Geometric Modeling

By Author: peter
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In computer-aided design, geometric modeling is concerned with the computer-compatible mathematical description of the geometry of an object. The mathematical description allows the image of the object to be displayed and manipulated on a graphics terminal through signals from the CPU of the CAD system. The software that provides geometric modeling capabilities must be designed for efficient use both by the computer and the human designer.

To use geometric modeling, the designer constructs the graphical image of the object on the CRT screen of the ICG system by inputting three types of commands to the computer. The first type of command generates basic geometric elements such as points, lines and circles. The second command type is used to accomplish scaling, rotation, or other transformations of these elements. The third type of command causes the various elements to be joined into the desired shape of the object being created on the ICG Replica Cartier Watches system. During this geometric modeling process, the computer converts the commands ...
... into a mathematical model, stores it in the computer data files, and displays it as an image on the CRT screen. The model can subsequently be called from the data files for review, analysis, or alteration.

There are several different methods of representing the object in geometric modeling.
At the early stage of computer-aided design, the computer graphic model has been successfully used in 2D drafting software to generate engineering drawings on computers. The computer graphic model is made up of simple lines, circles, curves, and other 2D entities. Because of its two-dimensional nature, it makes interactive input very easy. A user can simply use a mouse or other input devices to enter 2D data, and then the computer can generate the required graphic entities such as a straight line. A computer graphic model is represented by tables of lines and points. The start and the end points are stored in the line table and the coordinates of each point are stored in the point table. For each geometric entity such as a circle, line or 2D curve, mathematical representations can be developed in software. With other graphical functions added computer graphical models have been widely used in computer-aided design- and drafting software.

The same principle can be applied to three-dimensional cases. A wire¬frame model in 3D space is, in fact, a computer graphic model. The basic form uses wire frames to represent the object. In this form, the object is displayed by interconnecting lines, as shown in Fig. 6.3. A wire-frame model is also represented in the computer by tables of lines and points. The main advantage in using wire-frame models in 3D graphics is fast generation of graphic objects. This is because no additional evaluations for geometric and topological integrity and for shading of surfaces are carried out. Because of the lack of integrity evaluations, the model may be ambiguous. Also, some invalid objects may be created.

Even three-dimensional wire-frame representations of an object are sometimes Omega Replica inadequate for complicated shapes. Wire-frame models can be enhanced by several different methods. Fig. 6.4 shows the same object shown in the previous figure but with two possible improvements. The first uses dashed lines to portray the rear edges of the object, those which would be invisible from the front. The second enhancement removes the Cell decomposition;

Analytical solid modeling; Solid modeling, including. BREP and CSG are the most widely used representation schemes for solid modeling. However, for different applications, one may be more suitable than the other. For example, BREP is more suitable for representing complex designs, whereas with CSG, models are easy to create but are usually used in representing relatively simple objects. In some modelers, a hybrid scheme employing both BREP and CSG is used. Another feature of some CAD systems is color graphics capability. By means of color, it is possible to display more information on the graphics screen. Colored images help to clarity components in an assembly, or highlight dimensions, or a host of other purposes.