Lightness functions

Publication: Research - peer-reviewJournal article

  • Stefano Campi
    Stefano CampiUiversity of SienaItaly
  • Richard Gardner
    Richard GardnerWestern Wahington UniversityUnited States
  • Paolo Gronchi
    Paolo GronchiUniversity of FlorenceItaly
  • Markus Kiderlen
Variants of the brightness function of a convex body K in n-dimensional Euclidean are investigated. The Lambertian lightness function L(K; v , w ) gives the total reflected light resulting from illumination by a light source at infinity in the direction w that is visible when looking in the direction v . The partial brightness function R( K ; v , w ) gives the area of the projection orthogonal to v of the portion of the surface of K that is both illuminated by a light source from the direction w and visible when looking in the direction v . A class of functions called lightness functions is introduced that includes L(K;.) and R(K;.) as special cases. Much of the theory of the brightness function like uniqueness, stability, and the existence and properties of convex bodies of maximal and minimal volume with finitely many function values equal to those of a given convex body, is extended to lightness functions.
Original languageEnglish
JournalAdvances in Mathematics
Issue number6
Pages (from-to)3118 - 3146
Number of pages29
StatePublished - 2012


  • convex body, brightness function, lightness function, illumination, shadow boundary, geometric tomography

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