Part 41

We see by the agency of light, as all objects, except such as may be styled self-luminous, when placed in a dark chamber are not perceivable by us, except by touch, smell or hearing; we cannot see them; they are invisible. But when, by removing a shutter or igniting a flame, we introduce something to the chamber which was not present when the chamber was dark, we become at once conscious of the appearance of the object, we perceive it by the sense of sight.

This something which must always be present to enable us to see, is called Light; all objects are made visible to the sense of seeing by its agency.

Without light, natural or artificial, it would be impossible to distinguish one object from another.

That the Visual Rays pass from objects in straight lines to the eye may be proved by the following experiment (see fig. 306):--Pierce two screens with a large pin, and place them so that the holes are in a straight line with a flame, as the light of a candle or lamp. On fixing the eye to one of these holes we are able to see the flame; but if we slightly move the flame, one of the screens, or the eye, the flame is no longer visible. To be visible, the flame, the holes in the screens, and the eye must all be in the same straight line. See fig. 306.

In fig. 299 the picture plane is represented by the rectangle W X Y Z. Although the picture plane is here shown as a rectangle, it may be of any shape or of any size.

The observer is at S, looking through the picture plane at the cross R C O H. The observer is standing upon a horizontal surface, which is called the ground plane. If we are in a room, the window may be called a picture plane and the floor a ground plane.

The picture plane rests, as it were, upon the ground plane, in a line which passes from Y to Z. The two planes meet or intersect in this line, which is called the ground line. The ground line is sometimes called the picture line, or the measuring line.

The visual rays, by means of which the observer sees the cross, will, in their course from it to the eye, pass through the picture plane. These visual rays will intersect the picture plane in a number of points, and if we mark the true positions of these points the result will be a perspective image of the cross.

The rays are shown passing from the cross to the eye of the observer, and meeting the picture plane in points r, c, o, h; r being joined to o, and c to h, we have the perspective image of the cross as it would appear to the observer at S. Of course an infinite number of rays proceed from the cross to the eye of the observer; but it is quite evident that we need only consider those proceeding from the extremities of the object.

Scale or Approximate Perspective.

Real, or true perspective, represents the object exactly as it is seen in nature, where the parts that are far away from the eye of the observer appear smaller than those nearby. Occasions arise, however, in practical life, with its numerous phases of industrial requirements, where the convenience of showing the complete form of the object in a single view might preferably be coupled with the convenience of scale dimensions.

This has led to a modified perspective, that sacrifices some of the accuracy in the appearance of the object to gain the advantage of scale dimensions; this form of perspective may be distinguished by the name--approximate or scale perspective--which does not represent the object exactly as seen in nature, but where those parts that are afar off are shown of the same size as those that are near by, and where the lines that run out into space are parallel to each other and do not converge into a vanishing point.

To represent an object in perspective, the horizon and the point of vision will have to appear in the drawing as the fundamental starting points.

Three dimensions are distinguished for the fixing of an object in space from a certain reference point. They are height, breadth and thickness, and are in their direction square to each other. The height is the fundamental direction, being derived from the direction of gravity, that invariably extends to the center of the earth.

All directions in the perspective determination of an object are parallel to these.

Vertical lines and planes point toward the center of the earth, while horizontal planes, including the directions of breadth and thickness, are square to the vertical direction. In this, the principal visual ray extends in the direction of thickness.

For a clear understanding of perspective, it must be firmly fixed in mind, that for each prominent point of the object behind the picture plane, a corresponding point lies in the picture plane, in that position where a straight line or ray of sight that is going from the eye to the point of the object, cuts through the picture plane.

Suppose we could replace these rays of sight by thin, visible threads of wire that would go through little holes in the picture plane, we could then walk around this bundle of rays, and by looking at it from three different directions, we would get three different views of it. We may look upon it from the top, from the side or from the end, where the bundle of rays all concentrate in the eye of the observer.

Figs. 307 and 308 show, in two cases, how these three views would appear. The end views are those where the perspective picture appears on the plane, while the top and side views only show where the rays intersect the picture plane. The top view shows how far, for example, point A is distant from a vertical line O Z, while the side view shows how far point A is below horizontal line O X, which is at the same height above the ground as the eye of the observer, O. Thus, all points of the cube can be located on the picture plane, and the outlines of the cube reproduced in perspective.

Modified arrangements are shown in figs. 309 and 310 for parallel and angular perspective.

The views are so arranged in relation to each other that the picture plane in the top view is parallel to the horizon and the ground-line, which latter is the intersection of the picture plane with the level ground of the end or perspective view. At the same time the eye of the observer is in one and the same vertical line for both views, two vanishing points may be found in the horizon outside of the principal visual ray. To find the position of these two vanishing points in the picture plane, the modified top view, fig. 310, is used.

As all lines that end in a vanishing point must be parallel in reality, this parallelism may be seen in the top view and lines through the eye of the observer, parallel to the directions of the main lines of the object, will cut the picture plane at the vanishing points.

Through these two vanishing points the directions of two sets of lines are found, the starting points of which are determined from the plane of measurement. The third set of lines, being vertical, also appears vertical and parallel in the picture.

The position of each vertical line is found in the top view, where the light rays from the observing eye to the ends of the vertical lines intersect with the picture plane. Projecting these points down upon the rays to the vanishing points produces the vertical lines in the picture.

For example, in fig. 311, the purpose of perspective is entirely defeated by placing the eye of the observer directly in front of the object and arriving at the view taken in mechanical drawing which needs supplementary views for complete comprehension of the form of the object.

In fig. 312 the eye of the observer is first placed directly opposite the object, then it sees the object to the left but a short distance away, while in the third figure the observer is farther away from the object. In each case the picture plane and plane of measurement is at the front face of the cube.

For such simple objects, it is not necessary to draw the top view at all. The only reminder of the top view is the eye or point of vision, the picture plane that falls together for the sake of convenience with the horizon of the end view and the ray that determines the measurement point M, which is, in this suppressed reproduction, absolutely necessary, in order to find the apparent position of the real corners behind the picture plane.

So far, only square or sharp-cornered objects have been represented in perspective.