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[Japanese]

Optimized Topological Surgery
for Unfolding 3D Meshes

Shigeo Takahashi, Hsiang-Yun Wu, Seow Hui Saw,
Chun-Cheng Lin, and Hsu-Chun Yen

The 19th Pacific Conference on Computer Graphics and Applications
(Pacific Graphics 2011)

This web page is tentatively prepared for providing research materials of our mesh unfolding project. The page will be further rearranged in near future.


Unfolded patterns

Our mesh unfolding technique transforms an input 3D mesh into a single connected patch, which significantly facilitates us to construct the corresponding papercraft model. The boundary edges of the unfolded patch are rendered by arrows of different colors so that users can easily identify the correspondence between a pair of duplicated seams together with their directions. The mathematical concept of topological surgery guarantees that we can always find at least one such pair of duplicated seams that are next to each other on the boundary of the unfolded patch, thus we can easily construct the papercraft model just by stitching them one by one until all the seams are closed.   (You can click the thumbmail image for that of the original resolution.)

bunny (128 faces)
bunny (128 faces)
with labels
bunny (348 faces)
horse (312 faces)
dragon (344 faces)
hand (336 faces)
armagillo (386 faces)
moneybox (392 faces)
pooh (392 faces)
tower (412 faces)
mario (420 faces)
knot (480 faces)
chess (496 faces)
bumpy (528 faces)
snail (574 faces)
cat (702 faces)
fish (950 faces)


Sample source code

We like to make our program source available for those who are interested in our work. The program may be updated when necessary. We are not responsible for the future maintainance of this program while we will accept any feedback on the program code.  
  • Source code (206KB)
    This source code can be complied on Linux and Mac systems using g++, and can work on Windows systems using Visual Studio enviroment. Note that the code is based on OpenGL, OpenCV, CGAL(Computational Geometry Algorithm Library), BGL(Boost Graph Library), GSL(GNU Scientific Library) libraries.
  • Windows executable (4068KB)
    This is prepared for a demonstration purpose only. We noticed that unfolded patterns obtained using this executable version are not as good as those obtained using the one complied on the Unix platform. We recommend you to complie the source code on the Unix platform to create the fully elaborated version.

Paper & Video

Shigeo Takahashi, Hsiang-Yun Wu, Seow Hui Saw, Chun-Cheng Lin, and Hsu-Chun Yen, Optimized Topological Surgery for Unfolding 3D Meshes, to appear in Computer Graphics Forum (Proceedings of the 19th Pacific Conference on Computer Graphics and Applications (Pacific Graphics 2011), Vol. 30, No. 7, pp. 2077-2086, 2011. Paper-preprint (PDF, 5.3MB), Video(MOV, 19MB)

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