efficient antialiased rendering of 3-d linear fractals
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: (1) ray-fractal intersection 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.
efficiency antialiasing aliasing rendering fractal object instancing object method hierarchic directed graph graph tree reasoning intersection surface normalization sampling accuracy procedure determinism size perception concept covers estimates functional systems parallel implementation applications model ray tracing procedural modeling