Abstract 
This thesis presents a new algorithm for material boundary interface reconstruction from data sets containing volume fractions. The reconstruction problem is transformed to a problem that analyzes the dual data set, where each vertex in the dual mesh has an associated barycentric coordinate tuple that represents the fraction of each material present. After constructing the dual tetrahedral mesh from the original mesh, material boundaries are constructed by mapping a tetrahedron into barycentric space and calculating
the intersections with Voronoi cells in barycentric space. These intersections are mapped back to the original physical space and triangulated to form the boundary surface approximation. This algorithm can be applied to any grid structure and can treat any number of materials per element/vertex. It is a generalization of previous work done in other fields, allowing for any number of materials to be present in a given volume. This algorithm generates continuous surfaces. Experimental results shows the preservation of overall volume fractions within a difference range of 0.5
