## 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.

There are three types of commands used by the designer in CAD geometric modeling. Its first allows the user to input the variables needed by the computer to represent basic geometric elements such as points, lines, arcs, circles, splines, and ellipses. The second is used to transform these elements that include scaling, rotation, and translation. The third allows the various elements previously created by the first two commands to be joined into a desired shape. During the whole geometric modeling process, mathematical operations are at work that can be easily stored as computerized data and retrieved as needed for review, analysis, and modification.

There are different ways of displaying the same data on the CRT (cathode ray tube) screen, depending on the needs or preferences of the designer. One method is to display the design as a 2-D representation of a flat object formed by interconnecting lines. Another method displays the design as a 3-D view of the product. In 3-D representations, there are the four types of modeling of wireframe modeling, surface modeling, solid modeling, and hybrid solid modeling.

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.

With the surface modeling one defines not only the edge of the 3-D part, but also its surface. One of its major benefits is that it allows mass-related properties to be computed for the product model (volume, surface area, moment of inertia, etc.) and allows section views to be automatically generated. The surface modeling is more sophisticated than wireframe modeling. In surface modeling, there are the two different types of surfaces that can be generated: faceted surfaces using a polygon mesh and true curve surfaces. NLTRBS (Non-Uniform Rational B-Spline) is a B-spline curve or surface defined by a series of weighted control points and one or more knot vectors. It can exacdy represent a wide range of curves such as arcs and cones. The greater flexibility for controlling continuity is one advantage of NURBS. It can precisely model nearly all kinds of surfaces more robustly than the polynomial-based curves that were used in earlier surface models.

The computer still defines the object in terms of a wireframe but can generate a surface to cover the frame, thus giving the illusion of a real product. However, because the computer has the image stored in its data as a wireframe representation having no mass, physical properties cannot be calculated directiy from the image data. Surface models are very advantageous due to point-to-point data collections usually required for numerical control (NC) programs in CAM applications. Most surface modeling systems also produce the stereolithographic data required for rapid prototyping systems.

An important technique is the solid modeling that defines the surfaces of a product with the added advantages of volume and mass. It takes the surface model one step further in that it assures that the product being modeled is valid and realizable. This allows image data to be used in calculating the physical properdes of the final product. Solid modeling software uses one of two methods: constructive solid geometry (CSG) or boundary representation (B-rep). CSG method uses engineering Boolean operations (union, subtraction, and intersection) on two sets of objects to define composite models. B-rep is a representation of a solid model that defines a product in terms of its surface boundaries that are faces, edges, and vertices.

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

By using CAD software, its hidden-line command can remove the background lines of the part in a model. Certain features have been developed to minimize the ambiguity of wireframe representations. These features include using dashed lines to represent the background of a view, or removing those background lines altogether. This hidden-line removal feature makes it easier to visualize the model because the back faces are not displayed. Shading removes hidden lines and assigns flat colors to visible surfaces. Rendering adds and adjusts lights and materials to surfaces to produce realistic effects. Shading and rendering can greatly enhance the realism of the 3-D image.

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