Making papercraft toys from meshes using strip-based approximate unfolding

Abstract

a) (b) (c) Figure 1. (a) Mesh models. (b) Making papercraft toys with a computer. (c) Papercraft toys of the mesh models. AbstractWe 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.

Learning to segment and unfold polyhedral mesh from failures

“…Comparatively, the models studied in the literature are all significantly smaller than ours. For example, two models with 270 faces and 200 faces are crafted by [4]. The most complex model in [10] has 347 faces and requires 25 h of crafting time.…”

“…For paper crafting, shape segmentation techniques were employed to simultaneously decompose and approximate the mesh into smaller pieces [4,7,5] such that the unfolding problem becomes solvable and the approximated 3D model can be obtained by assembling the folded shapes together. These approaches decompose the mesh into a few patches and approximate each patch with a strip, a generalized cylinder or a developable surface.…”

“…To ensure that a surface patch can be flattened, existing methods [4,5] either approximate the patch by developable surfaces or ensure that the patch forms a net, i.e., a patch that can be cut and flattened by rotating its facets along one of the incident edges without overlapping with other facets [6]. The flattened patches are then cut out of planar materials and folded back to 3D.…”

Constructing developable surfaces by wrapping cones and cylinders

“…A dual-space approach is mathematically elegant, but it requires significant geometric expertise for an intuitive shape control [2,6]. Many practical methods have been proposed for constructing developable surfaces from other representations, including point clouds [10,11], boundary curves [12,13] and polygonal meshes [4,5,14,15].…”

Computing ruled surfaces using weighted graph

“…See Fig.1 ((b), (c), (d), (e) and (f)) for an illustration, several basic ruled surfaces are presented. Ruled surfaces are also very ubiquitous in computer aided design and computer graphics such as papercraft toy fabrication [10], 3D model segmentation and parameterization [7], [16].…”