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Discrete Line Congruences for Shading and Lighting
Author(s) -
Wang J.,
Jiang C.,
Bompas P.,
Wallner J.,
Pottmann H.
Publication year - 2013
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.12172
Subject(s) - congruence relation , computer science , curvature , polygon mesh , computer graphics (images) , gravitational singularity , graphics , line (geometry) , piecewise , computer graphics , congruence (geometry) , geometry , topology (electrical circuits) , mathematics , pure mathematics , mathematical analysis , combinatorics
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.