On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
Geometric modeling with conical meshes and developable surfaces
ACM SIGGRAPH 2006 Papers
Geometry of multi-layer freeform structures for architecture
ACM SIGGRAPH 2007 papers
Focal surfaces of discrete geometry
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Freeform surfaces from single curved panels
ACM SIGGRAPH 2008 papers
ACM SIGGRAPH 2009 papers
General planar quadrilateral mesh design using conjugate direction field
Proceedings of the 2011 SIGGRAPH Asia Conference
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Two-parameter families of straight lines (line congruences) are implicitly present in graphics and geometry processing in several important ways including lighting and shape analysis. In this paper we make them accessible to optimization and geometric computing, by introducing a general discrete version of congruences based on piecewise-linear correspondences between triangle meshes. Our applications of congruences are based on the extraction of a so-called torsion-free support structure, which is a procedure analogous to remeshing a surface along its principal curvature lines. A particular application of such structures are freeform shading and lighting systems for architecture. We combine interactive design of such systems with global optimization in order to satisfy geometric constraints. In this way we explore a new area where architecture can greatly benefit from graphics.