M.Sc Thesis | |

M.Sc Student | Massarwa Fady |
---|---|

Subject | Papercrafts from 3D Polygonal Models |

Department | Department of Computer Science |

Supervisors | PROF. Chaim Craig Gotsman |

PROF. Gershon Elber | |

Full Thesis text |

A developable surface has the property that it can be obtained by a length preserving transformation from a plane, Equivalently, it is a surface that can be generated by transforming a plane without metric distortion (i.e., folding, bending, rolling). Since developable surfaces can be constructed by bending a flat sheet, they are important in the manufacturing of objects from sheet metal, cardboard, material, paper and plywood. Developable surfaces are used extensively as building primitives in the shipbuilding and aircraft manufacturing industry.

In this work, we present an algorithm for approximating a general 2-manifold 3D mesh by a set of developable surfaces. Each developable surface is a generalized cylinder represented as a strip of triangles not necessarily taken from the original mesh.

The algorithm consists of three stages. In the first stage the mesh is
segmented into meaningful components; in the second stage, each mesh component
is approximated by a set of piece-wise developable triangle strips; and in the
last stage, the approximating strips are unfolded, producing the final flat
strips. Our algorithm is automatic, creates smooth and easy-to-assemble
pieces, and provides *L** _{ยต}*
global error bounds. The approximation quality is controlled by a user-supplied
parameter specifying the allowed Hausdorff distance between the input mesh and
its piecewise-developable approximation. The strips generated by our algorithm
may be parameterized to conform to the parameterization of the original mesh,
if given, to facilitate texture mapping. We demonstrate by physically
assembling papercraft models from the strips generated by the proposed schema
when run on several polygonal 3D mesh data sets.