I’m trying to make this shield-like surface that’s G2 continuous throughout.

The problem is, the ‘usual’ nose-cone trick to trim back doesn’t work here, because the edges are not G1 across the mirroring line by design. Could you please give me some guidance on how to build this surface (good ways to divide it up)?

I also tried to leverage the 4-sided nature of this shape to make it using one surface, but the results aren’t great.

Thanks a lot for your help Pascal! Sorry for the lack of information–the bottom curve is planar, when the top is not. I tried your method but, it’s hard to ensure the planar-ness from cutting a curved surface. I will try to get a file when I’m back to the computer (I can’t stop thinking about this surfacing problem )

There is a geometry limitation. The two lower curves being planar means that the normal of the surface at the intersection of the curves has to be the same as the direction perpendicular to the two curves if the surface has G1 or higher continuity. This results in the surface being “flat” at that point.

An alternative is to create a surface with infinite curvature at the point (a singularity in mathematical terms). The surface can be G1 or G2 everywhere except at that the point. At the point the normal direction and curvature of the surface are not defined. The apex of a cone is a simple example.

For a corner of a NURBS surface to be singular with infinite curvature the corner must be an edge with zero length. It is not possible for a regular corner to have infinite curvature. Simple example: SurfacePoint.3dm (2.1 MB)

Thanks very much for your detailed explanation David! This clears up my problem for me a lot!

This shape (as its shape suggests) is for a shield, and I wanted to fillet the tip at the bottom, rather than making it part of the surface (which would make the control points extra dense along the middle).

It looks like I need to relax the constraint on the lower two curves (so that they don’t have to be planar), as the fillet won’t work well with a singularity

If you just need the tip to be rounded and not a circular arc then an approach is.
InsertKnot to add two or three rows of control points near the tip.
Move control points down to move the tip down.
Trim the surface
Experiment with the location of the inserted knots and movement of the control points to obtain a satisfactory shape.