| There have been many effective methods developed for scattered data interpolation. However, most of them do not consider the fact that some scattered data have certain geometric structures. In oil exploration and mining applications, data are often sampled at varying depths in arbitrarily located wells. This type of track data may also occur in a 2D planar domain. In some applications, data may be sampled over some specified time interval. Thus, time-dependent scattered data are generated. To interpolate these types of data effectively, special interpolation methods are needed which consider the existence of the structures in the data. In this dissertation, special interpolation methods are presented to interpolate these types of scattered data. The special methods are compared with general-purpose interpolation methods.;In addition to representing track and time-dependent scattered data with special multivariate interpolants, techniques for visualizing multiple sets of volumetric data will also be presented. Although there are many techniques for rendering volumetric data, most of them can only render one set of volumetric data at a time. It is very common to sample several different types of data in the same volumetric space. For example, temperature, pressure, and density may be sampled at the specified locations in a volume. The multi-valued visualization techniques are used to render several sets of volumetric data simultaneously. Some of these data sets are special multivariate interpolants of well-log data. |
