Geometric modeling

Geometric modeling is one of the major uses of the CAD systems. It uses mathematical descriptions of geometric elements to facilitate the representation and manipulation of graphical images on the computer s screen. While the central processing unit (CPU) provides the ability to quickly make the calculations specific to the element, the software provides the instructions necessary for efficient transfer of information between user and the CPU. 

The wireframe model is a skeletal description of a 3-D part. It consists only of points, lines, and curves that describe the geometric boundaries of the object. There are no surfaces in a wireframe model. The 3-D wireframe representations can be confusing because all of the lines defining the object appear on the 2-D display screen. This makes it difficult for the viewer to tell whether the model is being viewed from above or below, inside or outside. It is the simplest of the CAD/CAM modeling methods. The simplicity of this modeling method also implies simplicity in the database. 

Hybrid solid modeling allows the user to represent a product with a mixture of wireframe, surface modeling, and solid geometry. 

CAD permits checking on interference potential problems. This procedure involves making sure that no two parts of a design occupy the same space at the same time. Automated drafting capabilities in CAD systems facilitate the design presentation, which is the final stage of the design process. CAD data, stored in computer memory, can be sent to a 

Three types of geometry models, commonly used to represent microelectronic packaging assemblies, will be discussed in this section (a) 2D model, (b) 2.5D or strip model, and (c) 3D model. The choice of these three models depends on the computational accuracy needed, the computing resources available, and the focus of the modeling study. 

For illustrative purposes, models of a Rip Chip on Board (FCOB) and a Chip Scale Package (CSP) on an organic board with underfill are described as follows, based on the work of Hanna (Ref 21) and Hanna et al. (Ref 22). 

Two-dimensional plane models can be used to represent a cross-section of a packaging as- 

Plane models provide a good understanding of the qualitative behavior of a package and the effect of variation of different material, geometry, and processing parameters. However, plane models do not capture the shape of the solder ball accurately, as they represent only a particular section. Also, they cannot capture the out-of-plane variation of material properties. Consequently, plane models do not provide quantitatively accurate results. The advantage of a 2D model is that it is computationally less intensive, as compared to a 2.5D and a 3D model. 

GPD models represent a compromise between 2D and 3D models. In a GPD model, a predetermined width of the package is modeled utilizing solid elements. Typically the width is chosen such that, at least one row of the solder balls is represented in the model. Also, only half of the package is modeled as a result of symmetry. 

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It is also possible to deal with the mean scattered intensity by using a geometrical model [11]. Following the procedure of that reference, we finally get... 

Perez Quintian, M.A.Rebollo, N.G. Gaggioli y C.A. Raffo, The non refractive effect in translucent diffusers A geometrical model . Aprobado para su publicacion en Journal of Modem Opties. 

At the start of the development, it had been intended use an expert system shell to implement this tool, however, after careful consideration, it was concluded that this was not the optimum strategy. An examination procedure can be considered as consisting of two parts fixed documentary information and variable parameters. For the fixed documentary information, a hypertext-like browser can be incorporated to provide point-and-click navigation through the standard. For the variable parameters, such as probe scanning paths, the decisions involved are too complex to be easily specified in a set of rules. Therefore a software module was developed to perfonn calculations on 3D geometric models, created fi om templates scaled by the user. 

Lin et al. [70, 71] have modeled the effect of surface roughness on the dependence of contact angles on drop size. Using two geometric models, concentric rings of cones and concentric conical crevices, they find that the effects of roughness may obscure the influence of line tension on the drop size variation of contact angle. Conversely, the presence of line tension may account for some of the drop size dependence of measured hysteresis. 

These fascinating bicontinuous or sponge phases have attracted considerable theoretical interest. Percolation theory [112] is an important component of such models as it can be used to describe conductivity and other physical properties of microemulsions. Topological analysis [113] and geometric models [114] are useful, as are thermodynamic analyses [115-118] balancing curvature elasticity and entropy. Similar elastic modulus considerations enter into models of the properties and stability of droplet phases [119-121] and phase behavior of microemulsions in general [97, 122]. 

S. Suresh and R. O. Ritchie, A Geometric Model for Fatigue Crack Closure Induced by Fracture Surface Morphology , Metallurgical Transactions, 13A, 1982, pp. 1627 1631. 

Quality of geometric modeling and spatial resolution of computational mesh... 

Heat or contaminant. sources can also be assigned to parts of the fluid volume to account for very small real sources or a distribution of a large number of small sources. Care must be taken, however, to make sure that this representation of distributed sources describes correctly the real situation (see the earlier section Geometric Modeling ). 

Westlake developed a geometric model which is fairly successful in predicting site occupation in ABs and AB2 hydride phases [9], It involves two structural constraints ... 

A simple geometric model, based on the hypothesis that water plus surfactant are subdivided in nanospheres and that their total surface is fixed by the amount of surfactant, can predict the dependence of the micellar radius (r) on R and that of the micellar concentration on R and on the surfactant concentration. 

Hyde, ST Ninham, BW Zemb, T, Phase Boundaries for Ternary Microemulsions. Predictions of a Geometric Model, Journal of Physical Chemistry 93, 1464, 1989. 

Mortenson ME (1985) Geometric modelling, John Wiley, New York... 

The elution of [60]- and [70]fullerenes was measured in water-methanol as a function of temperature on a poly(octadecylsiloxane) phase.67 The retention was shown to be dependent on the surface tension of the stationary phase through a simple geometrical model in which the solute formed a cavity in the stationary phase. In affinity chromatography, it was demonstrated that low ligand density may be a requirement for specificity of binding.68... 

Guillame, Y.C. and Peyrin, E., Geometric model for the retention of fullerenes in high-performance liquid chromatography, Anal. Chem., 71, 1326, 1999. 

FIG. 5. Geometric model for, e.g., conductivity measurements via a single atom contact. 

The existence of active sites on surfaces has long been postulated, but confidence in the geometric models of kink and step sites has only been attained in recent years by work on high index surfaces. However, even a lattice structure that is unreconstructed will show a number of random defects, such as vacancies and isolated adatoms, purely as a result of statistical considerations. What has been revealed by the modern techniques described in chapter 2 is the extraordinary mobility of surfaces, particularly at the liquid-solid interface. If the metal atoms can be stabilised by coordination, very remarkable atom mobilities across the terraces are found, with reconstruction on Au(100), for example, taking only minutes to complete at room temperature in chloride-containing electrolytes. It is now clear that the... 

Deceleratory a -time curves based on geometrical models ... 

Bartela, R. J. Beatty and B. Barsky. An Introduction to Splines for Use in Computer Graphics and Geometric Modeling. Morgan Kaufman Publishers, Los Altos, CA (1987). 

Electron diffraction provides experimental diffraction spectra for comparison with computed spectra obtained from various intuitive geometrical models, but this technique alone is generally insufficient to locate the hydrogen atoms. A quantum approach, on the other hand, indicates the positions of the H atoms, which can then be introduced into the calculation of the theoretical spectra in order to complete the determination of the geometry. 

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