Jean-Claude Léon

Static polyhedron simplification using error measurements

Abstract Polyhedral models of objects represent an efficient issue for reverse engineering applications and visualization purposes. Because digitizing devices can produce large amounts of points, the polyhedral representation of objects may require a treatment of simplification to preserve the efficiency of subsequent processes for machining or visualization. Here, a new approach is introduced to reduce the number of nodes of a polyhedral model in accordance to an error criterion which can be easily understood by the user. This criterion uses error zones assigned to each node of the initial polyhedron and guarantees that the simplified polyhedron intersects each of the error zones. This behaviour is equivalent to constraining the simplified polyhedron to be included into the geometric envelope defined by all the error zones attached to the initial polyhedron. The iterative treatments involved in the simplification process incorporate an inheritance mechanism to transfer the error zones from one iteration to the next one. Thus, an intuitive manner to monitor the simplification process is set up. A node selection criterion based on curvature approximation has been included to sort the nodes according to their probability of removal. A specific remeshing scheme has also been included to increase the robustness of the treatment when face arrangements around a node generate distorted polygon shapes. Examples highlight the predictable behaviour of the algorithm.

Automated generation of FEA models through idealization operators

This paper describes an automated idealization process of FEA models monitored by a mechanical criterion. This process, based on transformations of a polyhedral geometry, allows large geometric modifications including topology modifications (such as hole removal). Polyhedra are used as input geometry for model adaptation purposes because of their significant freedom for shape modifications compared with CSG or B-Rep models. These polyhedra act as intermediate models to form the adapted input geometry required for a finite element mesh generation. These idealizations are carried out through a vertex removal process which transforms the geometry of a part while preserving it within a discrete envelope defined around its initial geometry. This envelope is obtained from a mechanical criterion which can be based either on an a posteriori error estimator or on a priori estimation. The use of such a criterion ensures that all geometric transformations which keep the geometry of the part within this envelope do not significantly change the results of the FEA In addition to geometric transformations strictly respecting this envelope, operators used for idealization are also able to transfer specific data (like boundary conditions) from the initial geometry to the idealized geometry. Such operators allow an extended automation of geometry simplification and idealization processes and ensure that the new geometry is more suited to the element size requirements of the mesh generation process. This approach is illustrated and validated through an example. Copyright

Software environment for CAD/CAE integration

Computer Aided Design (CAD) and Computer Aided Engineering (CAE) are two significantly different disciplines, and hence they require different shape models representations. As a result, models generated by CAD systems are often unsuitable for Finite Element Analysis (FEA) needs. In this paper, a new approach is proposed to reduce the gaps between CAD and CAE softwares. It is based on new shape representation called mixed shape representation. This later, supports simultaneously the B-Rep (manifold and non-manifold) and polyhedral representation, and creates a robust link between the CAD model (B-Rep NURBS) and the polyhedral model. Both representations are maintained on the same topology support called the High Level Topology (HLT), which represents a common requirement for simulation model preparation. A new software environment for CAD/CAE integration based on the mixed representation is presented in this paper, thus a set of necessary tools is associated to the mixed shape representation which contribute to reduce as much as possible the time of model preparation process.

Incorporating free-form features in aesthetic and engineering product design: State-of-the-art report

The use of free-form shapes has become mainstream to design complex products that have to fulfil engineering requirements as well as aesthetic criteria. Even if todays CAD systems can easily represent free-form shapes by means of NURBS surfaces, their definition and modification still require a deep knowledge and a great skill in the manipulation of the underlying mathematical models. The implemented free-form shapes design operators are time consuming and do not enable fast modifications. To overcome these limits, some researches have been undertaken to try to adapt the feature concept, successfully adopted for the design of regular shapes, in the free-form domain. It gives rise to a set of free-form features modelling strategies. This paper gathers together the state-of-the-art of these advances. The various approaches are depicted and compared with respect to a very precise set of criteria expressing the needs in aesthetic and engineering designs. The limits and future trends are presented.

Parametrically deformed free-form surfaces as part of a variational model

A new approach is described which provides deformation methods for multi-patch tensor based free-form surfaces. The surface deformation generated is controlled by global geometric constraints. For example, the objective can be to deform a free-form surface until it becomes tangent to a pre-defined plane at a given point. This point can be fixed or free to slide on the surface. The parametric deformation of surfaces is dedicated to modifications of free-form surfaces within CAD software and to the design of objects submitted to aesthetic requirements. It is an alternative to previous approaches and it works with multiple surfaces through a simple mechanical model. The deformation method uses an analogy between the control polyhedron of each surface (based on a B-Spline model) and the mechanical equilibrium of a rigid bar network. The user can localize the surface deformation into an arbitrary shaped area through the selection of control polyhedron vertices spread over the entire surface. These vertices are used to automatically construct the associated bar network. The bar network equilibrium parameters are set up to achieve isotropic or anisotropic deformation as required by the designer. The surface deformation is then automatically carried through an optimization process which modifies mechanical parameters to agree with the global geometric constraint set up. The G1 continuity across the different during the deformation process using a set of geometric constraints in addition to mechanical ones. Parametric free-form surface deformation can be subjected to non-linear geometric constraints such as the tangency of a surface to a pre-defined plane. The resolution of such a problem uses an optimization process which minimizes the variation of the parameters governing the equilibrium of the bar network, namely the external forces applied to the nodes of the network. Several examples illustrate basic deformation types with various sets of constraints.

Functional restructuring of CAD models for FEA purposes

Purpose – Preparing digital mock-ups (DMUs) for finite element analyses (FEAs) is currently a long and tedious task requiring many interactive CAD model transformations. Functional information about components appears to be very useful to speed this preparation process. The purpose of this paper is to shows how DMU components can be automatically enriched with some functional information. Design/methodology/approach – DMUs are widespread and stand as reference model for product description. However, DMUs produced by industrial CAD systems essentially contain geometric models, which lead to tedious preparation of finite element Models (FEMs). Analysis and reasoning approaches are developed to automatically enrich DMUs with functional and kinematic properties. Indeed, geometric interfaces between components form a key starting point to analyze their behaviors under reference states. This is a first stage in a reasoning process to progressively identify mechanical, kinematic as well as functional properties ...

A new approach towards free-form surfaces control

Abstract Deformation of free-form surfaces encounters difficulties because more than one control point must be moved to achieve satisfying results. A new method is described which provides deformation methods involving simultaneous movements of control vertices. The method uses an analogy between the control polyhedron of a surface and the mechanical equilibrium of a bar network. Surface deformation is then carried out through changes of mechanical parameters. Then, surface inflation, tweaking, shrinking, etc. can be achieved. New equilibrium positions of the network match the solution of linear system of equations allowing real time shape modifications. An analytical approach of vertices movements is developed to give further explanations about the methods behaviour and the influence of mechanical parameters changes. Several examples illustrate basic deformation types with various changes of mechanical parameters.

Shape preserving polyhedral simplification with bounded error

Abstract A new approach is introduced to reduce the number of nodes of a polyhedral model according to several conditions which allow to produce high quality simplified geometries. The simplified polyhedron must satisfy everywhere a geometric restoration criterion based on an error zone assigned to each node of its initial model. These error zones can be specified by the user or automatically set up using the accuracy characteristics of the digitizing device. Moreover, specific criteria are used to preserve the shape of the object during the simplification process both from geometric and topologic points of view. Indeed, the uses of such polyhedra require a good geometric quality without topologic and geometric singularities. The simplification process is based on a node removal method. A new strategy is developed to produce the simplified polyhedron using front propagations and multiple remeshing schemes which take into account the discrete curvature characteristics of the object. Such an approach allows to increase the node reduction of the initial polyhedron and produces a smoothing effect on the simplified geometry. The front propagation technique also leads to a better preservation of the shape of the object. Examples illustrate the behaviour of the simplification algorithm in terms of data reduction, quality of the simplified geometry and shape preservation of objects.

Two-dimensional slicing method to speed up the fabrication of micro-objects based on two-photon polymerization

Generally, a layer-by-layer method along one specific direction (two-and-half-dimensional method) is used to fabricate three-dimensional (3D) microstructures. Ultrathin layers and long processing times are necessary to obtain smooth surfaces in near flat regions of microstructures. In their approach, the authors slice these nearly flat areas along another slicing direction to produce the scanning paths of the laser beam. Several examples, including a microdragon, have been produced to validate that this real 3D method can generate micro-objects with a good balance between surface accuracy and processing efficiency.

AESTHETIC DESIGN OF SHAPES USING FULLY FREE-FORM DEFORMATION FEATURES

Geometric models, such as B-Rep or CSG, are often used as a shared reference representation of the product along the whole design process. However, they do not provide capabilities for conveying complex information related to the involved product development tasks. This also applies for the initial styling activity, in which the shape is described by complex mathematical models handled by tools still not sufficiently suited to the creative designer mentality. To overcome these limits, we introduce the so-called Fully Free-Form Deformation Features (δ–F4) concept and the related manipulation tools. Advantages of both the free-form surface deformation method and the feature-based approach are combined to define these high-level modelling entities enabling the direct shape-oriented modification of surfaces through a restricted set of parameters. They are mainly defined by characteristic curves in order to better cope with the curve-oriented designers’ way of working. In addition, a (δ–F4) classification is proposed to enable a fast access to the desired shape. The proposed approach is illustrated with some examples from our prototype software.Geometric models, such as B-Rep or CSG, are often used as a shared reference representation of the product along the whole design process. However, they do not provide capabilities for conveying complex information related to the involved product development tasks. This also applies for the initial styling activity, in which the shape is described by complex mathematical models handled by tools still not sufficiently suited to the creative designer mentality. To overcome these limits, we introduce the so-called Fully Free-Form Deformation Features (δ–F4) concept and the related manipulation tools. Advantages of both the free-form surface deformation method and the feature-based approach are combined to define these high-level modelling entities enabling the direct shape-oriented modification of surfaces through a restricted set of parameters. They are mainly defined by characteristic curves in order to better cope with the curve-oriented designers’ way of working. In addition, a (δ–F4) classification is p...