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Abstract

Superquadrics are well known and often used 3D surface objects in computer graphics. They are used for modelling parts of scenes that are then rendered using photorealistic image synthesis algorithms (e.g., ray tracing). For some techniques, like texturing, which are part of these rendering methods, the type of the parameterization of such a surface has to be chosen carefully and is not intuitively obvious at first sight. There are cases, where the straight forward extension of quadric parameterizations to superquadrics do not produce satisfying results. We therefore investigate a number of different parameterizations in combination with the corresponding formulas, and point out some significant differences between them.

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@techreport{Loeffelmann-1994-PSQ,
  title =      "Parameterizing Superquadrics",
  author =     "Helwig L{\"o}ffelmann and Meister Eduard Gr{\"o}ller",
  year =       "1994",
  abstract =   "Superquadrics are well known and often used 3D surface
               objects in computer graphics. They are used for modelling
               parts of scenes that are then rendered using photorealistic
               image synthesis algorithms (e.g., ray tracing).  For some
               techniques, like texturing, which are part of these
               rendering methods, the type of the parameterization of such
               a surface has to be chosen carefully and is not intuitively
               obvious at first sight. There are cases, where the straight
               forward extension of quadric parameterizations to
               superquadrics do not produce satisfying results. We
               therefore investigate a number of different
               parameterizations in combination with the corresponding
               formulas, and point out some                 significant
               differences between them.",
  address =    "Favoritenstrasse 9-11/186, A-1040 Vienna, Austria",
  institution = "Institute of Computer Graphics and Algorithms, Vienna
               University of Technology",
  note =       "human contact: technical-report@cg.tuwien.ac.at",
  month =      nov,
  number =     "TR-186-2-94-5",
  keywords =   "parameterization, quadrics, superquadrics",
  URL =        "http://www.cg.tuwien.ac.at/research/publications/1994/Loeffelmann-1994-PSQ/",
}