Research issues in vector and tensor field visualization

Flow visualization motivates to a large extent recent research efforts in scientific visualization. The continuous improvement of resources for data generation and analysis allows researchers and engineers to produce large multivariate 3D data sets with improving speed and accuracy. Analyzing and interpreting such datasets without appropriate tools is beyond the capability of the human brain. Scientific visualization and flow visualization in particular aim to provide such tools. The approach we advocate is to follow a visualization process involving data preprocessing, visualization mapping, and rendering. We address the issues related to the second step, namely visualization mappings of vector and tensor data in flow fields. We place this process in perspective to other fields of scientific study by taking the point of view of representation theory. This allows us to classify visualization techniques and to provide a unified framework for analyzing various vector and tensor mappings