Every draftsman must know the fundamentals of perspective. The architectural draftsman must be thoroughly familiar with the intricate details of the subject, and the mechanical draftsman should be able to make perspectives from shop drawings just as readily as he makes shop drawings from perspectives.

Every perspective drawing involves THE HORIZON, THE EYE LEVEL AND THE VANISHING POINT.

These three things are inseparable, for the horizon is the eye level and the vanishing point is always on the horizon. The eye level and vanishing point are always on the horizon. The vanishing point, as the name implies, is that point on the horizon where all parallel lines meet, and while it does not actually exist in reality, it is very real in perspective drawing, for it is the basis of the entire subject. All parallel lines meet at the vanishing point.

There are two kinds of perspective: PARALLEL and ANGULAR. In parallel perspective, the sides of all block-line objects turned toward you are parallel to your two eyes, just as is the face of a mirror when you look into it and see yourself. Consequently, there is only one vanishing point which is on the horizon directly in front of you, between your two eyes. In angular perspective, the object is at an angle with your eyes and all parallel lines on the right side vanish to the vanishing point right (V.P.R.), while all parallel lines on the left side vanish to the vanishing point left (V.P.L.).

Because it is the simplest, let us first consider parallel perspective. In Figure A on page 69, we see the horizontal line X-Y, near the center of which is a tiny cross denoting the vanishing point V. If a number of lines are now drawn through this point V at various angles, we have the basis of a drawing in parallel perspective. Suppose we take the lines A-V and F-V and use them as guide lines for the rails of a track, as shown in Figure C. We will then use the lines A'-V and E-V as guide lines for a number of telegraph poles, as shown in the same figure. We now have the beginning of a perspective drawing. The track vanishes in the distance and so do the poles and they both vanish at V, the vanishing point. So far, we haven't used any of the other lines, so, in order to do so, let's rough in a fence on the left side of the track between the lines B-V and C-V, then put in a house, using the line D'-V as a guide for the roof. Now look at Figure D. Here we have added a number of other lines—all meeting at the vanishing point V. By using these lines as guides, we can put in another and somewhat taller house, a smokestack and a billboard. Now our picture is becoming more complete. With careful inking, touching up here and there and erasing the guide lines, we soon have the finished perspective shown in Figure E. Notice that the only lines which appear on the drawing are either horizontal or vertical, or they are lines which, if extended, pass through the vanishing point V. There are no other lines.

Now if you examine Figure D, you will see that the horizon line X-Y passes between the first and second-story window of the first house. This means that the eye level in this picture is about eight or ten feet above the track. Suppose you wanted to see this picture from a height of forty or fifty feet above the track. How would you go about doing it? To draw a picture where almost everything is below the eye level, start as before with a horizontal line X-Y (Figure F), and the vanishing point V. Now, instead of letting all the lines cross this V point as we did before, we bring them all up to it; but we cannot go above X-Y because there is nothing above the eye level at this height (except the top of the smokestack). Nothing above the eye level means nothing above the horizon. All converging lines, except the smokestack top, are below X-Y. We now have the rough sketch shown in Figure G, and the finished drawing shown in Figure H. This is about what the view shown in Figure E would look like from a height of about fifty feet.

In a similar manner, if you sat down on the track so that your eye level was only three feet above it, nearly all the converging lines would be above the horizon line X-Y, as shown in Figure J. Your finished drawing would resemble Figure L.

TO LAY OFF EQUAL DISTANCES IN PERSPECTIVE

It is often necessary to lay off equal distances in perspective. The method of doing this is simple and is shown in the diagram below. You must put in the first division (C-D) by eye and, after doing this, draw a straight line from the vanishing point through the center of this first division

(O). Now draw a line from A through the point O, meeting the top line in E. This is the next division, and a vertical line E-F should now be drawn. This vertical line cuts the center line in 0'; a line from D through this O' should be drawn to meet the top line in G. Now draw the line G-H to get the third division. Keep this method up until the entire space is divided equally in perspective.

On page 71 you will observe a number of boxes above and below the horizon, or at eye level. Note the extension lines meeting at the vanishing point V, which is right in front of you on the horizon. No matter where these boxes are, as long as the side toward you is parallel to the plane of your eyes, all parallel sides, if extended, will meet at the vanishing point V.

Now make one of these boxes yourself. Draw a horizontal line, mark on it a vanishing point somewhere in the center, and draw lines from this point in all directions. Use these lines as guides for the edges of various boxes which occur to the right, the left, above and below the eye level. Do this carefully and place in the picture as many boxes of different sizes as you can.

Look at the diagrams on page 72. These show five boxes and a building in angular perspective -that is, no side is parallel to your eyes. Here we have two vanishing points. The left sides of all the boxes and the building have edges which, if extended, would all meet in the left vanishing point (V.P.L.). The right sides all have edges which, if extended, would all meet in the right vanishing point (V.P.R.). In the drawing, all the sides of the boxes and the building are parallel to each other. That is why they all meet in the two vanishing points. If one of the boxes were turned so that its sides were not parallel to any of the others, we should have two other vanishing points for that particular box, as shown in box B at the lower left-hand corner. Note that in this case, the V.P.L. is far off the paper. It may be found by extending the lines from the left edge of the paper until they meet the horizon line extended to the left.

EVERY BLOCK-SHAPED OBJECT, NOT IN PARALLEL PERSPECTIVE, HAS TWO VANISHING POINTS

One at the left and one at the right, regardless of whether it is above, on, or below the eye level. If you are drawing a number of objects in angular perspective, and they are not parallel to each other, you will have two vanishing points for each object, although all the vanishing points will be on the horizon.

Practice drawing objects in angular perspective. Draw a table, below the eye level, with a box on the floor next to it. The sides of the box should not be parallel to any of the sides of the table. When you have the table roughed in, with the correct vanishing points and the box, with two other vanishing points, near it, draw them over again on another part of the paper, using the same vanishing points. Try drawing these two objects above the eye level. This will give you excellent practice.

On page 74 you will see a rough sketch of three objects: a wastepaper basket, a bureau and a rug. Since none of the edges of any one of these three objects is parallel to any other, they all have different vanishing points. The wastepaper basket has a VPL and a VPR. In most cases, the vanishing points are off the paper entirely. The rug has two different vanishing points, VPL and VPR; and the bureau has two other vanishing points, VPL and VPR.

All these vanishing points are on the eye level, which is on the heavy black line indicated. If you extend all these lines sufficiently far, you will find the six vanishing points of these three objects to be on this line. If a table were shown in this picture, and the face of this table were parallel to any one of these objects, its two vanishing points would be identical with the vanishing points of that object; but if it is not parallel to any one of the objects, it will have two new vanishing points.

It is important to be able to draw true and accurate perspectives from plans and elevations. As a matter of fact, architectural draftsmen must know the theory and practical application of at least one of the many projecting methods. For this reason we are giving one of the simplest methods in detail.

PERSPECTIVE-PROJECTION METHOD

The projection method shown on page 76 enables us to draw objects accurately in perspective. In the projection method we must have a plan, a side elevation (A), and a front elevation (D).

The first step is to decide at what particular angle you want to view the object—in this case, a very simple drawing of a house. Having decided upon the particular angle, the next step is to draw a perfectly straight horizontal line through the lowest point on the plan at that angle—the point P. This line is called the picture plane.

Now draw a vertical line through the point P, extending it all the way down the full length of the paper. This line is called the measuring line. Somewhere on this measuring line, near the bottom of the paper, mark the point S. This is the point where you yourself are located, and it is now up to you to decide whether you want to view the object from your eye level which is 6 feet above the ground, or to view it from a height 30 or 40 feet above the ground. Of course this decision will govern the position of the horizon.

S marks the lowest point on your measuring line—the bottom of your drawing and corresponds with the base of the elevations, as you can see. Everything on the measuring line is measured from S upwards. The height of your eye above the ground is determined by the distance from S to the horizon. If you are merely standing at the point S, observing the house, and your eyes consequently are approximately 6 feet above the horizon, measure 6 feet along the measuring line from S and the horizon will pass through this point. In the illustration, you can readily see that the distance from S to the horizon is about twice as high as the house, or approximately 40 feet. This means that you are viewing the house from a height of 40 feet, since your eye level is always on the horizon.

Having drawn the horizon, the next step is to draw two lines through S: one line SX parallel to the left side of the plan, and the other line SY parallel to the right side of the plan. Where these lines intersect the picture plane, draw two vertical lines. Where these two vertical lines intersect the horizon we have the vanishing points. The line SX, projected down from the picture plane, produces the left vanishing point, or V.P.L. The line SY intersects the picture plane at a point entirely off the paper; consequently, the right vanishing point V.P.R. is off the paper.

Three very important points are now to be considered: the two vanishing points and the point S. With your triangle, draw lines from all the corners, and from all the places where the windows and doors are on the plan, to meet at the point S; but stop these lines when they meet the picture plane, as shown. After the lines meet the picture plane, all of them are projected down vertically — all parallel to the measuring line. These lines, and the lines projected out to the vanishing points, are your guide lines; the entire perspective is drawn from these.

It becomes a simple matter to follow all the lines down, and to see how they play their parts in the perspective. The line A, for example, is the outside edge of the one-story entrance, and if you follow it down, you will see how it is actually shown in the perspective. The same is true of the lines C, M and O; all are outside edges. If you follow the other lettered lines down, you will see where the windows are placed, for these form guide lines for the vertical sides of the windows. You now have a number of vertical guide lines and two vanishing points.

The next step is to work the side and front elevations into the perspective. This is done by drawing horizontal lines from the top and bottom of the windows, as well as from the roof lines directly over to the measuring line, as shown. The points of intersection of these lines on the measuring line determine all the horizontal lines on the perspective—the roof, the tops and bottoms of the windows, etc. All you need to do is to connect these points with the vanishing points, and to note where these lines cross the vertical lines in order to determine the location of windows, doors, etc. This you can see from a careful inspection of the perspective; you can also understand it better by studying in this perspective the important part the various vertical lines, horizontal lines and two vanishing points play in its construction.

On page 77 we are given another view of the same house, drawn by the same projection method. Note that the plan makes a different angle with the picture plane. Also note that instead of being 40 feet above the ground, you are at eye level. The horizon is only 6 feet up from S. This is just the way the house would appear if you were standing looking at it from a short distance. By comparing this with the other perspective you can see that the two elevations and the plans are identical; the only difference is in your own position.

It would be excellent practice for you to copy this plan and the elevations, and to draw a perspective of them as viewed from some other point 20 feet above the ground.

This method of perspective projection is used by many architects and draftsmen. You have undoubtedly seen beautiful watercolor drawings of apartment house buildings on the walls of various real estate offices. These pictures are perspectives, done accurately from the architect's plans and elevations, either by this method or a similar method. If you understand the method thoroughly, you can draw any object in perfect perspective from any point of view you choose.

It sometimes may happen that objects on the plan come in front of the picture plane. For instance, you might have a fence or a tree located nearer to point S than to point P. If this is the case, follow the same general rule by connecting the tree or other object with the point S and projecting the line back to the picture plane, letting it come down vertically parallel to the measuring line. This will give the vertical location of the tree or other object on your perspective.

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