ANOTHER VIEWPOINT

To many, the idea of tackling the techniques of linear perspective conjures an image of a high school geometry class with its plethora of elusive equations and its reliance upon t-squares, protractors, triangles, and other instruments of torture. In reality, application of the principles of linear perspective when combined with observation from life can be surprisingly simple. In fact, the projects that follow require no tools other than a pair of eyes and a pencil or stick of charcoal. In most situations it is not even necessary to know or indicate where the horizon line or vanishing point(s) are.

In practice, artists use methods that simplify the process of applying the principles of perspective to make the drawing of reality more manageable. This brief essay offers several methods for creating images that adhere to the principles of perspective without the need for complex and rigid methods.

Before going on, however, we should take a quick look to find out what exactly linear perspective is and where it came from.

.

Match-up

Modern linear perspective was invented in the early 15th century by architect and artist, Filippo Brunelleschi. His system was developed from ideas conceived as far back as the late Roman Empire period, around 100 A.D. Although Brunelleschi's formal method appeared only in the 1400s, artists from the mid-1200s through the late 1300s were already exploring techniques for making the objects in their pictures look more solid and real. What they lacked was a consistent system, and that's what Brunelleschi provided.

Linear perspective is, very simply, a technique for representing our 3-dimensional world on a flat, 2-dimensional surface. Its techniques are based
upon a few rules.

.

Rule #1: The near is larger than the far, and the far is smaller than the near. Given two objects of equal size, a pair of candlesticks for instance as in Figure-1, the closer object appears taller and broader than the one farther away.

.

.

Rule #1A: The near half of an object appears deeper than the far half. Wrap a piece of twine around the middle of a box, and the forward portion looks deeper than the rear half (Figure-1A).

Rule #2: An object, such as the side of a building, shrinks to a vanishing point on the horizon. Several objects in a row do the same thing, like the posts in Figure-2.

.

That's It!

That's all there is to it. Those are the essentials of linear perspective. Now lets see what can be done in a few common situations.

Keep in mind as you continue reading that you will generally be drawing real objects that you can look at for guidance. There is seldom the need to actually draw a horizon line or vanishing points; as you sketch, however, it is helpful to visualize where they are located so that your drawings end up seeming believable and appearing consistent with reality.

.

Boxing Match

We frequently need to know where the optical center of an object is. When placing a handle in the middle of a desk drawer, for instance, we want the handle to appear as though it is indeed in the middle. The same is true for the peak of a roof: it should look like it is directly above the center of a wall of a house. To carry out these and similar tasks, we need a method for quickly locating the center of a four-sided shape like a rectangle.

To find the center of a rectangle laid out flat, such as a sheet of paper spread across the surface of a table, a ruler can be used (Figure-3A). This works fine when drawing an object viewed head-on. If you try the same method with a rectangular surface turned at an angle, though, things end up looking out-of-kilter. This is what happened with Figure-3B, which is at odds with Rule #1A. If you recall, Rule #1A states that the near half of an object looks deeper than the more distant half. In Figure-3B, the reverse is true: the far half appears deeper than the near half.

.

.

A different method is called for when dealing with such situations. Known as X-the-box, heres how to do it (see Figure-3C).

Step 1: Connect each pair of opposing corners of a quadrangle (4-sided shape) with diagonal lines. Where the two (dotted) lines intersect, that is the center of the four-sided figure.

Step 2: Draw a vertical or horizontal centerline through the intersection of the two X-the-box diagonals to divide the quadrangle into two halves. Figure-3C shows both a horizontal and a vertical centerline, which reduces the rectangle to 4 equal sections. (This technique is effective with any 4-sided shape: rectangle, parallelogram, trapezoid, and so on.)

Incidentally, you have just drawn a window in perspective.

.

Out Of The Box

Notice that the horizontal centerline in Figure-3C is not truly horizontal. Instead, it is at a slight angle so that, if extended to the left, it would eventually reach the same vanishing point as the top and bottom edges of the rectangle. Figure-4A shows a centerline that is actually horizontal; Figure-4B is a duplicate of Figure-3C with vanishing lines and vanishing point indicated. Compare the two figures and ask yourself which seems the most realistic spatially.

.

.

This is one of those instances when a measuring device like a ruler comes in handy. It is not always convenient to mark off a vanishing point, such as when it falls beyond the edge of your paper or canvas, so a ruler becomes useful.

Note that the verticals in Figure-4B are true verticals; that is, they do not tilt toward the viewer (you) or lean away. This suggests that they are parallel to your erect body, so any point along a vertical is the same distance from your eyes as any other point. This is also the case with the edges of the rectangle in Figure-3A, which is why a ruler worked so well in that situation. It will also work for Figures-4A and 4B.

.

.

Step 1: Using the same rectangular shape as in Figure-4B, measure each vertical line to locate its midpoint and make a tick-mark at each of those spots (Figure-5A).

Step 2: Connect the tick-marks with a line to establish a horizontal centerline that is consistent perspectively with the rectangle (Figure-5B). If this centerline was extended leftward, it would eventually meet up with the vanishing point of the quadrangle, as shown in Figure-4B.

.

Little Boxes (Made of Ticky-Tacky)

Youre now ready to construct a shed. Our shed will have a peaked roof and a door in the center of one wall.

Step 1: From observation, sketch the body of a shed. If drawn well, it will conform to Rule #1 of perspective, meaning that the near edge will be taller than the more distant edges. Each visible side of the structure is essentially a rectangle, but a rectangle rotated at an angle to our line of sight. For each wall, X-the-box (Figure-6A).

.

.

Step 2: On the narrow end of the shed, draw a vertical line through the center of the X. Extend the line upward well above the body of the shed. The roof's peak is somewhere on that vertical (Figure-6B).

Step 3: Determine how high the peak of the roof should be and place a tick-mark at that spot. With diagonal lines, connect the tick-mark to each of the two upper corners of the wall to describe the eaves, and then complete the rest of the roof (Figure-6C).

Step 4: X-the-box of the long side of the shed, and draw a vertical line through the X (Figure-7A).

.

.

Step-5: Sketch in a door that straddles the vertical centerline (Figure-7B). Keeping Rule #1A in mind, make sure that the nearer part of the door is a bit broader than the distant portion. Taking Rule #1 into account also, the near edge of the door frame should be slightly longer or taller than the far edge.

.

Box, Box, and Box Again

Using the techniques outlined above, any 4-sided shape can be divided into halves, quarters, eighths, or any fraction that is a multiple of two. Using a similar method, we can also break a rectangular form into a number of segments that are multiples of three.

For this project, we are going to construct a 3-story apartment building that has 3 windows across its face. Begin by sketching the shape of the structure, and then complete the following steps.

Step 1: For the face of the building, X-the-box and draw a vertical through the X (Figure-8A).

Step 2: With the top of the vertical as Point-A, draw a diagonal from Point-A to the near lower corner of the building (Point-B), and another to the far corner (Point-C). Refer to Figure-8B.

.

.

Step 3: Each of the two new diagonals (A-B and A-C) crosses one of the X-the-box diagonals. Those intersections (D and E in Figure-8C) measure off 1/3 of the width of the wall. Draw a vertical line through D and another through E to establish the three columns of windows across the face of the building as shown in Figure-8C.

.

.

Step 4: (For this and the next step, the construction lines used in Steps-1 through 3 have been erased for clarity.) Following the same approach illustrated in Figure-5A, divide both vertical edges of the buildings face into thirds with a ruler (Figure-9A).

Step 5: Connect the tick-marks to draw the floor-lines (Figure-9B).

.

Boxed In

When a rectangle must be broken up into many segments, the method outlined below is generally quicker and easier than those described above. In this case, we will build a 7-story office tower. Across its face are 5 windows, and along the side are 3 windows.

Step 1: As before, sketch the building. Then, along each of its three vertical edges, measure seven sections equal in height (you should have 6 tick-marks). This is shown in Figure-10A.

.

.

Step 2: Connect the tick-marks to establish the floor-lines (Figure-10B). We now have a 7-story edifice.

Step 3: Starting at the roofline as 0, count down 5 tick-marks along the right edge of the tower. Draw a diagonal from Point-A to Point-5 (Figure-11A).

.

.

Step 4: Where line A-5 crosses a floor-line, draw a vertical. You should end up with 4 verticals that describe 5 columns of windows.

Step 5: Using the same procedure for the left side of the tower as for the right face, count down 3 floors and draw a diagonal from Point-A to Point-3 on the left edge of the structure (Figure-12A).

.

.

Step 6: As in Step-5, draw verticals through the intersections of A-3 with the floor lines to define the 3 columns of windows (Figure-12B).

.

Box It Up

There is another technique that is sometimes convenient for subjects such as the columns of windows in our Boxed In office tower. It is a method that is also very effective for drawing evenly spaced objects like a line of telephone poles, steps on a staircase, ladder rungs, and fence posts. In fact, it is called the "fence post method," and we are going to draw a row of fence posts going off into the distance by using it.

Step 1: While looking at a fence, draw the two fence posts closest to you (Figure-13A).

Step 2: This is one of those cases where you may need to figure out the location of the vanishing point for the object. To do so, draw a line that connects the tops of the posts and extend the line into the distance (to the left in Figure-13B). Do the same with the bottoms of the fence posts. The vanishing point (labeled V.P.) is located at the intersection of the two vanishing lines. For clarity, a horizon line is also indicated in the diagram. (See note below under Step-3.)

.

.

Step 3: X-the-box formed by the vanishing lines and two posts. Run a line through the center of the X to the vanishing point; this is the horizontal centerline of the fence (Figure-13C).

(Note: If your paper is not large enough to stretch the lines all the way to the vanishing point, or if it is inconvenient to do so, simply extend the vanishing lines as far as you can. Then measure each fence post to find its midpoint. Connect the midpoints by a line and extend that line as far as possible into the distance (to the left in Figure-13C). As you continue to place fence posts, this centerline will mark the center of each new post.)

Step 4: Draw a line from the top of the nearest post (Point-A) and through the center of the second post (Point-B) to the ground-line (Point-C) as shown in Figure-14A.

Step 5: Point-C is the location of the base of the third post. Draw the post upward from this spot (Figure-14B).

.

.

Step 6: Repeat Steps-4 and 5 as often as needed to make the number of posts you want. Figure-15 shows 5 posts.

.

.

Punch Your Way Out of The Box

As you can see, linear perspective need not be difficult to apply. In fact, it took much, much more time to explain the above techniques than it takes to execute them.

.

.

<Return to top>

.