13. In the following explanations the notation usual in orthographic projections followed: . H = horizontal co-ordinate plane.• • • V = vertical co-ordinate plane. a = point in space.
av = vertical projection (or elevation) of the point.
ah = horizontal projection (or plan) of the point.
= shadow on V of the point a. = shadow on II of the point a. = ray of light in space.
Re =. vertical projection (or elevation) of ray of light.
Rh = horizontal projection (or plan) of ray of light.
GL= ground line, refers to a plane on which a shadow is to be cast, and is that projection of the plane which is a line.
14. In orthographic projection a given point is determined by "project ing" it upon a vertical and upon a horizOntal plane. In representing these planes upon a sheet of drawing paper it is evident, since they are at right angles to each other, that when the plane of the paper represents V (the vertical "co-ordinate" plane), the-hor izontal "co-ordinate" plane H, would be seen and rep resented as a horizontal line, Fig. 2. Vice versa, when. the plane of the paper represents H (the horizontal co ordinate plane) , the vertical co-ordinate plane V, would be seen and represented by a horizontal line, Fig. 2.
15. In architectural drawings having the eleva tion and plans upon the same sheet, it is customary to place the "elevation," or vertical projection, above the plan, as in Fig. 2.
It is evident that the distance between the two ground lines can be that which best suits convenience.
16. As the problems of finding the shades and shadows of objects are problems dealing with points, lines, surfaces, and solids, they are dealt with as problems in Descriptive Geometry. It is assumed that the student is familiar with the principles of orthographic projection. In the following problems, the objects are referred to the usual co-ordinate planes, but as it is unusual in architectural drawings to have the plan Paid elevation on the same sheet, two ground lines are used instead of one.
17. Ray of Light. The assumed direction of the conven tional ray of light R, is that of the diagonal of a cube, sloping downward, forward and to the right; the cube being placed so that its faces are either parallel or perpendicular to H and V. Fig. 3 shows the elevation and plan of such a cube and its diagonal. It will be seen from this that the If and V projections of the ray of light make angles of 45° with the ground lines. The true angle which the actual 'ray in space makes with the co-ordinate Plahes is 35° 15' 52' This true angle can be determined as shown in Fig. 4. Revolve the ray parallel to either of the co-ordinate planes, In Fig. 4, it has been revolved parallel to lr, hence T is its true angle.
18. It is important in the following explanations to realize the difference in the terms "ray of light," and "projections of the ray of light."