Groeller-1994-MRN

Information

• Publication Type: Technical Report
• Workgroup(s)/Project(s): not specified
• Date: November 1994
• Number: TR-186-2-94-12
• Keywords: Fractals, Iterated Functions Systems, nonlinear, Modeling, Rendering

Abstract

Iterated Function Systems are typically defined through sets of contractive linear transformations. The theory of Iterated Function Systems is based on the contractivity but not on the linearity of the defining functions. Piecewise bilinear distortions of grids are used in this work to specify nonlinear Iterated Function Systems. Nonlinear Iterated Functions Systems are characterized by a higher degree of flexibility and greater modeling capability than their linear counterparts. Modeling and rendering aspects are discussed. Limit sets of 2D nonlinear Iterated Function Systems are represented by approximating point sets. Limit sets of 3D nonlinear Iterated Function Systems are either rendered by displaying approximating point sets (z-buffer approach) or through ray tracing an approximate set of 3D solids. Example images of a test implementation are presented.

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BibTeX

@techreport{Groeller-1994-MRN,
  title =      "Modeling and Rendering of Nonlinear Iterated                
               Function Systems",
  author =     "Eduard Gr\"{o}ller",
  year =       "1994",
  abstract =   "Iterated Function Systems are typically defined through sets
               of contractive linear transformations. The theory of
               Iterated Function Systems is based on the contractivity but
               not on the linearity of the defining functions. Piecewise
               bilinear distortions of grids are used in this work to
               specify nonlinear Iterated Function Systems. Nonlinear
               Iterated Functions Systems are characterized by a higher
               degree of flexibility and greater modeling capability than
               their linear counterparts. Modeling and rendering aspects
               are discussed. Limit sets of 2D nonlinear Iterated Function
               Systems are represented by approximating point sets. Limit
               sets of 3D nonlinear Iterated Function Systems are either
               rendered by displaying approximating point sets (z-buffer
               approach) or through ray tracing an approximate set of 3D
               solids. Example images of a                 test
               implementation are presented.",
  month =      nov,
  number =     "TR-186-2-94-12",
  address =    "Favoritenstrasse 9-11/E193-02, A-1040 Vienna, Austria",
  institution = "Institute of Computer Graphics and Algorithms, Vienna
               University of Technology ",
  note =       "human contact: technical-report@cg.tuwien.ac.at",
  keywords =   "Fractals, Iterated Functions Systems, nonlinear, Modeling,
               Rendering",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/1994/Groeller-1994-MRN/",
}