@inproceedings{309922caaa0248e7a7c04d9da2750246,

title = "Efficient Antialiased Rendering of 3-D Linear Fractals",

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.",

keywords = "Covers, Fractal, Object instancing, Procedural modeling, Ray tracing",

author = "Hart, {John C.} and Defanti, {Thomas A.}",

year = "1991",

month = jul,

day = "1",

doi = "10.1145/122718.122728",

language = "English (US)",

isbn = "0897914368",

series = "Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1991",

publisher = "Association for Computing Machinery, Inc",

pages = "91--100",

booktitle = "Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1991",

note = "18th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1991 ; Conference date: 27-04-1991 Through 30-04-1991",

}