Efficient Antialiased Rendering of 3-D Linear Fractals

John C. Hart, Thomas A. Defanti

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Object instancing is the efficient method of representing an hierarchical object with a directed graph instead of a tree. If this graph contains a cycle then the object it represents is a linear fractal. Linear fractals are difficult to render for three specific reasons: (J) ray-fractaJ intersec-tion is not trivial, (2) surface normals are undefined and (3) the object aliases at all sampling resolutions. Ray-fractal intersections are efficiently approximated to sub-pixel accuracy using procedural bounding volumes and a careful determination of the size of a pixel, giving the perception that the surface is infinitely detailed. Furthermore, a surface normal for these non-differentiable surfaces is defined and analyzed. Finally, the concept of antialiasing "covers" is adapted and used to solve the problem of sampling fractal surfaces. An initial bounding volume estimation method is also described, allowing a linear fractal to be rendered given only its iterated function system. A parallel implementation of these methods is described and applications of these results to the rendering of other fractal models are given.

Original languageEnglish (US)
Title of host publicationProceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1991
PublisherAssociation for Computing Machinery, Inc
Pages91-100
Number of pages10
ISBN (Print)0897914368, 9780897914369
DOIs
StatePublished - Jul 1 1991
Event18th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1991 - Providence, United States
Duration: Apr 27 1991Apr 30 1991

Publication series

NameProceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1991

Other

Other18th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1991
CountryUnited States
CityProvidence
Period4/27/914/30/91

Keywords

  • Covers
  • Fractal
  • Object instancing
  • Procedural modeling
  • Ray tracing

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design

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  • Cite this

    Hart, J. C., & Defanti, T. A. (1991). Efficient Antialiased Rendering of 3-D Linear Fractals. In Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1991 (pp. 91-100). (Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1991). Association for Computing Machinery, Inc. https://doi.org/10.1145/122718.122728