Machinery's Handbook, 31st Edition
CAD/CAM
1391
Fig. 1. Simple Wireframe Cube with Hidden Lines Removed
Fig. 2. Simple Wireframe Cube
with Hidden Lines Shown Wireframes are the simplest two- and three-dimensional forms of drawing images and are created by defining all edges of a part, with, where required, lines defining surfaces. Wire - frame drawing elements consist primarily of lines and arcs that can be used in practically any combination. Hidden lines can be shown dashed or can be omitted from the view; hidden-line removal can be used to indicate relative elevations of the elements. A wireframe drawing of a cube, as in Fig. 1, consists of twelve lines of equal length (some are hidden and thus not shown), each perpendicular to the others. Fig. 2 shows the same wireframe drawing of a cube but with the hidden lines shown. Information about the inte- rior of the cube and the character of the surfaces is not included in the drawing. With such a system, if a 1-inch cube is drawn and a 0.5-inch cylinder is required to intersect the cube’s surface at the center of one of its faces, the intersection points cannot be determined, be- cause nothing is known about the area between the edges. A wireframe model of this type is ambiguous if the edges overlap or do not meet where they should. Two-dimensional drawing elements, such as lines, arcs, and circles, are constructed by specifying point coordinates, usually x and y , to identify the location, size, and orienta- tion of these elements. Three-dimensional (3D) drawings are also made up of a collection of lines, arcs, circles, and other drawing elements and are stored in a similar manner. A third point coordinate, z , indicates the elevation of a point in 3D drawings. On the drawing screen, working in the x–y plane, the elevation is commonly thought of as the distance of a point or object into the viewing screen (away from the observer) or out of the viewing screen (toward the observer). Coordinate axes are orientated according to the right-hand rule: If the fingers of the right hand point in the direction from the positive x axis to the positive y axis, the thumb of the right hand points in the direction of the positive z axis. Assigning a thickness (or extruding) to objects drawn in two dimensions gives some 3D characteristics to an object and can be used to create simple prismatic 3D shapes, such as cubes and cylinders. Usually, the greatest difficulty in creating 3D drawings is in picking and visualizing the 3D points in a 2D workspace (the computer display screen). To assist in the selection of 3D points, many CAD programs use a split or windowed screen draw- ing area that can simultaneously show different views of a drawing. Changes made in the current or active window are reflected in the other windows. A typical window setup might show three orthogonal (mutually perpendicular) views of the drawing and a perspective or 3D view. Usually, the views can be changed as required to suit the needs of the operator. Surface Images: A surface image defines not only the edges of the part, but also the “skin” of each face or surface. Surface models are necessary for designing free-form objects such as automotive body panels and plastics injection moldings used in consumer goods. For a surface model, the computer must be provided with the x, y, z coordinates de- fining each point, as in a wireframe drawing, plus much more information about the part. This may include tangent vectors, surface, and weighting information that determines how much influence one point has on another, twists, and other mathematical data that define abstract curves. For instance, Fig. 3 shows a typical 3D surface patch.
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