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Toward high-level modification of geometric models
There is a rich variety of geometric representations for describing and manipulating complex geometric shapes and especially, surface models. As explained in the previous chapter, the B-Rep representation is the most commonly used in commercial CAS system (Hoffmann, 1989). The key factor that contributes to this is the ability of a B-Rep to use NURBS allowing local shape modification (properties of NURBS curves and surfaces), which is used by a wide range of methods integrated in CAD systems. The most common use of the B-Rep is in the mechanical engineering field for representing regular shapes of mechanical parts. In this domain, the so-called features can be repeated many times in different objects (e.g. holes, shafts, screws, and so on). In order to avoid the repetition of the same part, the feature-based designing concept has been introduced.
Feature-based approaches
The concept of feature-based design is based on defining features that are high-level entities, and designers can use them to construct the final shape of the mechanical part. The main benefit of the implementation of feature-based designing concept is that designers do not manipulate directly the surfaces (e.g. the control points), but the parameterized features which can be parameterized by many numerical parameters such as length, width, height, depth, and so on. Hence, the designing process has been transformed into a construction process where the final shape of the mechanical part is constructed by combining different features preserving the relations between all construction entities (features). Moreover, the modification of the shape is reduced to simply changing values of the feature parameters that result with modifying the entire shape of the part (Pernot, Quao, & Veron, 2007). Unfortunately, the feature-based concept in mechanical design does not support definition of shapes using free-form surfaces in the entire design process. The free-form surface design process is in the scope of the thesis. Actually, the results of this thesis can be used to improve current free-form surface modeling tools whose use still requires a deep knowledge of the underlying mathematical models. Analyzing the advantages of feature-based design, it is evident that the manipulation of features is more intuitive and reduced to varying the value of few numerical parameters than manipulating directly the surfaces. Contrary to this, the manipulation of free-form surfaces (Bézier, B-splines and NURBS) is performed by direct manipulation of surfaces, and requires foreknowledge of geometry description, and great skills in geometry manipulation, which makes it tedious and less intuitive. The sublimation of both, the advantage of the feature- based designing and the requirement for the free-form shapes in terms of manipulation, drive to the need for defining higher-level free-form modification entities. Since, analytic surfaces cannot represent the complex shapes widely used in industrial (aesthetic and engineering) design, commonly defined by several NURBS patches connected together; the concept of form features has been extended to the free-form domain (Pernot, 2004). The objectives of defining high-level free-form entities are to have more application oriented elements than the mathematical low-level constructive elements (points, curves). The freeform entities are easy to be manipulated by using tools, which can play a role of intentdriven modifiers of free-form features (FFF). The introduction of the free-form features conceptopens perspectives for creating tools for high-level modification of geometric models.
Fontana et al. (Fontana, Giannini, & Meirana, 1999) have proposed a formal classification ,of detail free-form features (Figure 3.1). The proposed classification consists of two
ai lasses of featues that oespod to featues otaied defoatio -FFF), and featues otaied eliiatio τ-FFF). The classifiatio of defoatio featues -FFF) is based on the topological and morphological properties associated to the deformation function used to create the features.
The morphological property distinguishes the intrusion from the extrusion, while the topological property distinguishes the border, the internal, and the channel features. The lassifiatio of featues otaied eliiatio τ-FFF) distinguishes different classes regarding the finishing operation, either a sharp or a finished cut (Figure 3.1).
Declarative design process
All available geometric modelers make it possible to construct complex shapes in a more or less intuitive manner. Nevertheless, these geometric modelers restrict the designers in terms of description, using a set of point coordinates or basic geometric primitives, making the designing process very complex and tedious. The role of these modelers is to convert input data of the desired object into an internal numerical model through procedures, so called imperative or procedural modeling (Meiden, Hilderick, & Bronsvoort, 2007). The intention to avoid the use of low-level geometric quantities (points and curves) for defining the object motivates many researches to develop modelers that will help us to design ob38 jects using more abstract notions, based on properties (geometric, topological and physical) and constraints. This is why the concept of declarative modeling has been introduced (Lucas, Martin, Philippe, & Plémenos, 1990). The definition of more abstract notion for describing the surfaces opens perspectives for defining high-level modification tools for modifying the free-form shapes. The role of the computer is to provide a flexible environment for designers to create shapes and, using suitable tools, to modify the shape satisfying their requirements. Geometric declarative modeling tends to design a desired object by expressing its properties. The internal computations of all numerical values (e.g. control points), necessary for the definition of the object, are performed by the modeler and are hidden from the users. The designed object has to satisfy geometric properties or functional constraints. Daniel et al. (Daniel & Lucas, 1997) suggested that declarative modelers must have at its disposition tools for describing, generating and understanding the shape:
Description tools
The basic idea consists in using a set of necessary and sufficient condition to describe a set of objects completely. The main difficulty is to determine whether a precise vocabulary is adapted to a given application field. Specific vocabularies are shared by different applications. The study of vocabulary can be summarized as follows: how to describe a curve/surface without giving a list of coordinates? This does not mean that a set of words and/or an associated syntax can be easily deduced. The relevant vocabulary can be divided into three categories (Daniel & Lucas, 1997):
Mathematical vocabulary, which is universal and undisputable. Shades of meaning cannot be introduced. Concave, convex, inflexion, curvature, cups, … elog to this category.
Qualitative vocabulary, which allows shades of meaning, but is subjective and sometimes differently understood. Words such as flat, round, slender, … elog to this ategory.
Quantifiers such as too uh, little, uh, ore, less, er … enrich the description and allow variations to occur.
It can be pointed out that stating such properties does not exclude the need for very accurate modifications. Moving points directly, and thus their coordinates, seem unavoidable. The experiences gathered by the authors (Daniel & Lucas, 1997) confirm that it may be more difficult to apply a precise modification by giving a set of properties, than manipulate directly point coordinates (using a more or less automatic process). Declarative modeling must then be considered as a powerful tool for rough sketch realization, obtained from the given properties. These sketches can evidently be the inputs of a classical modeler that then appear as complementary to the declarative modeler, the user getting rid of the most tedious part of the design.
Table of contents :
1 Introduction
2. Geometric modeling in product design activities
2.1 Geometric representation methods
2.2 Parametric representations
2.2.1 Bézier, B-Spline and NURBS curves
2.2.1.1 B-Spline curves
2.2.1.2 B-Spline curves
2.2.1.3 NURBS curves
2.2.2 Bézier, B-Spline and NURBS surfaces
2.2.2.1 Bézier surfaces
2.2.2.2 B-spline surfaces
2.2.2.3 NURBS surfaces
2.3 Geometric modeling strategies
2.3.1 Surface Modeling in product design
2.3.1.1 Free-form surface
2.3.1.2 Subdivision surfaces
2.3.1.3 Boundary Representation (B-Rep)
2.3.2 Procedural design process
2.3.3 Needs for intuitive modification of geometric models
2.4 Synthesis and Conclusion
3 Aesthetic-oriented free-form shape description and design
3.1 Toward high-level modification of geometric models
3.1.1 Feature-based approaches
3.1.2 Declarative design process
3.1.2.1 Description tools
3.1.2.2 Generation techniques
3.1.2.3 Understanding tools
3.1.3 Target-driven design
3.1.4 Aesthetic-oriented design and modification of free-form shapes
3.1.4.1 Mapping of aesthetic properties to 3D free-form shapes
3.1.4.2 Defining Aesthetic Curves and Surfaces
3.2 Aesthetic properties of curves
3.2.1 Straightness
3.2.2 Acceleration
3.2.3 Convexity/Concavity
3.2.4 Other aesthetic properties of curves
3.2.4.1 Hollowness
3.2.4.2 Crown
3.2.4.3 S-Shaped curves
3.2.4.4 Tension
3.2.4.5 Lead-in
3.2.4.6 Sharpness/softness
3.2.5 Synthesis
3.3 Aesthetic properties of surfaces
3.4 Conclusion
4 Machine Learning Techniques
4.1 Data Mining and Knowledge Discovery
4.2 Categories of Machine Learning Techniques
4.3 Use of WEKA to identify classification rules and meaningful attributes
4.4 Different classification techniques
4.4.1 Single label classification
4.4.1.1 C4.5 decision trees or J48
4.4.1.2 IBk or k – Nearest Neighbors (k-NN) classification
4.4.1.3 SMO or Support Vector Machine (SVM)
4.4.1.4 NaiveBayes or Naïve Bayes (NB)
4.4.1.5 RIPPER or Decision Rules (JRip)
4.4.1.6 Training a classification model (classifier)
4.4.1.7 Classification efficiency analysis
4.4.1.8 Relevant attribute selection
4.4.2 Multi-label classification
4.4.3 Multi-dimensional classification
4.5 Applications in various domains
4.6 Conclusion and Synthesis
5 Classification framework specification and its validation on curves
5.1 Overall framework
5.2 Setting up of the framework
5.2.1 Space of shapes
5.2.2 Dataset of curves
5.3 Attributes
5.4 Classification
5.5 Considered learning methods
5.6 Experimentations
5.6.1 Modelig of the staightesss ules idetifiatio pole
5.6.2 Classification using dimensional attributes
5.6.3 Classification using dimensionless attributes
5.6.4 Relevant Attribute selection
5.7 Conclusion
6 Classification of surface shapes
6.1 Challenges for surfaces (versus curves)
6.2 Framework application
6.3 Generation of the instances data set
6.3.1 Diversity of shapes explored
6.3.2 Definition of the deformation paths and of the morphing process to generate shape surfaces
6.3.3 Definition of the surrounding surfaces
6.3.4 Generation of the initial Dataset of shapes
6.4 Definition of surface parameters using basic geometric quantities – Attributes
6.4.1 Geometric quantities and surface parameters
6.5 Classification of the surfaces by carrying out interviews
6.6 Experimentations
6.6.1 Organization of the Initial Data Set (IDS)
6.6.2 Pre-processing of the acquired data from the classification
6.7 Results and discussion
6.7.1 Comparison of the learning capability of different learning algorithms
6.7.2 Perception of flatness of every participant in the interviews
6.7.3 Influence of the surrounding (context) to the perception of flatness
6.7.4 Influence of different surrounding (objects) to the perception of flatness
6.7.5 Choosing the most relevant surface parameters
6.8 Conclusion
7 Conclusion and Perspectives
8 References ..
