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The Planes of Projection 26

plane, horizon, ground, horizontal, vertical, object and intersection

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THE PLANES OF PROJECTION.

26. Two planes of projection at right angles to one another, one vertical and the other horizontal, are used in making a per spective. In Fig. 7 these two planes are shown in oblique Pro jection. The vertical plane is the picture plane (§ 6 and Fig. 7) on which the perspective projection is made, and corresponds exactly to the vertical plane, or vertical coordinate used in ortho graphic projections.

27. The horizontal plane, or plane of the horizon (§ 20 and Fig. 7), always passes through the assumed position of the observer's eye, and corresponds exactly to the horizontal plane or horizontal coordinate used in orthographic projections.

28. All points, lines, surfaces, or solids in space, the per spective projections of which are to be found, are represented by their orthographic projections on these two planes, and their per spectives are determined from these projections.

29. Besides these two principal planes of projection, a third plane is used to represent the plane on which the object is sup posed to rest (Fig. 7). This third plane is horizontal, and is called the plane of the ground. Its relation to the plane of the horizon determines the nature of the perspective projection. To illustrate : The observer's eye must always be in the plane of the horizon (§ 27), while the object, the perspective of which is to be made, is usually supposed to rest upon the plane of the ground. In most cases the plane of the ground will also be the plane on which the observer is supposed to stand, but this will not always be true. The observer may be standing at a much higher level than the plane on which the object rests, or he may be standing below that plane. It is evident, therefore, that if the plane of the ground is chosen far below the plane of the horizon, the observer's eye will be far above the object, and the resulting per- • spective projection will be a " bird's-eye view." If, on the other hand, the plane of the ground is chosen above the plane of the horizon, the observer's eye will be below the object, and the re sulting perspective projection will show the object as though being viewed from below. This has sometimes been called a

worm's-eye view," or a "toad's-eye view." Usually the plane of the ground is chosen so that the dis tance between it and the plane of the horizon is about equal (at the scale of the drawing) to the height of a Man. This is the posi tion indicated in Fig. 7, and the resulting perspective will show the object as though seen by a man standing on the plane. on which the object rests.

30. The intersection of the picture plane and the plane of the horizon corresponds to the ground line used in the study of pro jections, in Mechanical Drawing. For more advanced work, how ever, there is some objection to this term. The intersection of the two coordinate planes has really no connection with the ground, and if the term " ground line " is used, it is apt to result in a confusion between the intersection of the two coordinate planes, and the intersection of the auxiliary plane of the ground, with the picture plane.

31. The intersection of the two planes is usually lettered VII on the picture plane, and HPP on the plane of the horizon. (See Fig. 7.) That is to say : When the vertical plane is being considered, VII represents the intersection of that plane with the plane of the horizon. It should also be considered as the vertical projection of plane of the horizon. See Mechani cl Drawing Part III, page 5, paragraph in italics. All points, lines, or surfaces lying in the plane of the horizon will have their vertical projection in VII.

32. On the other hand, when the horizontal plane is being considered, HPP repiesents the intersection of the two planes, and also the horizontal projection of the picture plane. All points, lines, or surfaces in the picture plane will have their horizontal projections in HPP. Thus, instead of considering the inter section of the two coordinate planes a single line, it should be considered. the coincidence of two lines, i.e.: First, the. vertical projection of the plane of the horizon; second, the horizontal projection of the picture plane.

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