# Diagonal mesh + curviloft

I have created a shell with a curvi loft. From what I have heard, curvy loft creates “quad geometry”.

However when I unsoften the shell it shows triangular faces everywhere. (maybe this is in the technical sense just fine and a quad doesn’t need to be flat to count as a quad. I am not deep into quad science)

What I’d like to achieve is the shell consisting of a mesh of rectangles and diagonal lines running in both directions.

Curvy loft creates the rectangles (quads) and diagonal lines running in one direction. So far so good.

In order to create a mesh with the diagonal lines running in the other direction as well. I have copied the shell, “-1 transformed” it and superimposed it over the existing shell.

But unfortunately the diagonal lines don’t line up perfectly with the quad faces because they are not flat.

What can I do to create a perfect mesh with diagonal lines running in both directions?

It may not be possible to have both diagonals. I think that might require the quad to be planar. A “quad” is normally two triangles with their common edge hidden.

Why do you need both diagonal lines?
Curviloft can create quad mesh and then the subd-extension gives the smooth look.
There is no automatic way to create both diagonals with intersection in the middle of both lines on non planar faces.

Basic geometry would tell you that the diagonals shouldn’t intersect each other.

1 Like

@ slbaumgartner

Ahh ok, I see. Until now I have been under the impression that a quad is a nice planar rectangle.

@tengle07

Well,for the coolness of creating a space frame consisting of diagonal lines. And also to use them as reference marks. I have flattened the shell to individual stripes and printed them out in order to clamp them together to recreate the shell in paper. The diagonal lines serve as reference marks to exactly line up the stripes. The paper shell could serve then as a template to build a diagonal space frame (with bamboo poles or something) on top of it.

1 Like

…because the quads are not planar I guess. In my ignorance I didn’t know that. If a quad would be planar my intuition tells me that the diagonals should intersect.

I mean the quads in my model are almost flat so they almost intersect.

Yes. Exactly. The diagonal wouldn’t be necessary if the four bounding edges were planar. Since two corners are lower than the opposite two, the diagonals wouldn’t intersect.

To be honest, I’ve always thought it kind of odd that it is called a quad face when it’s made of two triangles.

In real materials like the skin over your bamboo or pieces of plywood, you can put in subtle (and sometimes not so subtle twists) but then of course they aren’t planar either.

Yea, right, the diagonal wouldn’t be necessary if the edges are on the same plane. The diagonal can run either in one direction or the other.

I also feel now odd about the fact that a “quad” is just two ( or possible even more?) shitty triangles. I am very disappointed in quads.

Anyways, thanks for the clarification!

I’m sorry the quads have let you down. Fortunately we can blame someone else. It’s not Sketchup’s fault.

Long live the triangle! It’s worked for the milkmaids for centuries.

Have a great day and forget the quads.

I’ve never studied the math, so I won’t attempt to explain why, but I’ve read that quads are easier to work with when warping or subdividing a shape.

I tried to Google the subject, but found no general rule whether the quadrangles are expected to be planar or not.

For you purpose you do not need quads - you need 4 triangles instead a 4 side face.
A quad is as the name say, is a face build out of 2 triangles with a hidden line.
Quads can be easily subdivided with catmul-clark algorithm to get a smooth and clean surface.
A planar quad face can also divided into 2 triangles, more is possible but normally not required for 3d design.
So, you can use the curviloft mesh and must add the over diagonal line manually.

Well a work around in my particular case seems to just manually draw the “other diagonal lines” on the flattened stripes after running “unwrap and flatten”.

If I draw the “other diagonals” on the 3D shell and use this to run “unwrap and flatten”. It will create a mess.

Furthermore to manually draw the diagonals in each quad from " quad corner to diagonal midpoint to corner" leads to slightly funky looking diagonal curves. They have a vertex at each quad where the other diagonal have none.

What method could create a perfect diagonal mesh based on a curvi loft shape as start? I am interested in having any kind of 3D shape and applying various space grids on it.

Right, I have just done that. Thanks for your input regarding the “catmul-clark” algorithm. I’ll look into that

1 Like