We present a novel, topology-adaptive method for deformable interface tracking, called the Deformable Simplicial Complex (DSC). In the DSC method, the interface is represented explicitly as a piecewise linear curve (in 2D) or surface (in 3D) which is a part of a discretization (triangulation/tetrahedralization) of the space, such that the interface can be retrieved as a set of faces separating triangles/tetrahedra marked as inside from the ones marked as outside (so it is also given implicitly). This representation allows robust topological adaptivity and, thanks to the explicit representation of the interface, it suffers only slightly from numerical diffusion. Furthermore, the use of an unstructured grid yields robust adaptive resolution. Also, topology control is simple in this setting. We present the strengths of the method in several examples: simple geometric flows, fluid simulation, point cloud reconstruction, and cut locus construction.
Bibliographical note© ACM, 2012. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in A C M Transactions on Graphics, 31, 3, (May 2012) http://doi.acm.org/10.1145/2167076.2167082