Unfolding curved surfaces => flat surfaces

Unfolding curved surfaces => flat surfaces

Post by Charlie Bustaman » Sat, 26 Feb 1994 09:59:29



Leather basketballs and baseballs unfold to two hourglass like flat 2d shapes.

Can anyone point me to any papers, or example code (C is best for me) for
deriving the 2d flat shapes given the 3d shapes as splines (or any other
input)?

This is sometimes refered to as unfolding or transitioning algorithms.  I know
that it is used in ship-building,  sail-making,  tent-making,
and clothes-making industries.  Some of the above industries act like the
algorithms are trade secrets and what to charge big BIG bucks for the software.
I just can't believe there is not a published paper out there somewhere that
describes this to the public.

------ ______________________________________________________________ -------
----- /\ Charlie Bustamante        ... In balmy Boca Raton, Fl   USA \ ------
---- /  \                                                             \ -----

-- /______\ opinions are mine                        Fax: (407)982\9707 \ ---
---------- \_____________________________________________________________\ --

 
 
 

Unfolding curved surfaces => flat surfaces

Post by PROF D. Rogers (EAS F » Mon, 28 Feb 1994 01:30:40


!Leather basketballs and baseballs unfold to two hourglass like flat 2d shapes.
!
!Can anyone point me to any papers, or example code (C is best for me) for
!deriving the 2d flat shapes given the 3d shapes as splines (or any other
!input)?
!
!This is sometimes refered to as unfolding or transitioning algorithms.  I know
!that it is used in ship-building,  sail-making,  tent-making,
!and clothes-making industries.  Some of the above industries act like the
!algorithms are trade secrets and what to charge big BIG bucks for the software.
!I just can't believe there is not a published paper out there somewhere that
!describes this to the public.

What you want are books and papers on `developable' surfaces.
Look in a good technical library for books on algebraic geometry.
Most of the good ones will probably be from earlier than about 1950.

Also try the Naval Architecture literature.

BTW, in order for a surface to be developable it must be
`singularly' curved. Basketballs and baseballs do not qualify.
They are doubly curved and depend on the flexibility of the material
in order to `wrap' the flat piece around the sphere.

Dave Rogers

 
 
 

Unfolding curved surfaces => flat surfaces

Post by Milan Novac » Sat, 05 Mar 1994 01:11:33




>!Leather basketballs and baseballs unfold to two hourglass like flat 2d shapes.
>  ...

>What you want are books and papers on `developable' surfaces.
>  ...
>BTW, in order for a surface to be developable it must be
>`singularly' curved. Basketballs and baseballs do not qualify.
>They are doubly curved and depend on the flexibility of the material
>in order to `wrap' the flat piece around the sphere.

Yes, that is a hard part of the problem.  You need to _sensibly_ distort
the material (surface) in the non-developable case.

Any papers on that - might be worth posting pointers to; i'm interested.

 
 
 

Unfolding curved surfaces => flat surfaces

Post by Brian Sun Yue M » Wed, 09 Mar 1994 16:45:21




: !Leather basketballs and baseballs unfold to two hourglass like flat 2d shapes.
: !
: !Can anyone point me to any papers, or example code (C is best for me) for
: !deriving the 2d flat shapes given the 3d shapes as splines (or any other
: !input)?
: !
: !This is sometimes refered to as unfolding or transitioning algorithms.  I know
: !that it is used in ship-building,  sail-making,  tent-making,
: !and clothes-making industries.  Some of the above industries act like the
: !algorithms are trade secrets and what to charge big BIG bucks for the software.
: !I just can't believe there is not a published paper out there somewhere that
: !describes this to the public.
:
: What you want are books and papers on `developable' surfaces.
: Look in a good technical library for books on algebraic geometry.
: Most of the good ones will probably be from earlier than about 1950.
:
: Also try the Naval Architecture literature.
:
: BTW, in order for a surface to be developable it must be
: `singularly' curved. Basketballs and baseballs do not qualify.
: They are doubly curved and depend on the flexibility of the material
: in order to `wrap' the flat piece around the sphere.
:
: Dave Rogers
I am also very interested in the problems:
        I wonder there is any classical books or papers or surver materials
        on the topics *Unfolding Algorithms*


Thanks in Advance!

Brian :)

 
 
 

Unfolding curved surfaces => flat surfaces

Post by Joseph O'Rour » Wed, 09 Mar 1994 20:42:58



Quote:>    I wonder there is any classical books or papers or surver materials
>    on the topics *Unfolding Algorithms*

I have little to add to the current thread, but I thought this might
be an appropriate place to mention an old outstanding open problem:
Can every convex polyhedron but cut along edges and laid flat in one
piece without overlap?  I worked * this myself, but only made
progress on related questions when the cuts are permitted to slice
through faces (citation below).  I am always on the lookout for information
on the polyhedron unfolding problem, in case anyone has references.

, author =      "B. Aronov and J. O'Rourke"
, title =       "Nonoverlap of the star unfolding"
, journal =     "Discrete Comput. Geom."
, volume =      8
, pages =       "219--250"
, keywords =    "polytopes, shortest paths, Voronoi diagrams, edge sequences"
Quote:}

 
 
 

Unfolding curved surfaces => flat surfaces

Post by Kirk Hall » Thu, 10 Mar 1994 02:52:31




> :
> : BTW, in order for a surface to be developable it must be
> : `singularly' curved. Basketballs and baseballs do not qualify.
> : They are doubly curved and depend on the flexibility of the material
> : in order to `wrap' the flat piece around the sphere.
> :
> : Dave Rogers
> I am also very interested in the problems:
>    I wonder there is any classical books or papers or surver materials
>    on the topics *Unfolding Algorithms*


> Thanks in Advance!

> Brian :)

As Prof. Rogers stated, unless one wants to allow deformations in the  
material being "unfolded", the surface must be developable. Haller and  
Heisey have look at this in the special case were the material was woven  
fabric. I suspect that some understanding of the relationship between the  
Gaussian curvature and distance of the surface from the set of all  
developable surfaces is key to tackling this problem.

If you are interested in "unfolding" a developable surface, you should  
look at

author =      "Erwin Kreyszig"
title =       "A New Standard Isometry of Developable Surfaces in CAD/CAM"
journal =     "SIAM J. Math. Anal."
volume =      25
pages =       "174-178"
keywords =    "developable surface, isometric mapping into the plane"

Kirk Haller

 
 
 

1. How to curve a flat surface.

1. make the cube

2. subdivide the top as much as you dare to

3. use the magnet tool to pull the top up in a curve as much as you
need.

This is, of course, just one of many ways that this could be done.

Dave Paige
Alfheim Imaging

2. DXF to GDSII convertor???

3. Map a planar surface onto a curved surface

4. 3D-MODELS, Download, Pictures, Animations -- Jobs -- G?lls

5. Looking for Mercator World Map

6. Surface->Curves possible in Lightwave?

7. Arbitrary dot surface -> line/mesh surface

8. Implicit Surface -> Parameter Surface

9. Flat Surface Reflection problem

10. PRMan flat surface reflections

11. simulate image projected on a non-flat surface?