Topologia computazionale e analisi della forma

No abstract availableNell\u27ambito della grafica computazionale, una forma, cio? uno spazio che ha apparenza visuale ed ? connesso, compatto e ha dimensione finita, ? generalmente approssimata da un modello digitale. Riconoscere l\u27informazione qualitativa contenuta in un modello discreto, ossia quella legata ad una interpretazione semantica della forma e la sua struttura morfologica, ? uno degli obiettivi principali nella modellazione di forme. Per rappresentare in modo efficace ed efficiente la forma geometrica di un oggetto nelle varie fasi di costruzione e percezione della forma ? necessario definire dei descrittori che siano unici, indipendenti dall\u27orientamento, invarianti rispetto a trasformazioni rigide, ecc. Una possibile risposta a questo genere di problemi ? fornita dalla topologia computazionale, un\u27area di ricerca recentemente sviluppatasi come specializzazione della matematica computazionale. Nell\u27ambito della modellazione di forme, ad esempio, sono state sviluppate varie tecniche di topologia computazionale quali la teoria di Morse e il calcolo automatico dei numeri di Betti e dei gruppi di omologia. In questa presentazione si affronta la discretizzazione della teoria di Morse dei punti critici nel dominio delle funzioni definite su una mesh triangolare. Il modello concettuale proposto rappresenta una superficie attraverso la combinazione di topologia e geometria, codificandone la topologia, definendone una astrazione ad alto livello sulla base del grafo di Reeb e, nel contempo, codificando informazioni sulla geometria del modello. In questo modo dettagli irrilevanti possono essere tralasciati pur garantendo la correttezza topologica del modello. Per la definizione e la costruzione automatica del modello concettuale, ? stato sviluppato un nuovo metodo per analizzare e caratterizzare una superficie rispetto al comportamento di una funzione reale e almeno continua definita sul modello stesso. La soluzione proposta ? in grado di analizzare anche situazioni degeneri quali, ad esempio, punti critici non isolati. Il modello concettuale che si ottiene ha un alto livello di astrazione ed ? adatto a rappresentare e manipolare superfici continue, lineari a tratti. Il metodo di rappresentazione proposto ? stato applicato con successo in diversi contesti applicativi quali la classificazione, l\u27analisi e la valutazione della similarit? tra forme, la suddivisione della forma in parti caratteristiche, la rappresentazione di attori virtuali e il riconoscimento di parti comuni. In particolare queste applicazioni sono sviluppate nell\u27ambito del progetto europeo AIM@SHAPE (FP6-EU IST Network of Excellence, contratto n? 506766) in collaborazione con altri istituti di ricerca europei

Recognition of feature curves on 3D shapes using an algebraic approach to Hough transforms

Feature curves are largely adopted to highlight shape features, such as sharp lines, or to divide surfaces into meaningful segments, like convex or concave regions. Extracting these curves is not sufficient to convey prominent and meaningful information about a shape. We have first to separate the curves belonging to features from those caused by noise and then to select the lines, which describe non-trivial portions of a surface. The automatic detection of such features is crucial for the identification and/or annotation of relevant parts of a given shape. To do this, the Hough transform (HT) is a feature extraction technique widely used in image analysis, computer vision and digital image processing, while, for 3D shapes, the extraction of salient feature curves is still an open problem. Thanks to algebraic geometry concepts, the HT technique has been recently extended to include a vast class of algebraic curves, thus proving to be a competitive tool for yielding an explicit representation of the diverse feature lines equations. In the paper, for the first time we apply this novel extension of the HT technique to the realm of 3D shapes in order to identify and localize semantic features like patterns, decorations or anatomical details on 3D objects (both complete and fragments), even in the case of features partially damaged or incomplete. The method recognizes various features, possibly compound, and it selects the most suitable feature profiles among families of algebraic curves

Edge-Sharpener: A geometric filter for recovering sharp features in uniform triangulations

3D scanners, iso-surface extraction procedures, and several recent geometric compression schemes sample surfaces of 3D shapes in a regular fashion, without any attempt to align the samples with the sharp edges and corners of the original shape. Consequently, the interpolating triangle meshes chamfer these sharp features and thus exhibit significant errors. The new Edge-Sharpener filter introduced here identifies the chamfer edges and subdivides them and their incident triangles by inserting new vertices and by forcing these vertices to lie on intersections of planes that locally approximate the smooth surfaces that meet at these sharp features. This post-processing significantly reduces the error produced by the initial sampling process. For example, we have observed that the L2 error introduced by the SwingWrapper9 remeshing-based compressor can be reduced down to a fifth by executing Edge-Sharpener after decompression, with no additional information

Three-Dimensional Modelling of the Terra Nova Bay Sea Floor (Ross Sea - Antarctica)

The importance of gathering data on the Antarctic coastline and its adjacent waters has been widely recognised by the Antarctic Treaty Consultative Meeting (ATCM), the Council of Managers of National Antarctic Programs (COMNAP) and the Scientific Committee on Antarctic Research (SCAR). In particular, both for navigational safety and environmental monitoring, it is very desirable to increase hydrographic activity in those areas which have the most significant importance from a scientific or navigational point of view - such as in the continental shelf and continental slope areas of the western part of the Ross Sea. Quite apart from the safety of navigation requirements, knowledge of the seabed topography is necessary to study and understand the various phenomena taking place in the marine environment. For example, the movement of water masses and their mixing processes depend on the shape of the seabed and adjacent coastline. The sea area surrounding Antarctica is one of the least explored parts of the world’s oceans and the available bathymetric data is only sufficient to allow a very general analysis to be made. With the probable growth of tourism and fishing around Antarctica and with the increasing need to understand the effects on the world’s climate of Antarctic water patterns, it is necessary to consider powerful new techniques - such as threedimensional modelling of the sea floors - in order to build up more quickly an effective and reliable bathymetric data base of Antarctic waters

Interoperability between CAD and simulation models

No abstract availabl

Aesthetic-oriented classification of 2D free-form curves

Nowadays, it is commonly admitted that the aesthetic appearance of a product has an enhanced role in its commercial success. Therefore, understanding and manipulating the aesthetic properties of shapes in the early design phases has become a very important field of research. There exists an appropriate vocabulary for describing the aesthetic properties of 2D free-form curves that includes terms such as straightness, acceleration, convexity and tension, which are normally used by stylists when describing and modifying shapes. However, the relationships between this vocabulary and the geometric models are not well established. This work investigates the possibility of applying Machine Learning Techniques (MLT) to discover possible classification patterns of 2D free-form curves with respect to the so-called straightness of the curve. First, we verified that MLT can correctly (99.78%) reapply the classification to new curves. In addition, we verified the abilities of the Attribute Selection methods to identify the most important attributes for the considered classification, among a larger set of attributes. As a result, it was possible to recognize as the most characterizing parameters the same curve attributes previously used to compute the measure of straightness (S). Moreover, Linear Regression (LR) was able to extract automatically an exact mathematical model, which can correlate the geometric quantities with the class of the curve, congruent to one we previously specified. This work indeed demonstrates that MLT are very suitable and can be efficiently used in this context. The work is a first step towards the characterization and classification of free form surfaces giving the general directions on how MLT can be exploited to characterize free-form surfaces with respects to the aesthetic properties.This work has been partially supported by the VISIONAIR project funded by the European Commission under grant agreement 262044

Filleting sharp edges of multi-partitioned volume finite element meshes

International audiencePurpose – The purpose of this paper is to set up a new framework to enable direct modifications of volume meshes enriched with semantic information associated to multiple partitions. An instance of filleting operator is prototyped under this framework and presented in the paper.Design/methodology/approach – In this paper, a generic mesh modification operator has been designed and a new instance of this operator for filleting finite element (FE) sharp edges of tetrahedral multi-partitioned meshes is also pro-posed. The filleting operator works in two main steps. The outer skin of the tetrahedral mesh is first deformed to round user-specified sharp edges while satisfying constraints relative to the shape of the so-called Virtual Group Boundaries. Then, in the filleting area, the positions of the inner nodes are relaxed to improve the aspect ratio of the mesh elements.Findings – The classical mainstream methodology for product behaviour optimization involves the repetition of four steps: CAD modelling, meshing of CAD models, enrichment of models with FE simulation semantics and FEA. This paper highlights how this methodology could be simplified by two steps: simulation model modification and FEA. The authors set up a new framework to enable direct modifications of volume meshes enriched with semantic information associated to multiple and the corresponding fillet operator is devised.Research limitations/implications – The proposed framework shows only a paradigm of direct modifications of semantic enriched meshes. It could be further more improved by adding or changing the modules inside. The fillet operator does not take into account the exact radius imposed by user.With this proposed fillet operator the mesh element density may not be enough high to obtain wished smoothness.Originality/value – This paper fulfils an identified industry need to speed up the product behaviour analysis process by directly modifying the simulation semantic enriched meshes

Tailor: understanding 3D shapes using curvature

Tools for the automatic decomposition of a surface into shape features will facilitate the editing, matching, texturing, morphing, compression, and simplification of 3D shapes. Different features, such as flats, limbs, tips, pits, and various blending shapes that transition between them may be characterized in terms of local curvature and other differential properties of the surface or in terms of a global skeletal organization of the volume it encloses. Unfortunately, both solutions are extremely sensitive to small perturbations in the surface smoothness and to quantization effects when they operate on triangulated surfaces. Thus, we propose a multi-resolution approach, which not only estimates the curvature of a vertex over neighborhoods of variable size, but also takes into account the topology of the surface in that neighborhood. Our approach is based on blowing a spherical bubble at each vertex and studying how the intersection of that bubble with the surface evolves. For example, for a thin limb, that intersection will start simply connected and will rapidly split into two components. For a point on the tip of a limb, that intersection will usually simply remain connected, but the ratio of its length to the radius of the bubble will be decreasing. For a point on a blend, that ratio will exceed 2p. We describe an efficient approach for computing these characteristics for a sampled set of bubble radii and for using them to identify features, based on easily formulated f i lters, that may capture the needs of a particular application

Curve and skeleton based shape deformation In product design

In this report we present an intuitive curve and skeleton based approach for digital product modelling. Morphing-like deformations have been developed to allow for the evaluation of a larger set of alternative shapes compared to the set of shapes generated by the current modelling tools. The method helps designers to search in the product domain for alternative shapes in a straightforward way and eliminates the work-arounds. Through a slide-bar control, these alternative shapes are generated by the transformation of an initial shape into the target one by means of a suitable skeleton extraction transparent to the user and a user-defined profile curve for the target surface. The initial shape is abstracted by a skeleton and a distance function from the skeleton to the surface. For the target surface two categories have been considered, namely revolution-like and sweep-like surfaces. They are both defined through curves: an axis or a path and a profile. The user has to specify only the profile curve, as the axis or the path is represented by the skeletal curve extracted from the initial surface. The distribution of the morphing-like deformation is computed based on the skeletal curve, the distance function and the user-defined profile curve. The use of the skeleton guarantee the generated shapes belong to specific product domains and are therefore context-dependent

Direct modification of semanticaly-enriched finite element meshes

International audienceBehaviour analysis loop is largely performed on virtual product model before its physical manufacturing. The last avoids high expenses in terms of money and time spent on intermediate manufacturing. It is gainful from the reality to the virtuality but the process could be further optimized especially during the product behaviour optimization phase. This process involves repetition of four main processing steps: CAD design and modification, mesh creation, Finite Element (FE) model generation with the association of physical and geometric data, FE Analysis. The product behaviour analysis loop is performed on the rst design solution as well as on the numerous successive product optimization loops. Each design solution evaluation necessitates the same time as required for the first product design that is particularly crucial in the context of maintenance. In this paper we propose a new framework for CAD-less product optimisation through FE analysis which reduces the model preparation activities traditionally required for FE model creation. More concretely, the idea is to directly operate on the rstly created FE mesh, enriched with physical/geometric semantics, to perform the product modi cations required to achieve its optimised version. In order to accomplish the proposed CAD-less FE analysis framework, modification operators acting on both the mesh geometry and the associated semantics need to be devised. In this paper we discuss the underlying concepts and present possible components for the development of such operators. A high-level operator speci cation is proposed according to a modular structure that allows an easy realisation of di erent mesh modification operators. Here, two instances of this high-level operator are described: the planar cracking and the drilling. The realised prototypes validated on industrial FE models show clearly the feasibility of this approach