In engineering, geographical applications, scientific visualization, and bio-informatics, a varie... more In engineering, geographical applications, scientific visualization, and bio-informatics, a variety of phenomena is described by a large set of data modeled as the values of a scalar function f : M→ R defined on a surface M. A low quality of the discrete representations of the input data, unstable computations, numerical approximations, and noise might produce functions with a high number of critical points. In this context, we propose an algorithmic framework for smoothing an arbitrary scalar function, while simplifying its redundant critical points and preserving those that are mandatory for its description. From our perspective, the critical points of f are a natural choice to guide the approximation scheme; infact, they usually represent relevant information about the behavior of f or the shape itself. To address the aforementioned aims, we compute a smooth approximation f̃ : M→ R of f whose set of critical points contains those that have been preserved by the simplification pro...
A new hierarchical model for solid object representation is described. This model, called a hiera... more A new hierarchical model for solid object representation is described. This model, called a hierarchical face adjacency hypergraph (HFAH), is based on a relational description of the object boundary, called a face adjacency hypergraph (FAH), which considers faces as the primary topological entities defining the object boundary. The HFAH consists of a hierarchy of FAHs describing the decomposition of the boundary of an object into form features. In this paper the HFAH is described together with its internal encoding structure. Two basic transformations, called refinement and abstraction, are defined on the hierarchical model; these allow effective and efficient modifications of the hierarchical boundary model.
The use of network-based parallel computing is gaining an increasing popularity for different rea... more The use of network-based parallel computing is gaining an increasing popularity for different reasons. Its exploitation depends on the availability of simple but effective methodologies to parallelize applications, and the availability of portable and efficient communication libraries to develop parallel programs. These two items are necessary to obtain performance advantages, and to ensure software portability and reusability. In this paper
... Polytechnic Institute of Grenoble, BP 53X, 38041 Grenoble France, email : Jean-Claude.Leon@ i... more ... Polytechnic Institute of Grenoble, BP 53X, 38041 Grenoble France, email : Jean-Claude.Leon@ inpg.fr, tel ... Applicata e Tecnologie Informatiche - Department of Genova, Consiglio Nazionale delle Ricerche, via De Marini, 6 - 16149 Genova - Italy, email: bianca.falcidieno@ge ...
In engineering, geographical applications, scientific visualization, and bio-informatics, a varie... more In engineering, geographical applications, scientific visualization, and bio-informatics, a variety of phenomena is described by a large set of data modeled as the values of a scalar function f : M→ R defined on a surface M. A low quality of the discrete representations of the input data, unstable computations, numerical approximations, and noise might produce functions with a high number of critical points. In this context, we propose an algorithmic framework for smoothing an arbitrary scalar function, while simplifying its redundant critical points and preserving those that are mandatory for its description. From our perspective, the critical points of f are a natural choice to guide the approximation scheme; infact, they usually represent relevant information about the behavior of f or the shape itself. To address the aforementioned aims, we compute a smooth approximation f̃ : M→ R of f whose set of critical points contains those that have been preserved by the simplification pro...
A new hierarchical model for solid object representation is described. This model, called a hiera... more A new hierarchical model for solid object representation is described. This model, called a hierarchical face adjacency hypergraph (HFAH), is based on a relational description of the object boundary, called a face adjacency hypergraph (FAH), which considers faces as the primary topological entities defining the object boundary. The HFAH consists of a hierarchy of FAHs describing the decomposition of the boundary of an object into form features. In this paper the HFAH is described together with its internal encoding structure. Two basic transformations, called refinement and abstraction, are defined on the hierarchical model; these allow effective and efficient modifications of the hierarchical boundary model.
The use of network-based parallel computing is gaining an increasing popularity for different rea... more The use of network-based parallel computing is gaining an increasing popularity for different reasons. Its exploitation depends on the availability of simple but effective methodologies to parallelize applications, and the availability of portable and efficient communication libraries to develop parallel programs. These two items are necessary to obtain performance advantages, and to ensure software portability and reusability. In this paper
... Polytechnic Institute of Grenoble, BP 53X, 38041 Grenoble France, email : Jean-Claude.Leon@ i... more ... Polytechnic Institute of Grenoble, BP 53X, 38041 Grenoble France, email : Jean-Claude.Leon@ inpg.fr, tel ... Applicata e Tecnologie Informatiche - Department of Genova, Consiglio Nazionale delle Ricerche, via De Marini, 6 - 16149 Genova - Italy, email: bianca.falcidieno@ge ...
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