51 Long Lane

Upper Darby, PA 19082

ph: 610-734-1231

kaplanpi

**basics**

contents

*- Match-up (fundamental rules)*

*- That's It!*

*- Boxing Match (principle of near and far) - Size Counts (halving a quadrangle)*

*- Out of The Box (alternate method for halving a quadrangle)*

*- Box It Up (row of evenly spaced posts) - Punch Your Way Out of The Box (conclusion)*

*ANOTHER VIEWPOINT*

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**T**o 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.*

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**MATCH-UP**

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.

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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., and possibly earlier. 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.

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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 simple rules.

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**rule #1 ***The near is larger than the far, and the far is smaller than the near. *

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Given two objects of equal size, like the pair of candlesticks in Figure-1A, the closer object appears taller and broader than the one farther away.

The same is true of the nearer half of an object versus the more distant half. This is evident in Figure-1B in which a cube is wrapped midway with a strand of ribbon. The near half appears thicker or deeper than the far portion.

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**rule #2** *The near half of an object appears deeper than the far half. *

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Several objects in a row do the same thing, like the posts in Figure-2. Each is smaller than the one before it. Note that the row of posts recedes in a logical fashion to a vanishing point (V.P.) placed at the horizon.

**rule #3** *Objects shrink in size to a vanishing point on the horizon. *

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**THAT'S IT!**

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

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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 seem believable and appear consistent with reality.

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**BOXING MATCH**

According to Rule #1, the near is larger than the far. This applies to an individual object as well as to groups of objects. Since it is so easy to do, it is well worth checking your drawing while it is in progress to determine whether it adheres to this rule.

In Figure-3A, the box appears “odd,” not at all convincing. After measuring, it was found that the face of the box and the back of the box were both 4" across. That is a violation of Rule #1; the face should be wider than the back. An adjustment was therefore made, with the result shown in Figure-3B where the back is now only 3" wide.

In checking the vertical edges of the box (Figure-3C), it was discovered that the back edge was actually taller than the front edge, just the opposite of what should occur. The error was corrected in Figure-3D. The box now looks fully believable and consistent with the effects of perspective, with front being taller and wider than the back.

*(It should be noted that all edges *appear* to recede to the *same* vanishing point. While this may or may not be true, it is important that they at least appear to do so, which is why it is helpful to visualize where the vanishing point is located while drawing.) *

It is not necessary to use a ruler to check your drawings, and a ruler is often limiting. It can be done just as easily with a pencil, slip of paper, or any number of items. For example, the method for making comparison measurements with a pencil is shown in Figure-3E.

**SIZE COUNTS**

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. 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 true rectangle, such as a sheet of paper spread flat across a table, a ruler can be used (Figure-4A). If you pick up the paper and turn it at an angle, however, it no longer appears truly rectangular; it looks more like a trapezoid or parallelogram and a ruler is no longer helpful. If we tried using a ruler in such a situation, the results would be at odds with Rule #2 above which states: “The near half of an object appears deeper than the far half.”

A ruler was used in Figure-4B, and the centerline does not really look like it is in the center. Some other method must, therefore, be applied.

A simple method is to “X-the-box.” Here's how to do it (see Figure-4C):

**step 1**

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

**step 2**

Draw a vertical or horizontal centerline (blue in Figure-4) through the intersection of the diagonals to divide the quadrangle into two halves either vertically or horizontally. For comparison purposes, the ruled measurements and centerline have been left in place in Figure-4C.

In Figure-4D, all construction lines have been removed. The illustration shows both a horizontal and a vertical centerline, which reduces the rectangle to 4 optically equal sections so that it resembles a window.

Using the X-the-box technique, it is possible to reduce a quadrangle to any number of sections that are a multiple of two. For example, simply divide a shape in half, and then divide each of the halves in two to yield four optically equal segments. These can be further divided as many times as required.

**OUT OF THE BOX**** **Notice that the horizontal centerline in Figure-4D is not truly horizontal. Instead, it is at a slight angle and if extended to the left, it would eventually reach the same vanishing point as the top and bottom edges of the rectangle. Figure-5A shows a centerline that is actually horizontal; Figure-5B is a duplicate of Figure-4C with vanishing lines and vanishing point indicated. Compare the two figures and ask yourself which seems the most realistic spatially.

For greater clarity, the vanishing lines have been erased below. Figure-6A is the same as Figure-5A, and Figure-6B is equivalent to Figure-5B.

This is one of those instances when a measuring device like a ruler comes in handy. It is not always convenient to mark the location of a vanishing point, such as when it falls beyond the edge of your paper or canvas. In a situation like that shown in Figure-6, where the vertical edges are true verticals, a measuring instrument may be useful.

Like the edges of the sheet of paper in Figure-4, the vertical edges in Figure-6 are parallel to your body. In other words, they do not tilt toward you or angle away from you. Thus, any point along each vertical is the same distance from your eyes as any other point and can be measured with a ruler..

**step 1**

The rectangular shape in Figure-6B has been duplicated in Figure-7A. Measure each vertical edge of the trapezoid to locate its midpoint and make a tick-mark at each of those spots (“0” in the illustration).

**step 2**

Connect the "0" tick-marks with a line to establish a horizontal centerline that is consistent perspectively with the rest of the quadrangle (Figure-7B). If this centerline was extended leftward, it would eventually meet up with the vanishing point of the quadrangle's frame as shown in Figure-5B.

**BOX IT UP**

There is a technique similar to X-the-box that is convenient 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 use it to draw a row of fence posts going off into the distance.

**step 1**

Draw the two fence posts closest to you (Figure-8A).

**step 2**

If your paper is large enough, mark the location of the fence’s vanishing point (Figure-8B). Otherwise, measure to find the midpoint of each of the two fence posts and connect the midpoints with a line as was done in Figure-8C. Then extend that line into the distance (to the left in Figure-8C) as far as possible. In either case, connect the tops and bottoms of the posts with lines that go to the V.P. (Figure-8B), or into the distance (Figure-8C).

**step 3**

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-8D.

**step 5**

Point-C is the location of the base of the third post. Draw the post upward from this spot (Figure-8E).

**step 6**

Repeat Steps-4 and 5 as often as needed to make the number of posts you want. Figure-8F shows 5 posts.

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**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.

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51 Long Lane

Upper Darby, PA 19082

ph: 610-734-1231

kaplanpi