# Divide curved surface by angle

Anybody has a quick way to divide a curved surface into a determined number of staight segments with the same angle between them?
The scope of this is to substitute a curved surface by a succession of linear bends.

Edit: by “linear” surfaces I mean “planar”

In this case the division is also fairly regular by length.
This is not necessary for the intended outcome.

Is the angle between panels to be constant along each edge with each panel being planar? If so then (I believe) a solution is only possible if the initial surface is developable.

A developable surface would be okay in my specific case (which means I could model said surface as a developable surface closely enough to what is desired design wise)

What is the input to the design?

If two opposite edges of the surface need to be straight then there is a specific requirement on the other two edge curves for the surface to be developable. The corresponding ends of those curves need to be “aligned”. Draw a straight line between the ends. The directions at the end of each curve normal to curve and the straight line need to be the same.

I can take the two straight edges and one of the curves and make a develop able sweep, that is definitely close enough to what I want to achieve (I still have some wiggle room for my design)

Hi Norbert, could you use divide on both upper and lower edges then connect the points and split?—- Mark

That would result in the angle along the connecting lines varying unless the end curves were identical.

Hi Mark.
That would leave the angles between surface arbitrary.
Edit. : David was faster than me.

To explain the situation further: the piece is part of a prototype that will be covered in lightly padded fabric. The structure therefore can “simulate” curved surfaces by multiple successive bends. These will be executed on an appropriate sheet bending machine, but the whole process will be semi automatic, with lots of manual input. I therefore want to standardize the multiple bend operations by giving them the same angle (preferably a not to odd degree) having 2 or 3 angle degrees might be acceptable too.

In the end, I might have to eyeball it, but this seems quite a tedious process.

Instead of using Divide, you could try _Convert with an angle setting (and everything else 0). I am not sure what will happen near the ends of the curves though… Then Loft through the resulting polylines… hopefully they have the same number of points, that is the kicker.

Also will in general not result in a constant angle along the creases nor flat panels.

Flat panels, most likely not if the upper and lower curves are different, you will get a warped surface - but maybe one that can be accommodated with some sort of cloth. This is however a method which should try to keep the most constant angle between segments - I don’t know of any other method in Rhino to use on an arbitrary curve to get that.

One other way might be to Loft the two curves, then Mesh the resulting surface with all set to 0 except some Max Angle setting, plus Simple Planes checked. If all goes well, you will have a quad mesh that represents the strips. The strips, like the mesh quads will still most likely be warped.

Are the curves certain to be planar and in parallel planes. If so then the method may work.

@norbert_geelen is designing sheet metal for under cloth, and the sheet metal is to be bent on a brake. That means the angles have to constant along the straight lines and the panels planar - a developable surface.

Yeah, first thing I tried was doing -mesh- with only angle value defined.
That gave me a nice coarse mesh with just quads but the angles between them are not constant.