@techreport{TR-IC-06-11,
  number = {IC-06-11},
  author = {Arnaldo J. Montagner and Jorge Stolfi},
  title = {General convex hull using the gem data structure},
  month = {May},
  year = {2006}, 
  institution = {Institute of Computing, University of Campinas},
  note = {In English, 14 pages.
    \par\selectlanguage{english}\textbf{Abstract}
       We describe in detail a general algorithm for constructing the
       convex hull of a finite set of points in Euclidean space of
       arbitrary dimension $n$. The algorithm handles degenerate
       situations, such as non-simplicial faces and point sets
       contained in a lower-dimensional subspace. The topology of the
       hull is kept in a graph encoded map (gem) data structure, a
       novel representation for $n$-dimensional triangulations. The
       gem representation, which was introduced as a mathematical
       device by S. Lins in 1982, extends the cell-tuple (or
       generalized map) representation proposed by Brisson and
       Lienhardt to maps that are not barycentric subdivisions, to
       manifolds with borders, and to non-manifold (but triangulable)
       topological spaces.
  }
}