Discrete Line Congruences for Shading and Lighting

Jun Wang, Caigui Jiang, Philippe Bompas, Johannes Wallner, Helmut Pottmann

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)53-62
Number of pages10
JournalComputer Graphics Forum
Issue number5
StatePublished - Aug 19 2013

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01

ASJC Scopus subject areas

  • Computer Networks and Communications


Dive into the research topics of 'Discrete Line Congruences for Shading and Lighting'. Together they form a unique fingerprint.

Cite this