“Making papercraft toys from meshes using strip-based approximate unfolding” by Mitani and Suzuki

We propose a new method for producing unfolded papercraft patterns of rounded toy animal figures from triangulated meshes by means of strip-based approximation. Although in principle a triangulated model can be unfolded simply by retaining as much as possible of its connectivity while checking for intersecting triangles in the unfolded plane, creating a pattern with tens of thousands of triangles is unrealistic. Our approach is to approximate the mesh model by a set of continuous triangle strips with no internal vertices. Initially, we subdivide our mesh into parts corresponding to the features of the model. We segment each part into zonal regions, grouping triangles which are similar topological distances from the part boundary. We generate triangle strips by simplifying the mesh while retaining the borders of the zonal regions and additional cut-lines. The pattern is then created simply by unfolding the set of strips. The distinguishing feature of our method is that we approximate a mesh model by a set of continuous strips, not by other ruled surfaces such as parts of cones or cylinders. Thus, the approximated unfolded pattern can be generated using only mesh operations and a simple unfolding algorithm. Furthermore, a set of strips can be crafted just by bending the paper (without breaking edges) and can represent smooth features of the original mesh models.

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