Making contour trees subdomain-aware

time, where is the size of the input mesh and is the total number of critical points of the scalar field and of the restriction of to . We show how to use our algorithm to label the edges of the contour tree of a 3D scalar field with complete information on the topology of the corresponding contours in time. Contour trees (CTs) are considered an important tool allowing one to concisely describe the structure of isosurfaces in volume data as well as the way they evolve and interact as the isovalue is varied. A CT can be defined as a quotient space where is the domain of a scalar field and, for , if and only if and belong to the same contour, i.e. a connected component of a set of the form for some scalar . A scalar field is typically represented as a simplicial complex with values at vertices or a regular (rectilinear) grid of samples. Linear or multilinear interpolation is used to obtain values at points other than the samples. Most scalar fields that appear in applications are define d on simply connected domains. In this case the CT is indeed a tree. Contour trees been used as a tool to enhance scalar field visualization [1], speed up certain types of queries in geographical information systems [2] and facilitate isosurface extraction from volume datasets by helping to compute small seed sets [5, 6]. These applications motivated efforts to develop increasingly simpler, faster and more general algorithms for computing contour trees. An algo