Fraction Data and Function Fields

While the scientific visualization community is comfortable with isosurfacing and volume rendering of scalar fields, data from simulations and sensors often have additional constraints or dimensions that are not easily handled by these algorithms. In the first part of this dissertation we consider volume fraction data and the material interface reconstruction problem, for which existing isosurfacing and segmentation methods do not produce satisfactory results. Optimization-based methods are introduced that produce accurate multimaterial segmenting surfaces through volume fraction data. In the second part, we discuss visualization techniques for function fields. A dimension reduction approach based upon probing and range-space segmentation is introduced, allowing function fields to be analyzed with traditional visualization algorithms. Finally, queries are considered for explicit feature extraction.