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ENGR126 – Engineering Computer Graphics Lecture 6 Jaehwan Choi, Ph.D. Adjunct Faculty Department of Mechanical Engineering Today’s Topics Fundamentals of Descriptive Geometry 1/2/2014 2 INTRODUCTION Descriptive geometry is the graphic representation of plane, solid, and analytical geometry used to describe real or imagined technical devices and objects. The concepts of descriptive geometry can be applied to solving spatial problems. The basic geometric elements of points, lines, and planes are defined by example problems. 1/2/2014 3 Descriptive Geometry Methods The application of descriptive geometry is used in the design of chemical plants. 1/2/2014 4 Descriptive Geometry Methods Direct view method Revolution method Fold-line method 1/2/2014 5 Descriptive Geometry Methods 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. 1/2/2014 6 Descriptive Geometry Methods In the revolution method geometry, such as 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. 1/2/2014 7 Descriptive Geometry Methods An oblique face has been revolved to bring it parallel to the profile plane, in which the true shape of that surface is shown. The revolution method is satisfactory when a single entity or simple geometry is revolved; however, when the geometry is complex, this method tends to be confusing. 1/2/2014 8 Descriptive Geometry Methods The folding line method is also referred to as the glass box method, which was discussed in previous classes. 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 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. 1/2/2014 9 Descriptive Geometry Methods 1/2/2014 10 Points 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. 1/2/2014 11 The Coordinate System With the Cartesian coordinate system, points are located with respect to the origin (0,0,0) and to each other. 1/2/2014 12 LINES 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. 1/2/2014 13 LINES A vertical line is defined as a line that is perpendicular to the horizontal plane. 1/2/2014 14 LINES A line is defined as horizontal if all points are at the same height or elevation. Multiview representation of horizontal lines 1/2/2014 15 LINES 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. 1/2/2014 16 LINES 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. 1/2/2014 17 LINES A line can also appear as a point, called an end or point view. This occurs when the line of sight is parallel to the true-length line. The point view of a line cannot be orthographically determined without first drawing the line in a true length position. 1/2/2014 18 LINES Z X Y Z Y X 1/2/2014 19 LINES 1/2/2014 20 LINES In orthographic projection, the point view of a line is found in an adjacent view of the true-length line view. 1/2/2014 21 LINES 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. A frontal line is a principal line that is parallel to, and therefore true length in, a frontal plane. 1/2/2014 22 LINES Frontal Line 1/2/2014 23 LINES A horizontal line is a principal line that is parallel to, and therefore true length in, a horizontal plane. 1/2/2014 24 LINES A profile line is a principal line that is parallel to, and therefore true length in, a profile plane. 1/2/2014 25 LINES If a point lies on a line, it must appear as a point on that line in all views of the line. 1/2/2014 26 LINES 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. 1/2/2014 27 LINES Finding the true length of a line by the auxiliary view method. 1/2/2014 28 LINES 1/2/2014 29 LINES An application of finding the true length of a line. Exhaust system 1/2/2014 30 LINES It sometimes is more practical to find the true length of a line by the revolution method. 1/2/2014 31 LINES Finding the true length of a line by the revolution method. 1/2/2014 32 LINES 1/2/2014 33 PLANES A plane is positioned by locating any three points on the plane that are not in a straight line. Theoretically, planes are limitless; in actual practice, planes are bounded by straight or curved lines. In orthographic projection planes can appear as: (1) edges, (2) true size and shape, or (3) foreshortened. 1/2/2014 34 PLANES Planes can be graphically represented in four ways: (1) two intersecting lines, (2) two parallel lines, (3) three points not in a straight line, or (4) a point and a line. 1/2/2014 35 PLANES 1/2/2014 36 PLANES 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. 1/2/2014 37 PLANES A vertical plane always appears as an edge in the top and bottom views, however it may appear in several positions in the front and profile views. When a vertical plane appears as an edge view in the front view and is parallel to the profile projection plane it called a profile plane. A vertical plane that is parallel to the frontal plane and appears as an edge in the profile view is called a frontal plane. 1/2/2014 38 PLANES 1/2/2014 39 PLANES 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. 1/2/2014 40 PLANES A plane that appears as a surface in all three principal views is called an oblique plane. 1/2/2014 41 PLANES Any surface view of a plane must have a similar configuration as the plane (i.e., the same number of sides and similar shape.) 1/2/2014 42 PLANES 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. 1/2/2014 43 PLANES Finding the edge view of a plane using the auxiliary view method. 1/2/2014 44 PLANES 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. 1/2/2014 45 PLANES 1/2/2014 46 PLANES To measure the angle between two planes or surfaces, you must construct a view where both planes are on edge. Angle between surfaces – windshields on airplane Intersection of the two sloping sections of the roof on a house 1/2/2014 47 PLANES 1/2/2014 48 .
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