 
Summary: Interpolation over Light Fields
with Applications in Computer Graphics
F. Betul Atalay
David M. Mount
Abstract
We present a data structure, called a ray interpolant tree, or RItree, which stores a discrete set of
directed lines in 3space, each represented as a point in 4space. Each directed line is associated with
some small number of continuous geometric attributes. We show how this data structure can be used for
answering interpolation queries, in which we are given an arbitrary ray in 3space and wish to interpolate
the attributes of neighboring rays in the data structure. We illustrate the practical value of the RItree
in two applications from computer graphics: ray tracing and volume visualization. In particular, given
objects defined by smooth curved surfaces, the RItree can produce highquality renderings significantly
faster than standard methods. We also investigate a number of tradeoffs between the space and time used
by the data structure and the accuracy of the interpolation results.
1 Introduction
There is a growing interest in algorithms and data structures that combine elements of discrete algorithm
design with continuous mathematics. This is particularly true in computer graphics. Consider for example
the process of generating a photorealistic image. The most popular method for doing this is raytracing
[18]. Raytracing models the light emitted from light sources as traveling along rays in 3space. The color of
a pixel in the image is a reconstruction of the intensity of light traveling along various rays that are emitted
