Developable Surfaces are ones with 0 gaussian curvature, they have only one direction of curvature.

Parallel Extrusion

Conic Extrusion

Types

• There are 3 primary types of developable surfaces in Rhino and most other 3D modeling software.

  • Parallel Extrustions
  • Conic Extrusions

  Extrusions

  • Faceted polysurfaces.

• Faceted polysurfaces

  • Faceted polysurfaces are composed of any surfaces which are all planar.
  • Common examples include:
    • Polyhedra
    • Polysurfaces with all planar faces
    • Meshes composed of triangular faces

Fabrication

• All developable surfaces can be laid flat. This allows them to be produced from bendable sheet material like paper.
• Using the unroll command, developable surfaces and polysurfaces can be laid flat.
• Lasercutters, Waterjets, and CNC Routers can all cut the curves generated from unroll using the dupborder and dupedge command.
• An example of fabrication with developable surfaces can be found here.

Origami