Institute for Data Analysis and Visualization

Visualization of scattered data over a volumetric spatial domain is often done by reconstructing a trivariate function on some grid using scattered data interpolation methods and visualizing the function using standard visualization techniques. Scattered data reconstruction algorithms are often computationally expensive and difficult to implement. In order to visualize streaming scattered data, where visualization needs to take place in real time while new data is constantly streaming in, efficient approaches to scattered data reconstruction are required. We present a general framework for scattered data interpolation operating on discrete domains. Since common visualization methods require an underlying grid, it suffices to compute the scattered data reconstruction over the same grid. The key idea for speeding up the reconstruction is a re-factorization of the algorithm. The re-factorized version is designed such that it easily maps to graphics hardware architectures exploiting their performance and parallelism. Moreover, it naturally extends to applications for streaming data. As a proof of concept, we have implemented inverse-distance-weighted interpolation, natural neighbor interpolation, and radial Hermite interpolation using our general framework. We apply the framework to two kinds of streaming data: progressive scattered data and real-time sensor data with moving sensors delivering asynchronous measurements. To account for the scattered spatial and temporal distribution of streaming sensor data, we use a four-dimensional extension of our framework, which elegantly handles representation of time-varying data and leads to reconstructions that are smooth in both space and time.