Discrete Line Congruences for Shading and Lighting

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 ver...

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Bibliographic Details
Published in:Computer graphics forum 2013-08, Vol.32 (5), p.53-62
Main Authors: Wang, J., Jiang, C., Bompas, P., Wallner, J., Pottmann, H.
Format: Article
Language:English
Subjects:
Architecture
Computer graphics
Computer Graphics [I.3.5]: Computational Geometry and Object Modeling
Computer science
Congruences
Curvature
Illumination
Lighting
Optimization
Shading
Straight lines
Studies
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Summary: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.
ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12172