@article {13333,
	title = {Supercubes: A High-Level Primitive for Diamond Hierarchies},
	journal = {Visualization and Computer Graphics, IEEE Transactions on},
	volume = {15},
	year = {2009},
	month = {2009///},
	pages = {1603 - 1610},
	abstract = {Volumetric datasets are often modeled using a multiresolution approach based on a nested decomposition of the domain into a polyhedral mesh. Nested tetrahedral meshes generated through the longest edge bisection rule are commonly used to decompose regular volumetric datasets since they produce highly adaptive crack-free representations. Efficient representations for such models have been achieved by clustering the set of tetrahedra sharing a common longest edge into a structure called a diamond. The alignment and orientation of the longest edge can be used to implicitly determine the geometry of a diamond and its relations to the other diamonds within the hierarchy. We introduce the supercube as a high-level primitive within such meshes that encompasses all unique types of diamonds. A supercube is a coherent set of edges corresponding to three consecutive levels of subdivision. Diamonds are uniquely characterized by the longest edge of the tetrahedra forming them and are clustered in supercubes through the association of the longest edge of a diamond with a unique edge in a supercube. Supercubes are thus a compact and highly efficient means of associating information with a subset of the vertices, edges and tetrahedra of the meshes generated through longest edge bisection. We demonstrate the effectiveness of the supercube representation when encoding multiresolution diamond hierarchies built on a subset of the points of a regular grid. We also show how supercubes can be used to efficiently extract meshes from diamond hierarchies and to reduce the storage requirements of such variable-resolution meshes.},
	keywords = {(computer, adaptive, approach;nested, bisection, crack-free, datasets;computational, decomposition;nested, diamond, generation;rendering, geometry;mesh, graphics);, hierarchies;edge, mesh;supercubes;tetrahedra, meshes;polyhedral, representations;multiresolution, rule;highly, sharing;volumetric, tetrahedral},
	isbn = {1077-2626},
	doi = {10.1109/TVCG.2009.186},
	author = {Weiss,K. and De Floriani, Leila}
}
@conference {13335,
	title = {The half-edge tree: a compact data structure for level-of-detail tetrahedral meshes},
	booktitle = {Shape Modeling and Applications, 2005 International Conference},
	year = {2005},
	month = {2005/06//},
	pages = {332 - 337},
	abstract = {We propose a new data structure for the compact encoding of a level-of detail (LOD) model of a three-dimensional scalar field based on unstructured tetrahedral meshes. Such data structure, called a half-edge tree (HET), is built through the iterative application of a half-edge collapse, i.e. by contracting an edge to one of its endpoints. We also show that selective refined meshes extracted from an HET contain on average about 34\% and up to 75\% less tetrahedra than those extracted from an LOD model built through a general edge collapse.},
	keywords = {application;, compact, computational, data, detection;, edge, encoding;, generation;, geometry;, half-edge, iterative, level-of-detail, mesh, meshes;, methods;, model;, structure;, structures;, tetrahedral, tree, tree;},
	doi = {10.1109/SMI.2005.47},
	author = {Danovaro,E. and De Floriani, Leila and Magillo,P. and Puppo,E. and Sobrero,D. and Sokolovsky,N.}
}
@conference {13281,
	title = {Constant-time navigation in four-dimensional nested simplicial meshes},
	booktitle = {Shape Modeling Applications, 2004. Proceedings},
	year = {2004},
	month = {2004/06//},
	pages = {221 - 230},
	abstract = {We consider a recursive decomposition of a four-dimensional hypercube into a hierarchy of nested 4-dimensional simplexes, that we call pentatopes. The paper presents an algorithm for finding the neighbors of a pentatope along its five tetrahedral faces in constant time. To this aim, we develop a labeling technique for nested pentatopes that enables their identification by using location codes. The constant-time behavior is achieved through bit manipulation operations, thus avoiding traversing the simplicial hierarchy via pointer following. We discuss an application of this representation to multi-resolution representations of four-dimensional scalar fields. Extracting adaptive continuous approximations of the scalar field from such a model requires generating conforming meshes, i.e., meshes in which the pentatopes match along their tetrahedral faces. Our neighbor finding algorithm enables computing face-adjacent pentatopes efficiently.},
	keywords = {4-dimensional, adaptive, algorithm;, approximations;, bit, codes;, computational, constant-time, continuous, decomposition;, face-adjacent, faces;, fields;, finding, following;, four-dimensional, generation;, geometry;, hierarchy;, hypercube;, location, manipulation, mesh, meshes;, multiresolution, navigation;, neighbor, nested, operations;, pentatopes;, pointer, recursive, representation;, scalar, simplexes;, simplicial, tetrahedral},
	doi = {10.1109/SMI.2004.1314509},
	author = {Lee,M. and De Floriani, Leila and Samet, Hanan}
}
@conference {13317,
	title = {Multiresolution tetrahedral meshes: an analysis and a comparison},
	booktitle = {Shape Modeling International, 2002. Proceedings},
	year = {2002},
	month = {2002///},
	pages = {83 - 91},
	abstract = {We deal with the problem of analyzing and visualizing large-size volume data sets. To this aim, we consider multiresolution representations based on a decomposition of the field domain into tetrahedral cells. We compare two types of multiresolution representations that differ on the rule applied to refine an initial coarse mesh: one is based on tetrahedron bisection, and one based on vertex split. The two representations can be viewed as instances of a common multiresolution model, that we call a multiresolution mesh. Encoding data structures for the two representations are briefly described. An experimental comparison on structured volume data sets is presented},
	keywords = {(computer, bisection;vertex, cells;tetrahedron, data, generation;rendering, geometry;data, graphics);solid, meshes;rendering;tetrahedral, modelling;, refinement;multiresolution, representations;multiresolution, sets;mesh, split;computational, structures;data, tetrahedral, visualisation;mesh, visualization;experiment;large-size, volume},
	doi = {10.1109/SMI.2002.1003532},
	author = {Danovaro,E. and De Floriani, Leila and Lee,M. and Samet, Hanan}
}
