Folding Shapes

Is there a better way to fold an unfolded shape back up? Folding.3dm (60.7 KB)

If this was paper folding edge 1 until it touched edge 2 would be simple but I’m finding that it takes quite a bit of trial and error to find the point of intersection. It makes me think I’m missing something. So whats the best way to find the point where the two edges 1 and 2 would intersect when folded?

Try drawing circles centered on edge 3 & 4. rotate the edges to the intersection.

Here’s one way with some helper geometry using 2x Circle>AroundCurve and 2x Rotate3D…

For brevity, only did the first two sides, for the rest only Rotate3D is needed, as the first two rotated sides can be used as the reference… --Mitch

A more general method is to use Revolve to create the surface which will be swept by edges when the flaps are folded.

For each flap to be folded:

  • Revolve command
  • For objects to be revolved select the edges of the flap
  • For start of revolve axis select one end of the crease
  • For end of revolve axis select other end of the crease
  • Start angle 0 degrees
  • Revolve angle 360 degrees

Corner points of the folded object will be at the intersections of the perimeters of the swept surfaces.

Folding Revolve DC 1.3dm (210.3 KB)

Thanks everybody. Those solutions seem so obvious now that you point them out. It’s always good to see all the different ways rhino can solve a problem.