M.Sc Thesis

M.Sc StudentMassarwa Fady
SubjectPapercrafts from 3D Polygonal Models
DepartmentDepartment of Computer Science
Supervisors PROF. Chaim Craig Gotsman
PROF. Gershon Elber
Full Thesis textFull thesis text - English Version


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 Lยต 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.