Is it possible in MoI by some method, to flatten a curved surface? I am working on designs of shapes such as these with faceted faces formed by cylindrical curved surfaces:

I would like to construct this type of design and similar by cutting the facet shape from flat stock, bending the shape and joining the individual facets at the edges. (I use clay slabs but the construction could work for paper, sheet metal, or any other material that comes in deformable sheet material.)

The design is simple. I construct a curve in Right View,

then extrude the curve along its XY axis, in order to create a cylindrical surface.

Then in Top View use Circular Array around the Origin.

Then select all surface objects and Trim them using the mutual trim option to construct a mitered/faceted form.

After that I can add a top and bottom planar surface, join to create a solid, shell and fillet the edges.

BUT, in order to construct the form, I need to flatten each unique surface in order to make a cutting template. Is this possible to do in MoI? I would not mind spending considerable time if I knew that it would work. I have tried several things without success. For example: If I start with a simple curve with a known length, in this example a 45° arc of a circle with a 10 unit radius:

Since circumference = 2πr and 45° is ⅛ of 360°, the length of this arc before and after flattening should be 7.854 units. I tried to flatten the curved surface by viewing the surface on its edge and rotating the control points to be coplanar.

This does produce a flat surface, but the length is not 7.854, rather it is 8.284 units.

I know that I can approximate the form using thin polygonal flat surfaces. I construct the original nurbs curve ………., then array a series of points along the curve, connect those points with a Polyline, then Extrude and construct according to the original method as described above. With this approximation, the fewer points along the curve, the easier it is to rotate to a flat surface but the less accurate it is. The more control points, the greater the accuracy of the approximation but the more difficult and time consuming it is to rotate each polygonal segment to a flat surface. Thanks for any advice.

-Dan