## 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.## Additional Files and Images

## Weblinks

No further information available.## 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/", }