# How to join continuously, surfaces of different curvature radii?

Hello all !
The objective to be solved (the goal) is to have a surface which joins the both internal and external surfaces, as “smooth” as possible (I mean, with no big variation of the radius of curvature),
with splines, so as to be tangent on its edges, to have a continuous final round surface.
I join a grasshopper canvas to explain.
Thank you for your help !
To explain my issue about binding surface.ghx (344.3 KB)
JLuc

Too many possible solutions, can you narrow down what you expect by posting a sketch of the “bridge” surface?

Hello,

I tried to explain what I expect by posting a side view done in a Powerpoint.

Sorry for the approximation of the sketch.
Jluc

Here’s an image of the right side view in Rhino, with the red surface flatter than the yellow surface. I would like to link the 2 surfaces continuously with splines, so that in the end the 3 surfaces (red, binding surface and yellow) form one.

If I use Grasshopper’s “Ruled surface” component, it generates a bond surface with discontinuities. This is not what I want.

Oh dear, until you said that I thought these surfaces were flat (looking at top view). The bridge surface I derived is planar… I guess I missed the subtlety of this puzzle.

binding_surface_2020Dec28a.gh (46.6 KB)

Looking at it this way (baked using Rhino ‘Analyze | Surface | Curvature Analysis’), I see that your two surfaces have different curvature, the small one less than the large one, and my “bridge” has zero curvature, as expected from a planar surface.

I have no idea what the top view shape of your bridge surface looks like? Or how it can resolve the different curvature of the two surfaces?

I’ve analyzed your response, but that’s not quite what I’m looking to resolve.
The goal is to connect the 2 surfaces (red and yellow) with a green surface, as soft and continuous as possible, over the entire contour.
Here is a top view :

JLuc

With Grasshopper’s “Ruled surface” component, the generated surface has a big hollow, whereas I would like a green surface that makes a continuous bond with the yellow surface.

Too bad you can’t untrim that big hole to get the full (spherical?) surface it was cut from. Other than projecting your small surface onto that untrimmed surface, I see no way to resolve your goal.

With a red triangle that goes to the edge of the yellow surface, I had succeeded in making a continuous connecting surface, with splines

But if the red triangle doesn’t go all the way to the edge of the yellow surface, I can’t.
Too bad you can’t help me …
Thanks anyway.
JLuc

binding_surface_2020Dec28b.gh (42.6 KB)

It’s tried, thank you.

But the challenge is precisely to keep the radius of curvature of the internal surface (white on your canvas) equal to 349.82 mm. In this case, the blue bonding surface would have to look like a soft wave, like in the image in my previous post (green lines). You see what I mean ?

On the other hand, if the radius of curvature of the inner surface (white on your canvas) is reset to 96.36 mm, like that of the outer surface, then the blue connecting surface should look like the sphere which fills the hole.

If you agree and are available tomorrow, I will try to explain the tests that I have already undertaken, but without success.
It’s late at home (I’m in France, in Paris).
Thank you again and have a good day !

JLuc

I’m done.