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Descriptive geometry is the graphic representation of plane, solid, and analytical geometry used to describe real or imagined technical devices and objects. It is the science of graphic representation in engineering design. Students of technical or engineering graphics need to study plane, solid, analytical, and descriptive geometry because it forms the foundation or grammar of technical drawings.
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DESCRIPTIVE GEOMETRY METHODS |
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| 12.1 The application of descriptive geometry is used in the design of chemical plants. For the plant to function safely, pipes must be placed to intersect correctly, and to clear each other by a specified distance, and they must correctly intersect the walls of the buildings. Descriptive geometry is used to solve these problems. |
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| 12.2 The direct view method, sometimes referred to as the natural method, places the observer at an infinite distance from the object, with the observer's line of sight perpendicular to the geometry in question. |
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| 12.3 In the revolution method geometry, a point, line, plane, or entire object is revolved about an axis until that geometry is parallel to the plane of projection that will show the true shape of the revolved geometry. |
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| 12.4 The folding line method is also referred to as the glass box method, which was discussed in Chapter 4, 8, and 11. Using the folding line method the oblique face is projected onto an auxiliary plane, which is placed parallel to it. The difference between this method and the revolution method is that in the revolution method, the geometry is revolved to one of the principal projection planes, while the fold-line method uses an auxiliary plane parallel to the desired geometry. The auxiliary projection plane then is "unfolded" so the projection plane is perpendicular to the line of sight. |
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REFERENCE PLANES |
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| 12.5 The reference plane AA is placed on the back of the object. This would place the edge view of the reference plane on the back of the top and profile views in the multiview drawing. The reference plane can be placed anywhere with respect to the object. In this example, it is placed in front of the object which places it between the horizontal and frontal views. All measurements are taken from this reference plane on specific points on the object in the front and profile views. |
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POINTS |
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| 12.6-7 A point has no width, height, or depth. A point represents a specific position in space as well as the end view of a line or the intersection of two lines. The graphical representation of a point is a small symmetrical cross. |
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THE COORDINATE SYSTEM |
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| 12.8-9 With the Cartesian coordinate system, points are located with respect to the origin (0,0,0) and to each other. |
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LINES |
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| 12.10 A line is a geometric primitive that has no thickness, only length and direction, A line can graphically represent the intersection of two surfaces, the edge view of a surface, or the limiting element of a surface. Lines are either vertical, horizontal, or inclined. A vertical line is defined as a line that is perpendicular to the plane of the earth (horizontal plane). |
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| 12.11 A line is defined as horizontal if all points are at the same height or elevation. |
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| 12.12 An inclined line has one end higher than the other (but not at 90 degrees). An inclined line can only be described as inclined in a front or side view; in the top view, it can appear in a variety of positions. |
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| 12.13 A true length line is the actual straight-line distance between two points. In orthographic projection, a true-length line must be parallel to a projection plane. |
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| 12.14 A line can also appear as a point, called an end or point view. This occurs when the line of sight is parallel to a true-length line. The point view of a line cannot be orthographically determined without first drawing the line in a true length position. |
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| 12.15 A principal line is parallel to one of the three principal projection planes. A line that is not parallel to any of the three projection planes is called an oblique line and will appear foreshortened in any of these planes. |
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| 12.15A A frontal line is a principal line that is parallel to, and therefore true length in a frontal plane. A frontal line can be viewed true length from either a front or back view. |
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| 12.15B A horizontal line is a principal line that is parallel to, and therefore true length in, a horizontal plane. A horizontal line can be viewed true-length from either a top or bottom view. |
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| 12.15C A profile line is a principal line that is parallel to, and therefore true length in, a profile plane. A profile line can be viewed true length in either a left or right side view. |
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| 12.16 If a point lies on a line, it must appear as a point on that line in all views of the line. |
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| 12.17 If a line is positioned parallel to a projection plane and the line of sight is perpendicular to that projection plane, the line will appear as true length. |
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| 12.18 Finding the true length of a line by the auxiliary view method. |
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| 12.19 An application of finding the true length of a line. |
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| 12.20 It sometimes is more practical to find the true length of a line by the revolution method. |
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| 12.21 Finding the true length of a line by the revolution method. |
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| 12.22 A point view of a line occurs when the line of sight is parallel to the line. The back end of the line is directly behind the front end. |
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| 12.23 In orthographic projection, the point view of a line is found in an adjacent view of the true-length line view. |
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| 12.24 Using CAD to determine the point view of a line. |
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PLANES |
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A plane is a flat surface containing a straight line that, in any position, will connect two points that lie on the surface. Theoretically, lines are limitless; in actual practice, planes are bounded by straight or curved lines. In orthographic projection planes can appear as: edges, true size and shape, or foreshortened. |
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| 12.26 Planes are classified as horizontal, vertical, or inclined. A horizontal plane always appears true size and shape (TSP) in the top and bottom views, and as an edge in the front, back, and profile views. A vertical plane that is parallel to the frontal plane and appears as an edge in the profile view is called a frontal plane. An inclined plane is perpendicular to a principal projection plane but not parallel. A inclined plane never appears true size and shape in a principal view. A plane that appears as a surface in all three principal views is called an oblique plane. |
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| 12.27 Any surface view of a plane must have a similar configuration as the plane (i.e., the same number of sides and similar shape.) |
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| 12.28 The edge view of a plane occurs when your line of sight is parallel to the plane. If a line in the plane appears as a point, a plane appears as an edge. Finding the edge view of a plane using the auxiliary view method. |
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| 12.29 A true-size plane must be perpendicular to the line of sight and must appear as an edge in all adjacent views. Finding a true-size plane view of a plane using the auxiliary view method. |
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SUMMARY |
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The principles of descriptive geometry are used for the graphic representation of plane, solid, and analytic geometry used to describe real or imagined technical devices and objects, thus it is the science of graphic representation used in engineering design. Descriptive geometry is the foundation of technical drawings. This chapter described the concepts of descriptive geometry through the use of traditional and CAD applications. The basic geometric elements of points, lines, and planes which are used extensively in traditional descriptive geometry applications were defined by example problems. |