Discrete Line Congruences for Shading and Lighting
Article first published online: 19 AUG 2013
© 2013 The Author(s) Computer Graphics Forum © 2013 The Eurographics Association and John Wiley & Sons Ltd.
Computer Graphics Forum
Volume 32, Issue 5, pages 53–62, August 2013
How to Cite
Wang, J., Jiang, C., Bompas, P., Wallner, J. and Pottmann, H. (2013), Discrete Line Congruences for Shading and Lighting. Computer Graphics Forum, 32: 53–62. doi: 10.1111/cgf.12172
- Issue published online: 19 AUG 2013
- Article first published online: 19 AUG 2013
- Computer Graphics [I.3.5]: Computational Geometry and Object Modeling
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.