Robert L. Cook, John Halstead, Maxwell Planck, David Ryu
May 2007
Many renderers perform poorly on scenes that contain a lot of detailed geometry. The load on the renderer can be alleviated by simplification techniques, which create less expensive representations of geometry that is small on the screen. Current simplification techniques for high-quality surface-based rendering tend to work best with element detail (i.e., detail due to the complexity of individual elements) but not as well with aggregate detail (i.e., detail due to the large number of elements). To address this latter type of detail, we introduce a stochastic technique related to some approaches used for point-based renderers. Scenes are rendered by randomly selecting a subset of the geometric elements and altering those elements statistically to preserve the overall appearance of the scene. The amount of simplification can depend on a number of factors, including screen size, motion blur, and depth of field.
Additional materials: [SiggraphSlides.pdf], [WithAndWithoutSimplification.mov]
Available in the Proceedings of Siggraph 2007.
Available as Pixar Technical Memo #06-05a
Other versions:
Robert L. Cook, Tony DeRose
August 2005
Noise functions are an essential building block for writing procedural shaders in 3D computer graphics. The original noise function introduced by Ken Perlin is still the most popular because it is simple and fast, and many spectacular images have been made with it. Nevertheless, it is prone to problems with aliasing and detail loss. In this paper we analyze these problems and show that they are particularly severe when 3D noise is used to texture a 2D surface. We use the theory of wavelets to create a new class of simple and fast noise functions that avoid these problems.
Additional materials: [RapLyrics.txt]
Available in the Proceedings of SIGGRAPH 2005
William T. Reeves, David H. Salesin, Robert L. Cook
July 1987
We present a solution to the aliasing problem for shadow algorithms that use depth maps. The solution is based on a new filtering technique called percentage closer filtering. In addition to antialiasing, the improved algorithm provides soft shadow boundaries that resemble penumbrae. We describe the new algorithm in detail, demonstrate the effects of its parameters, and analysze its performance.
Available in the Proceedings of SIGGRAPH 1987.
Robert L. Cook, Loren Carpenter, Edwin Catmull
July 1987
An architecture is presented for fast high-quality rendering of complex images. All objects are reduced to common world-space geometric entities called micropolygons, and all of the shading and visibility calculations operate on these micropolygons. Each type of calculation is performed in a coordinate system that is natural for that type of calculation. Micropolygons are created and textured in the local coordinate system of the object, with the result that texture filtering is simplified and improved. Visibility is calculated in screen space using stochastic point sampling with a z buffer. There are no clipping or perspective calculations. Geometric and texture locality are exploited to minimize paging and to support models that contain arbitrarily many primitives.
Robert L. Cook
January 1986
Ray tracing, ray casting, and other forms of point sampling are important techniques in computer graphics, but their usefulness has been undermined by aliasing artifacts. In this paper it is shown that these artifacts are not an inherent part of point sampling, but a consequence of using regularly spaced samples. If the samples occur at appropropriate nonuniformly spaced locations, frequencies above the Nyquist limit do not alias, but instead appear as noise of the correct average intensity. This noise is much less objectionable to our visual system than aliasing. In ray tracing, the rays can be stochastically distributed to perform Monte Carlo evaluation of integrals in the rendering equation. This is called distributed ray tracing and can be used to simulate motion blur, depth of field, penumbrae, gloss, and translucency.
Available in ACM Transactions on Graphics, Volume 6, Number 1, January 1996.
Robert L. Cook, Thomas Porter, Loren Carpenter
July 1984
Ray tracing is one of the most elegant techniques in computer graphics. Many phenomena that are difficult or impossible with other techniques are simple with ray tracing, including shadows, reflections, and refracted light. Ray directions, however, have been determined precisely, and this had limited the capabilities of ray tracing. By distributing the directions of the rays according to the analytic function they sample, ray tracing can incorporate fuzzy phenomena. This provies correct and easy solutions to some previously unsolved or partially solved problems, including motion blur, depth of field, penumbras, translucency, and fuzzy reflections. Motion blur and depth of field calculations can be integrated with the visible surface calculations, avoiding the problems found in previous methods.
Available in the Proceedings of SIGGRAPH 1984
Robert L. Cook
July 1984
Shading is an important part of computer imagery, but shaders have been based on fixed models to which all surfaces must conform. As computer imagery becomes more sophisticated, surfaces have more complex shading characteristics and thus require a less rigid shading model. This paper presents a flexible tree-structured shading model that can represent a wide range of shading characteristics. The model provides an easy means for specifying complex shading characteristics. It is also efficient because it can tailor the shading calculations to each type of surface.
Available in the Proceedings of SIGGRAPH 1984.
Robert L. Cook, Kenneth E. Torrance
January 1982
A new reflectance model for rendering computer sythesized images is presented. The model accounts for the relative brightness of different materials and light sources in the same scene. It describes the directional distribution of the reflected light and a color shift that occurs as the reflectance changes with incidence angle. A method for obtaining the spectral energy distribution of the light relfected from an object made of a specific real material is presented, and a procedure for accurately reproducing the color associated with the spectral energy distribution is discussed. The model is applied to the simulation of a metal and a plastic.
Published in Transactions on Graphics, Vol. 1, No. 1, January 1982.