"Andrea Tagliasacchi" <andrea.tagliasacchi@gmail.com> wrote in message
news:iqeo9h$kek$1@newscl01ah.mathworks.com...
> "Johannes Korsawe" wrote in message <i5qho2$ihh$1@fred.mathworks.com>...
>> Dear community,
>>
>> is there any tool to unwind (simply) warped (triangulated) 3d surfaces,
>> e.g. the surface shell of a cylinder (height h, radius r), which should
>> then result in a rectangle of height h and width 2*pi*r.
>>
>> I know that the resulting surface will be nonoverlapping only in some
>> cases, especially not in the case of bidirectional warped surfaces.
>>
>
> Beside for surface of (piecewise) zero gaussian curvature (developable
> surface)
> it's impossible to perfectly flatten a surface to a plane. On the other
> hand, if some distortion is allowed, you should look into the so-called
> "parametrization" problem.
>
> Yes, it's VERY not trivial. It's an entire field of research in applied
> math which has developed in the last 10 years. I would not suggest coming
> up with your own heuristic.. unless you want to re-discover the wheel.
>
> Read the parametrization chapter of this book for an easy introduction:
> http://www.pmp-book.org
If I understand what the OP is asking, the problem is even older and harder
than that even for the case of an object as simple as a sphere (well,
technically an oblate spheroid, but close enough) and there are many
different solutions depending on your goal.
http://en.wikipedia.org/wiki/Map_projection
Mapping Toolbox contains several dozen such projections.
http://www.mathworks.com/help/toolbox/map/ref/maplist.html
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Steve Lord
slord@mathworks.com
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