Descriptive geometry . ve but one trace ? 2. Hew must a line be placed so as to have no truer ? 3. How must a line be placed so that its horizontal (or ver-tical) trace is indeterminate ? -?tv X Fig. 54. CHAPTER IV SIMPLE SHADOWS 39. Shadows. The shadow of a point on a plane is the pointin which a ray of light passing through the given point is in-tercepted by the plane. The conventional ray of light is a line sloping downward,backward, to the right, with both projections inclined at 45°with the ground line. Such a ray is shown by the line L,Fig. 55. 40. Shadow of a Point. The shadow on V of t
Descriptive geometry . ve but one trace ? 2. Hew must a line be placed so as to have no truer ? 3. How must a line be placed so that its horizontal (or ver-tical) trace is indeterminate ? -?tv X Fig. 54. CHAPTER IV SIMPLE SHADOWS 39. Shadows. The shadow of a point on a plane is the pointin which a ray of light passing through the given point is in-tercepted by the plane. The conventional ray of light is a line sloping downward,backward, to the right, with both projections inclined at 45°with the ground line. Such a ray is shown by the line L,Fig. 55. 40. Shadow of a Point. The shadow on V of the point a,Fig. 55, is the point, aa in which the ray of light, L, passing through a, intersects V. The shadowon H is the point, as, where L pierces will be noted that the points atand as are the traces (§ 37) of the lineL on V and H respectively. Hencethe shadow of a point on the coordinateplanes is found by drawing throughthe point a line representing the rayof light, and then finding the tracesof this Fig. 55. 41. Opaque and Transparent order that an actual shadow maybe cast, it is necessary that the planereceiving the shadow be opaque. Thus, in Fig. 55, if V be con-sidered opaque, at is the actual shadow of the point a; but ifV be considered transparent and H opaque, as will be theactual shadow. In work with shadows, it is customary toplace the object in the first quadrant, and to consider both//and Fas opaque. Since the two projections of the ray of light make equalangles with the ground line, it follows that the actual shadow 20 IV, § 43] SIMPLE SHADOWS 27 of a point must always fall on the nearer coordinate plane. Inthe case of a solid object, the actual shadow may fall wholly onH, wholly on V, or partly on both planes, according to the sizeand position of the object. 42. Shadow of a Line. The shadow of a line will consist of theshadows of the points which compose the line. If the line isstraight, only the shadows of the two ends of the line need
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