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.

[Peter Blomberg]

I now have a case where I'd need to fill in the area between
1 16 0 0 0 -43 0 0 0 0 -37 0 1 0 48\3-16edge.dat
and
1 16 0 0 0 -47 0 0 0 0 -41 0 1 0 48\1-6edge.dat

I can put a tang on the inside, but what about the outside?
Must I rotate a chord?
The 1-6 (8 segments) is not divisible with 3, so I cannot use aring.

Rings might also do it, but in several parts. First a ring37 (which doesn't exist for 1-6 or 1-4+1-8 yet), then a ring19 (1-4+1-8), and then a ring40(1-4 exists, but not 1-8). Other combinations with fewer prims or fewer new prims might exist. However, since 43/37 is an irrational number, I'd have to approximate it with 5 decimals.

[Rene Rechthaler]

sometimes, hi-res prims are just connected directly...
this can still cause gaps at higher prim substitutions.
in normal res, this could be solved with an ering (manually drawn p16 vertices inside, outside scalable, normally invisible).
on 16->48 prim subst, this gets replaced with an aring (p16 inside, p48 outside).
the same aring gets invisible at this prim subst (because inside and outside prims are now both p48).
in your case, we would need something like a hi-res ering (manually drawn p48 inside, outside scalable).
While we are at it, we could even need a hi-res tang (a p96 outer polygon) for even thinner gaps (if a normal tang is too wide or at different angles).

[Peter Blomberg]

Chris Böhnke has submitted a partial tang (48\1-6tang.dat) to the parts tracker. This is interesting in that it expands the tang prims to sweeps other than those divisible by three. Here, I could see also the 48\5-48 and the 48\11-48 be implemented at some point.

Even more interesting is the use of two partial tangs; one in the beginning and one in the end. This would allow the creation of 48\1-12, 48\7-48, and 48\5-24, thus completing the set.

48\1-48 and 48\1-24 are not needed since these can be handled with tndises.

The same kind of thinking could be used for complementing the tangs on the other side.

Picture shows the proposed partial 1-6 tang and a corresponding adapter chord.

  tang.png (Size: 1.8 KB / Downloads: 11)