier/faster to calculate the intersection of adjacent chords.

[Gerald Lasser]

The case you have shown above can be done with an 1-4ering

or two 1-8chrds

Small  Issue arises if a 1-8 or 1-16 needs a rotation

[Rene Rechthaler]

we could still expand the tang/ering prims to hi-res (useful for thin walls at big radii)
hi-res ering (for manually p48 to p48 prims)
hi-res tang (for p48 prims to manually p96 outside)
-> both also for in-between values which cant be covered with normal prims like 1-12, 1-6 and odd values

[Peter Blomberg]

The case you have shown above can be done with an 1-4ering

The ering leaves 5 points on the outside and 9 points (from the tang) on the inside. That would allow the use of alternating triangles and quads, which could work without generating long narrow triangles. I'll test that.