A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Approximate nearest neighbor queries in fixed dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Computational Line Geometry
Variational shape approximation
ACM SIGGRAPH 2004 Papers
A planar-reflective symmetry transform for 3D shapes
ACM SIGGRAPH 2006 Papers
Partial and approximate symmetry detection for 3D geometry
ACM SIGGRAPH 2006 Papers
Geometric modeling with conical meshes and developable surfaces
ACM SIGGRAPH 2006 Papers
ACM SIGGRAPH 2007 papers
Geometry of multi-layer freeform structures for architecture
ACM SIGGRAPH 2007 papers
Discovering structural regularity in 3D geometry
ACM SIGGRAPH 2008 papers
Freeform surfaces from single curved panels
ACM SIGGRAPH 2008 papers
Procedural modeling of structurally-sound masonry buildings
ACM SIGGRAPH Asia 2009 papers
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
ACM SIGGRAPH 2010 papers
Triangle surfaces with discrete equivalence classes
ACM SIGGRAPH 2010 papers
Quadric surface extraction by variational shape approximation
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
ACM SIGGRAPH 2010 papers
Triangle surfaces with discrete equivalence classes
ACM SIGGRAPH 2010 papers
ACM SIGGRAPH 2011 papers
SMI 2011: Full Paper: Cyclic twill-woven objects
Computers and Graphics
General planar quadrilateral mesh design using conjugate direction field
Proceedings of the 2011 SIGGRAPH Asia Conference
Darboux cyclides and webs from circles
Computer Aided Geometric Design
Beady: interactive beadwork design and construction
SIGGRAPH Asia 2011 Sketches
Beady: interactive beadwork design and construction
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Guided exploration of physically valid shapes for furniture design
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Position-correcting tools for 2D digital fabrication
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Rationalization of Triangle-Based Point-Folding Structures
Computer Graphics Forum
Structural optimization of 3D masonry buildings
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Reciprocal frame structures made easy
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Designing unreinforced masonry models
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
ACM Transactions on Graphics (TOG)
Smooth surfaces from rational bilinear patches
Computer Aided Geometric Design
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The emergence of large-scale freeform shapes in architecture poses big challenges to the fabrication of such structures. A key problem is the approximation of the design surface by a union of patches, so-called panels, that can be manufactured with a selected technology at reasonable cost, while meeting the design intent and achieving the desired aesthetic quality of panel layout and surface smoothness. The production of curved panels is mostly based on molds. Since the cost of mold fabrication often dominates the panel cost, there is strong incentive to use the same mold for multiple panels. We cast the major practical requirements for architectural surface paneling, including mold reuse, into a global optimization framework that interleaves discrete and continuous optimization steps to minimize production cost while meeting user-specified quality constraints. The search space for optimization is mainly generated through controlled deviation from the design surface and tolerances on positional and normal continuity between neighboring panels. A novel 6-dimensional metric space allows us to quickly compute approximate inter-panel distances, which dramatically improves the performance of the optimization and enables the handling of complex arrangements with thousands of panels. The practical relevance of our system is demonstrated by paneling solutions for real, cutting-edge architectural freeform design projects.