A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Interactive geometry remeshing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
A remeshing approach to multiresolution modeling
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
ACM SIGGRAPH 2008 papers
Freeform surfaces from single curved panels
ACM SIGGRAPH 2008 papers
Isotropic remeshing with fast and exact computation of Restricted Voronoi Diagram
SGP '09 Proceedings of the Symposium on Geometry Processing
ACM SIGGRAPH 2010 papers
Paneling architectural freeform surfaces
ACM SIGGRAPH 2010 papers
Triangle surfaces with discrete equivalence classes
ACM SIGGRAPH 2010 papers
Editing operations for irregular vertices in triangle meshes
ACM SIGGRAPH Asia 2010 papers
Hexagonal Global Parameterization of Arbitrary Surfaces
IEEE Transactions on Visualization and Computer Graphics
Designing unreinforced masonry models
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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In mechanical engineering and architecture, structural elements with low material consumption and high load-bearing capabilities are essential for light-weight and even self-supporting constructions. This paper deals with so called point-folding elements – non-planar, pyramidal panels, usually formed from thin metal sheets, which exploit the increased structural capabilities emerging from folds or creases. Given a triangulated free-form surface, a corresponding point-folding structure is a collection of pyramidal elements basing on the triangles. User-specified or material-induced geometric constraints often imply that each individual folding element has a different shape, leading to immense fabrication costs. We present a rationalization method for such structures which respects the prescribed aesthetic and production constraints and finds a minimal set of molds for the production process, leading to drastically reduced costs. For each base triangle we compute and parametrize the range of feasible folding elements that satisfy the given constraints within the allowed tolerances. Then we pose the rationalization task as a geometric intersection problem, which we solve so as to maximize the re-use of mold dies. Major challenges arise from the high precision requirements and the non-trivial parametrization of the search space. We evaluate our method on a number of practical examples where we achieve rationalization gains of more than 90%. © 2012 Wiley Periodicals, Inc.