Your example model uses the "two edges colinear / corner disappears" method for making triangles. I'm sorry i can't help, because that method is a dead end for my purposes.
My model joins two SURFACES to a single SURFACE along one edge. I only brought it up because i misunderstood you.
You said
triangle will not work well in FreeCAD since it cannot join two faces unless the edges are identical
we don't mean the same thing in regards to
cannot join two faces unless the edges are identical
in my picture, i join a surface half way along an edge. half an edge is not identical to the whole edge. for me this qualifies, but i totally understand that for your case it doesn't.
My model only shows that the triangle/three-quadrangle scheme can work in FreeCAD.
[edit: in case this wasn't blindingly obvious, the picture below is not from FreeCAD, it's just an example of existing methods to deal with triangles in NURBS]
- nurbs triangle by quads.png (57.14 KiB) Viewed 2144 times
if the triangle is in red, the quad decomposition split each edge in 2, my method allows a single surface along each side the triangle instead of two as shown in the picture.
last minute addition. i re-extruded your collapsed corner triangle and tried a single boolean. it works ok. Unless you are willing to say how you split the edge, i can't help you join the two parts.
- bad tri good boolean.png (11.87 KiB) Viewed 2144 times
maybe the problem is the other triangle? how did you make it?