 
Summary: Interpolation over Light Fields
with Applications in Computer Graphics£
F. Betul AtalayÝ
David M. MountÞ
Abstract
We present a data structure, called a ray interpolant tree, or RI
tree, 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 interpo
lation 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 vi
sualization. In particular, given objects defined by smooth curved
surfaces, the RItree can produce highquality renderings signifi
cantly 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
