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The paper presents an algorithm for material interface reconstruction for data sets where fractional material information is given as a percentage for each element of the underlying grid. The reconstruction problem is transformed to a problem that analyzes a dual grid, where each vertex in the dual grid has an associated barycentric coordinate tuple that represents the fraction of each material present. Material boundaries are constructed by analyzing the barycentric coordinate tuples of a tetrahedron in material space and calculating intersections with Voronoi cells that represent the regions where one material dominates. These intersections are used to calculate intersections in the Euclidean coordinates of the tetrahedron. By triangulating these intersection points, one creates the material boundary. The algorithm can treat data sets containing any number of materials. The algorithm can also create nonmanifold boundary surfaces if necessary. By clipping the generated material boundaries against the original cells, one can examine the error in the algorithm. Error analysis shows that the algorithm preserves volume fractions within an error range of 0.5 percent per material.