[88] Parallel Light Rays (Sunlight) Parallel To Observer's Face (And Picture Plane) -
The top view at left shows observer looking at a table which has a pencil (small circle) stuck into it. The parallel light rays arriving from the left are parallel to the observer's face and to the picture plane. Therefore, the pencil's shadow must lie along the light ray shown dotted.
The shadow's length depends on the angle of the light ray, but this can only be seen in perspective (right). All angles are possible. Here, we use 45 degrees, which makes the shadow's length equal to the pencil's length. The light ray from eraser to dotted line locates the eraser shadow and hence fixes the length of the pencil's entire shadow.
Here, the two pencils at lower left are "bridged" by a third pencil which casts a new shadow line connecting the eraser shadows of the first two. This new shadow must be parallel to its shade line (bridging pencil), therefore, in perspective, both shade line and shadow use the same vanishing point. The other pencils in this drawing are "filled in" to form an opaque, two-dimensional plane. Its shadow is outlined exactly as before, so in both cases the outline pencils are the shade lines which determine the shadow's shape.
Now let's build two cubes using the existing two planes as sides. This creates new shade points at 1 and 2 which cast shadow points Is and 2s. These points help locate the shadow lines (shown dotted in top view) of the new top and vertical shade lines. Note the two vertical shade lines of the above drawing that have ceased to be shade lines here, since they are no longer boundaries between light and shade.
The Following Application Sketches All Have Shadows Cast By Parallel Light Rays [89]
Parallel To The Observer's Face
Therefore, the principles developed on the previous page will be evident. Note: Arrowed lines are light rays used to locate important shadow points. Dotted lines are temporary guide lines required to locate shadows.
[90] Parallel Light Rays (Sunlight) Oblique To Observer's Face (And Picture Plane)
1. When the rays are not parallel to observer's face (and picture plane) then they must appear to converge. This means more complex drawing but it does enable us to represent shadows the way we usually see them in sunlight.
In the top view below, light rays arrive at the angle shown by arrows. Therefore the pencil's shadows must lie along the dotted lines. As before, equal pencils cast equal and parallel shadows. In this case, though, the shadows are oblique to picture plane, so in perspective (right) they converge to a point on the horizon line.
LIGMT RAYÔ VAN. POINT
2. How do we draw the light rays that determine the shadow lengths? Previously, when the rays were parallel to the picture plane, we simply drew them parallel to one another. But now, being oblique, they must converge.
Their vanishing point, furthermore, must lie on the same vertical vanishing line as the shadows' vanishing point. Why? Because both the rays and the shadows lie on parallel planes (see top view. For a review of vertical vanishing lines, see pages 77-80).
Once this point is fixed, light rays passing through the erasers locate the correct shadow lengths.
LIGMT RAYÔ VAN. POINT
Though difficult to visualize, this vanishing point is actually the SUN many millions of miles away radiating a handful of parallel (converging because of perspective) light rays.
3. Now bridge a pencil across the eraser ends of the two lower left pencils below. Its shadow on the table will naturally connect the shadows of the eraser ends. Since the upright pencils cast shadows of equal length this new shadow must be parallel to the bridging pencil (shade line).
The other two pencils are "filled in" to create an opaque, two-dimensional plane. Again the new top shade line casts a parallel shadow line on the table top.
Though difficult to visualize, this vanishing point is actually the SUN many millions of miles away radiating a handful of parallel (converging because of perspective) light rays.
4. In perspective, these two new sets of parallel horizontal lines will each converge to a vanishing point. Note, though, that these new vanishing points are not essential to the drawing, since all key shadow points can be determined by the same light rays and shadow lines as above. (The new vanishing points can help, however, to verify the results.)
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