The mapping of images onto surfaces may substantially increase the realism and information content of computer-generated imagery. The projection of a flat source image onto a curved surface may involve sampling difficulties, however, which are compounded as the view of the surface changes. As the projected scale of the surface increases, interpolation between the original samples of the source image is necessary; as the scale is reduced, approximation of multiple samples in the source is required. Thus a constantly changing sampling window of view-dependent shape must traverse the source image. To reduce the computation implied by these requirements, a set of prefiltered source images may be created. This approach can be applied to particular advantage in animation, where a large number of frames using the same source image must be generated. This paper advances a "pyramidal parametric " prefiltering and sampling geometry which minimizes aliasing effects and assures continuity within and between target images. Although the mapping of texture onto surfaces is an excellent example of the process and provided the original motivation for its development, pyramidal parametric data structures admit of wider application. The aliasing of not only surface texture, but also highlights and even the surface representations themselves, may be minimized by pyramidal parametric means.

This paper appeared in IEEE Computer Graphics and Applications, Nov. 1986, pp. 56-67. An earlier version of thi aper appeared in Graphics Interface '86, May 1986, pp. 207-212. This postscript version is missing all of the paste-up -

Filtering is an essential but costly step in many computer graphics applications, most notably in texture mapping. Several techniques have been previously developed which allow prefiltering of a texture (or in general an image) in time that is independent of the number of texture elements under the filter kernel. These are limited, however, to space-invariant kernels whose shape in texture space is the same independently of their positions, and usually are also limited to a small range of filters. We present here a technique that permits constant-time filtering for space-variant kernels. The essential step is to approximate a filter surface in texture space by a sum of suitably-chosen basis functions. The convolution of a filter with a texture is replaced by the weighted sum of the convolution of the basis functions with the texture, which can be precomputed. To achieve constant time, convolutions with the basis functions are computed and stored in a pyramidal fashion, and the right le...

Blinn and Newell introduced reflection maps for computer simulated mirror highlights. This paper extends their method to cover a wider class of reflectance models. Panoramic images of real, painted and simulated environments are used as illumination maps that are convolved (blurred) and transformed to create reflection maps. These tables of reflected light values are used to efficiently shade objects in an animation sequence. Shaders based on point illumination may be improved in a straightforward manner to use reflection maps. Shading is by table-lookup, and the number of calculations per pixel is constant regardless of the complexity of the reflected scene. Antialiased mapping further improves image quality. The resulting pictures have many of the reality cues associated with ray-tracing but at greatly reduced computational cost. The geometry of highlights is less exact than in ray-tracing, and multiple surface reflections are not explicitly handled. The color of diffuse reflections can be rendered more accurately than in ray-tracing.

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