Bianca Falcidieno

From exact to approximate maximum common subgraph

This paper presents an algorithm for the computation of the maximum common subgraph (MCS) between two directed, acyclic graphs with attributes. The core of the contribution resides in the modularity of the proposed algorithm which allows different heuristic techniques to be plugged in, depending on the application domain. Implemented heuristics for robust graph matching with respect to graph structural noise are discussed. As example of its effectiveness, the algorithm is applied to the problem of 3D shape similarity evaluation through structural shape descriptors.

Polyhedral Surface Decomposition Based on Curvature Analysis

This paper describes a method to characterize the shape of a generic surface approximated with a triangulation. Combining classical topological techniques and differential geometry provides simple methods for evaluating several shape descriptors. Based on this idea a qualitative analysis is defined to estimate the curvature “along” edges and “around” triangles in order to identify regions whose shape is classified as concave, convex, plane or saddle. The proposed curvature regions are defined as connected components of the graph surface model and give rise to a unique surface decomposition which is suitable for parallel implementation and has a linear computational complexity.

Shape abstraction using computational topology techniques

This paper investigates the possible role of the new field of computational topology for incorporating abstraction mechanisms in shape modelling. The effectiveness of computational topology techniques is exemplified with an application of discrete differential topology. In particular, a method is proposed for the extraction of a critical point configuration graph from a triangulated surface. Starting from the definition of the Reeb graph in the smooth domain, the concept of critical point is extended to critical areas, which may represent isolated as well as degenerated critical points in the discrete domain. The resulting graph effectively represents the surface shape and has been successfully used as a basis for model compression and restoring purposes.

Using CAD Models and Their Semantics to Prepare F.E. Simulations

The preparation of simulation models from Computer Aided Design (CAD) models is still a difficult task since shape changes are often required to adapt a component or a mechanical system to the hypotheses and specifications of the simulation model. Detail removal or idealization operations are among the current treatments performed during the preparation of simulation models. Most of the time, model exchanges are required between the engineering office and the simulation engineers, often producing losses of information and lacking of robustness. Thus, inefficient processes and remodelling phases form the usual practice. In this paper we show that geometric models can be extracted from CAD software as well as some of their semantics. This semantics can then be transferred, used and eventually preserved during the shape adaptation process required for a given Finite Element Analysis (FEA). The software environment enabling this transfer simultaneously requires the description of the initial B-Rep NURBS model as well as that of the adapted one. The process set up is based on STandard for the Exchange of Product model data (STEP) to provide a robust link between CAD and shape adaptation environments. In order to describe the appropriate variety of shapes required for the Finite Element (FE) preparation, a specific data structure is proposed to express the corresponding topology of the models. Hence, it is shown that the operators associated to the FE preparation process can take advantage of this data structure and the semantics of the initial CAD model that can be attached to the adapted model. Examples illustrating the various process steps and corresponding operations are provided and demonstrate the robustness of the approach.Copyright

Discrete Surface Models: Constraint-based Generation and Understanding

A two level description is proposed for natural surface modelling: a geometric model, in terms of low level primitive entities, and a conceptual model, which is a symbolic surface representation based on its prominent shape characteristics. The geometric and conceptual level can exchange information using two operators: the abstraction operator and the generation operator.

From CAD Models to F.E. Simulations Through a Feature-Based Approach

The preparation of simulation models from CAD models is still a difficult task since shape changes are often required to adapt a component or a mechanical system to the hypotheses and specifications of the simulation model. Detail removal or idealization operations are among the current treatments performed during the preparation of simulation models. In this paper we introduce the concept of simplification features, which allows a user to improve the efficiency of the analysis model generation process. Therefore Form Feature semantics and simulation data are attached to a polyhedral model during the preparation phase, to ease the Finite Element (FE) details identification and removal. The process flow corresponding to the insertion of the FE model preparation phase into the CAD/FEA framework is described in detail to highlight the versatility of the process according to the category of the input model as well as the main steps of the simplification process. This process flow stresses also the influence of the different information sources involved in the preparation task. They consist of the geometric and feature data of the object and the mechanical data of related to the process under examination. The need of a topological model able to represent non-manifold components is discussed as well as the need for the to user to specify the analysis attributes over the boundary of components either isolated or part of an assembly. The proposed topological representation of allows the software application to combine several geometric representations such as Form feature and polyhedral representations; therefore it is possible to propagate the B-Rep information from a STEP file, as well as feature information into the polyhedral representation used during the simplification process.Copyright

Geometric Reasoning for the Extraction of Surface Shape Properties

Shape descriptions are essential in computer graphics to provide effective representations of the objects to be modelled. A geometric reasoning approach is here proposed to extract curvature information from a surface approximated by a triangulation. In particular, a curvature measure is defined which is qualitatively-similar to the mean curvature. This curvature measure enhances the descriptive power of the shape characterisation previously defined by the authors, based on the decomposition of the surface in its convex, concave, plane and saddle regions.

A hybrid models deformation tool for free-form shapes manipulation

This paper addresses the way models mixing various types of geometric representations (e.g. NURBS curves and patches, polylines, meshes), potentially immersed in spaces of different dimensions (e.g. NURBS patch and its 2D trimming lines), can be deformed simultaneously. The application domains range from the simple deformation of a set of NURBS curves in a 2D sketcher to the simultaneous deformation of meshes, patches as well as trimming lines lying in parametric spaces. The deformation itself results from the solution of an optimization problem defined by a set of geometric constraints and deformation behaviors. This new breakthrough on how geometric models can be manipulated has been made possible thanks to our linear mechanical model of deformation that can be coupled to manifolds of dimension zero (e.g. points, vertices) and one (e.g. edges, segments) whatever the spaces dimension. An extended constraints toolbox is also proposed that enables the specification of both characteristic points/curves and continuity conditions between the various geometric models. The link between the semantics of the deformation behaviors and the geometric models is ensured through the use of multiple minimizations. The approach is illustrated with several examples coming from our prototype software.Copyright

Comparing sets of 3D digital shapes through topological structures

New technologies for shape acquisition and rendering of digital shapes have simplified the process of creating virtual scenes; nonetheless, shape annotation, recognition and manipulation of both the complete virtual scenes and even of subparts of them are still open problems. Once the main components of a virtual scene are represented by structural descriptions, this paper deals with the problem of comparing two (or more) sets of 3D objects, where each model is represented by an attributed graph. We will define a new distance to estimate the possible similarities among the sets of graphs and we will validate our work using a shape graph [1].

Insertion of Planar Areas Into Free-Form Surfaces in Early Product Design

Surfaces, like planes, cylinders or spheres, are basic primitive surfaces not only for mechanical engineering but also for aesthetic design, world of free-form surfaces, where they are essentially used to answer some functional constraints, like assembling and manufacturing ones, or to achieve specific light effects. The early design steps are characterised by the uncertainty in the definition of the precise geometry and most of the time, product constraints are only partially available. Unfortunately, until now, the insertion of primitive surfaces requires precise curve and surface specifications together with trimming operations, thus imposing that the free-form geometry is recreated each time a modification occurs. In this paper we present a method for the insertion of planar surfaces suitable to handle the uncertainty in the first draft of a product. The approach does not provide effective precise primitive surfaces, but it is able to introduce regions resembling such a behaviour in a free-form surface, without requiring trimming operations, so allowing more efficient shape alternative evaluations.Copyright