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Item Two-manifold cell-decomposition of r-sets.(Blackwell Science Ltd and the Eurographics Association, 1992) Falcidieno, Bianca; Ratto, OrnellaThis paper discusses the relationships studied between manifold solids and r-sets by defining an r-set as a decomposition in two-manifold cells. This decomposition is represented as a graph (Two-manifold Cell Decomposition graph TCD) in which each node corresponds to a 2 manifold component of the regular set, while each arc or hyperarc defines a non-manifold adjacency between components. The TCD model and data structure encoding it were designed in order to be compatible with a traditional boundary architecture.Item Extraction and Organization of Form Features into a Structured Boundary Model(Eurographics Association, 1987) Falcidieno, Bianca; Giannini, FrancaA method is presented for the automatic identification and extraction of feature information from the solid model of an object. The procedure consists of recognizing shape features, extracting those features as solid volumes and arranging them in a hierarchical structure. In this hierarchical model the main shape of the object is represented at the highest levels of abstraction, while form features are described at lower levels of specification. The system is divided into three modules: feature recognition, feature extraction and feature organization. The recognition step works on a face-based representation of solid objects, called Face Adjacency Hypergraph [1] and it takes advantage of the Kyprianou's method [12]. In the extraction phase every recognized form feature is completed with dummy entities to form a feasible object and in the organization step the completed features are arranged in a hierarchical graph, called Structured Face Adjacency Hypergraph, which is a modification of a model defined in a previous work [1].Item 3D Shape Description and Matching Based on Properties of Real Functions(The Eurographics Association, 2007) Biasotti, Silvia; Falcidieno, Bianca; Frosini, Patrizio; Giorgi, Daniela; Landi, Claudia; Marini, Simone; Patané, Giuseppe; Spagnuolo, Michela; Karol Myszkowski and Vlastimil HavranThis tutorial covers a variety of methods for 3D shape matching and retrieval that are characterized by the use of a real-valued function defined on the shape (mapping function) to derive its signature. The methods are discussed following an abstract conceptual framework that distinguishes among the three main components of these class of shape matching methods: shape analysis, via the application of the mapping function, shape description, via the construction of a signature, and comparison, via the definition of a distance measure. Goal of the tutorial is to facilitate the understanding of the performance of the various methods by a methodical analysis of the properties of various methods at the three different stages.Item CHARACTERIZATION OF TOPOGRAPHIC SURFACES(Eurographics Association, 1990) Falcidieno, Bianca; Spagnuolo, MichelaThis paper presents a method for extracting and representang features of a topographic surface approximated by triangular tales An algorithm as given which computes characteristic regions (a. e. regions having concave, convex or planar shape), characteristic lanes (ridges, ravines, generic creases) and characteristic points (maxima, minima, saddle points) The result as a new surface description an terms of an attributed hypergraph representation called Characteristic Region Configuration Graph, an which characteristic regions are considered the basic describers of the surface shape and correspond to the nodes of the graph, whale the arcs and hyperarcs represent the relationships between regions derived from characteristic lanes and pointsItem Representing Tolerance Information in Feature-Based Solid Modelling(Eurographics Association, 1989) Falcidieno, Bianca; Fossati, BrunoIn this paper a system for defining dimensions and tolerances is presented which deals with the geometric representation of the objects in a coherent and compact way. This model is a combination of a hierarchical boundary model to represent geometry of the object with features and a relational graph model to encode dimensions and tolerances. In this way, the proposed model can be considered a ”product model” that, besides geometric and topological information about the feature components of a solid object, also codifies information about dimensions represented by relative positron operators connected to faces which are the primitive geometric entities of the object model. The method can automatically control the validity of the geometric and topological model of the object each tame that a new tolerance node is added to the structure or a tolerance constraint already existing is modified. In this case, it also translates changes in dimensional values into corresponding changes an geometry and topology.