@techreport{kno-hij-ken-sch-han-hag-07-aa-gpuray,
  title = {Fast and Robust Ray Tracing of General Implicits on the {GPU}},
  author = {Aaron Knoll and Younis Hijazi and Andrew Kensler and Mathias Schott and Charles Hansen and Hans Hagen},
  year = 2007,
  institution = {University of Utah},
  number = {UUSCI-2007-014},
  comment = {Reduced AA},
  abstract = {Existing methods for rendering arbitrary implicit functions are limited, either in performance, correctness or flexibility. Ray tracing methods in conjunction with an inclusion algebra such as interval arithmetic (IA) or affine arithmetic (AA) have historically proven robust and flexible, but slow. In this paper, we present a new stackless ray traversal algorithm optimized for modern graphics hardware, and a correct inclusion-preserving reduced affine arithmetic (RAA) suitable for fragment shader languages. Shader metaprogramming allows for immediate and automatic generation of functions and their interval or affine extensions, enhancing user interaction. Ray tracing lends itself to multi-bounce effects, such as shadows and depth peeling, which are useful modalities for visualizing complicated implicit functions. With this system, we are able to render even complex implicits correctly, in real-time at high resolution.}
}