| Linear fractals are the fractal attractors of recurrent iterated function systems. Current computer graphics algorithms are not well suited for rendering such sets. This dissertation solves these problems by introducing new rendering methods designed specifically for linear fractals.;The new contributions to rendering linear fractals include: two methods for efficiently computing the intersection of a ray with a linear fractal, thereby solving the hidden surface problem; derivation of the bounds of the size of the projection of a pixel into object space, thereby eliminating the unnecessary computation of overly fine detail; two methods for computing an optimal initial bounding volume, thereby allowing arbitrary linear fractal models to be visualized; a method for shading the surface of a linear fractal, thereby producing orientation cues for surfaces lacking tangent planes; and a method for antialiased rasterization, thereby removing the jagged edges and twinkling pixels that often accompany fractal images and animations.;The dissertation begins with a formal treatment of the iterated function system model, the recurrent iterated function system model, fractals in general, and specifically linear fractals. Interactive and automatic methods for modeling objects as linear fractals are also described. |
