Constructing material interfaces from data sets with volume-fraction information

We present a new algorithm for material boundary interface reconstructionfrom data sets containing volume fractions. We transformthe reconstruction problem to a problem that analyzes the dual dataset, where each vertex in the dual mesh has an associated barycentriccoordinate tuple that represents the fraction of each materialpresent. After constructing the dual tetrahedral mesh from the originalmesh, we construct material boundaries by mapping a tetrahedroninto barycentric space and calculating the intersections withVoronoi cells in barycentric space. These intersections are mappedback to the original physical space and triangulated to form theboundary surface approximation. This algorithm can be appliedto any grid structure and can treat any number of materials per element/vertex.