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Developable Surfaces
Developable surfaces can be formed by rolling a flat sheet of material without stretching it. When a surface is linear in one direction (u/v) it MUST NOT mean that it is developable!
 

 


 

Compound Curvature
With Rhino you can display the Gaussian curvature graph and analyse if a surface is developable. If the Gaussian curvature is not zero on any point on a surface, then it‘s not possible to unroll it without stretching the material. A sphere for example is a surface with compound curvature.
 

 


 

Unroll Surfaces
Cones and cylinders are basic examples of shapes that can be perfectly unrolled.

Common Point of Intersection
A surface can be unrolled, if all its ruling lines have a common point of intersection.
 

 


 

Parallel Ruling Lines
Surfaces with parallel ruling lines also can be unrolled. In this case „parallel“ means, that the ruling lines intersect in infinitiy.You can create developable surfaces with parallel ruling lines by extruding any curve
 

 

 
 

PolySurfaces and Freeform Curves
As long all the ruling lines of each sub-surface have a common point of intersection they are developable. The sub-surfaces‘ points of intersection can be different. Developable "conelike" surfaces can follow any curve and can be created by lofting the curve to a point.
 

 


 

Trim developable Surfaces
If the underlying surface is developable it can be trimmed in any way.
 

 


 

Developable Loft
Here you can see what may happen, if you create a loft with developable style from the above trim curves. Though there is a solution with a single developable surface the loft command might fail to find it. You can try to simplify the result of the developable loft by using it's rebuild or refit option.

 


   

Developable Surfaces in Marine Industry
The Fregatte 124 Sachsen for example is mainly made from developable surfaces. Check out how more stylish work can be done with developable surfaces in yacht design.

 


 

Developable Surfaces in Architecture
 

 

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