### 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 language | English (US) |
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Title of host publication | Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1991 |

Publisher | Association for Computing Machinery, Inc |

Pages | 91-100 |

Number of pages | 10 |

ISBN (Print) | 0897914368, 9780897914369 |

DOIs | |

State | Published - Jul 1 1991 |

Event | 18th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1991 - Providence, United States Duration: Apr 27 1991 → Apr 30 1991 |

### Publication series

Name | Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1991 |
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### Other

Other | 18th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1991 |
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Country | United States |

City | Providence |

Period | 4/27/91 → 4/30/91 |

### 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

*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