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Marching Cubes' methods first offered visual access to experimental and theoretical data. The implementation of this method usually relies on a small lookup table. Many enhancements and optimizations of Marching Cubes still use it. However, this lookup table can lead to cracks and inconsistent topology. This paper introduces a full implementation of… (More)

Morse theory is a powerful tool in its applications to computational topology, computer graphics and geometric modeling. It was originally formulated for smooth manifolds. Recently, Robin Forman formulated a version of this theory for discrete structures such as cell complexes. It opens up several categories of interesting objects (particularly meshes) to… (More)

Morse theory is a fundamental tool for investigating the topology of smooth manifolds. This tool has been extended to discrete structures by Forman, which allows combinatorial analysis and direct computation. This theory relies on discrete gradient vector fields, whose critical elements describe the topology of the structure. The purpose of this work is to… (More)

The definition of a good view of a 3D scene is highly subjective and strongly depends on both the scene content and the 3D application. Usually, camera placement is performed directly by the user, and that task may be laborious. Existing automatic virtual cameras guide the user by optimizing a single rule, e.g. maximizing the visible silhouette or the… (More)

Vector fields analysis traditionally distinguishes conservative (curl-free) from mass preserving (divergence-free) components. The Helmholtz-Hodge decomposition allows separating any vector field into the sum of three uniquely defined components: curl free, divergence free and harmonic. This decomposition is usually achieved by using mesh-based methods such… (More)

In this work, it is presented a complete set of operators , called Morse operators, to build and unbuild any combinatorial orientable &dimensional manifolds embedded in R " (n 3 3). Also, a suitable data structure, called Handl~Face, is introduced in order to represent 3manifolds with or without boundary. The main emphasis is on the boundary of the manifold… (More)

Morse theory is a powerful tool for investigating the topology of smooth manifolds. It has been widely used by the computational topology, computer graphics, and geometric modeling communities to devise topology-based algorithms and data structures. Forman introduced a discrete version of this theory which is purely combinatorial. This work aims to build,… (More)

The Edgebreaker is an efficient scheme for compressing triangulated surfaces. A surprisingly simple implementation of Edgebreaker has been proposed for surfaces homeomorphic to a sphere. It uses the Corner-Table data structure, which represents the connectivity of a triangulated surface by two tables of integers, and encodes them with less than 2 bits per… (More)