Mathematics Colloquia and Seminars

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The material interface problem is a simply-defined problem that has wide application in the visualization field. Simply stated, suppose we have $n$ materials in a data set, and for each cell in the data set, we are given the fraction of each material that occupies the cell. Can we, under some reasonable assumptions, calculate the boundary surface between the materials in the data set. This surface should be continuous, induce the same fractions for each cell, be quickly computable, and have "minimal" geometry. We will review several methods that attempt to solve this problem, and illustrate some new techniques. These methods are applicable in volume-of-fluid methods, neuroscience, and combustion visualization. We will also review some of the other research currently performed in the Institute for Data Analysis and Visualization at UC Davis.