Perspectival Shadows cast from Before

Last time, we considered the method of showing a proper shadow cast from a light source which is behind the viewer. This lesson today will demonstrate the opposite situation, where the light source is before the viewer.

Andrew Loomis in his book Successful Drawing shows us the method of solving how to draw shadows in proper perspective. The first point which needs stating is a concept hinted at from 2 postings past, which I hope to make concrete by the end of this lesson. The aforementioned idea is that if the light source is Behind, the angle of light is below the horizon. When the light source is before the viewer, the angle of the light is above the horizon. Hold onto this thought, and I will review it at the end of the lesson, where I am sure it will form an integration for you.

Here are the steps for casting a perspectival shadow from a light source which is before.

Set up your horizon and the object using proper perspective. Establish the Vanishing Points for the object’s sides, and draw the appropriate angles. Draw the guidelines for the perspective on a separate layer of vellum or digitally, then remove the guidelines when the object is perspective. Save the layer.
Since the light source in this exercise is before the viewer, it is proper to next establish the position of where that light is coming from specifically. This should be done with precision within the layout phase of your drawing. Even if the light is not going to be within the boundaries of your finish crop for the illustration, you must lay it out with exact placement, or else your shadows will appear unconvincing. Drop a line vertically down at 90 degrees from the centre of the light source to the horizon line.
The point where the vertical line crosses the horizon will be the VP of the shadows. This is a crucial step, so pay close attention to it. As a rule, the Vanishing Point of shadows is directly below the light source when the light is cast from a Before placement. The blue lines below represent the projection for the Shadow VP. Please not that these guidelines cross through the corners of the object you are drawing, laying on the ground plane.
Next we will cast the lines of light, which will fall like a triangle from the light source. Each corner of the object you are drawing will interrupt the light, but the perspective you have chosen may conceal certain corners. In this drawing there are 3 corners which will cast a shadow we can see, so there will be 3 lines. If your object and perspective yields more corners which will cast a shadow, use the appropriate amount of lines. Note how the light lines emanate from the centre of the light source, not its perimeter. Cast the light lines further than where the Shadow VP lines lay on the plane.
Now, turn on the layer with the original perspective lines showing. These perspective lines will give us the other half of the information we ned regarding where the shadow’s perimeter will lay.
Where the red light lines cross either the blue Shadow VP lines or the black object perspective lines with demarcate the corners of the cast shadow your object will make, given the perspective you have chosen, and the placement of the light source. I have numbered these 1-4. Numbers 5 and 6 are the points where your object touches the plane it rests on, and from these points the shadow will originate.
Outline the cast shadow perimeter, then fill it in with the value appropriate for the light intensity you are describing. The darker the shadow, the brighter the light. Add half-tones to the shaded sides of the object (the sides facing away from the light) Flat planes have even shading, curving planes will appear as a gradation.
Remove the guidelines to reveal your illustration of a properly done shadow, in perspective, with the light source before the viewer. Congratulations!

As a last comment, think back the the idea of the angle of light above and below the horizon which I mentioned at the beginning. If you think about it, it is natural to recognize that the angle will come from above when the light is before, because when standing on the earth, you perceive the horizon above you. If the light is coming from behind, the angle must come from below for the same reason. It is possible, tho rare that one’s point of view can be distorted, such that the horizon is perceived as below you. This could occur if you are inverted or suspended in the air. Such points of view will break this rule. Luckily, there are limited calls for illustrations of that type. I will cover such considerations at a much later date, due to their peculiarity.

There are many more subtleties related to cast shadows, but I believe I will go onto showing organic cast shadows in perspective next week. It will be a difficult one!

Cast Shadows: Behind and Before

When you are drawing shadows, there are a couple of rules which need to be remembered in order to create a natural looking illusion of light. Fortunately, Andrew Loomis helps us negotiate these points in his book Successful Drawing.

The first rule he indicates is an observation regarding the two location choices of light source when representing cast shadows; that is, a behind light source or a before light source. Behind and before are designations of where the light source is in relation to the viewer of the picture, not the subject. Examine these samples I’ve drawn for you below.

In the picture of the Ogre below, the primary cast shadow on the ground plane shows us that the light source is behind you– the viewer of this picture. The ogre’s actual body is interrupting the direction the light is falling, and hence, it casts a shadow behind. Notice that cast shadows which are even somewhat to the side of the subject are still considered the result of a behind light source.

If the light source is behind, the shadow will fall behind.

(NB. In this drawing there happens to be two light sources, as you can see in the secondary small cast shadow under the ogre’s chin, and likewise below his hands. For this matter, we are regarding only the large cast shadow on the ground.)

This drawing is considered to be a light source which is before the viewer. One can tell on account of the fact that the shadow is falling between where we the viewers are, and the subject matter of the lady, as she sits on the plane. One can imagine the sun above her, in the sky, before where you are standing, looking at this lady. The sun before you, therefore constitutes a before light source.

If the light source is before, the shadow will fall between.

Now that the terms before and behind have been established, there are several rules about casting shadows from before and behind light. Here are Loomis’ rules about drawing cast shadows.

If the light source is behind the viewer, the angle of the light comes from below the horizon.
If the light source is before the viewer, the angle of light comes from above the horizon.
If the light source is before the viewer, put the shadow VP on the horizon nearby, below the light source.
When the light source is before the viewer, the angle of light is the nearest of the 3 cast shadow considerations;
- position of light source
- angle of light
- VP of shadow on the horizon
All shadows radiate from a point on the ground directly below the light source. This point is the shadow vanishing point (SVP)
All shadows within a drawing recede to the same SVP.
The length of shadow on the ground plane is determined by the angle of light.

That is a lot to digest, so at this point, it may be of use to my readers to think on these concepts for a while, before diving into how one actually draws before and behind light source shadows. Next week, I will demonstrate that process, as well as how to cast shadows of organic shapes, like those in my samples above.

Thank you very much for your continued interest.

Bye for now.

Types of Light, Cast Shadows & Perspective of Shadows

Greetings, this week we will be continuing our discussion of Andrew Loomis’ book Successful Drawing, and considering types of light and how to represent shadow.

He begins by indicating that there are two main types of light. These types are

Direct light
Indirect light

Loomis emphasizes that the decision to treat a scene or subject which an artist is attempting to represent, begins with choosing one or the other of these 2 types. It is important to choose only one of these types, and to stick to it because the treatment of light in a drawing is what gives the art an impression of consistency. The absence of light could technically also be a 3rd category, but Loomis doesn’t even mention it because the drawing would be pure black. Any small amount of a subject matter, regardless of shadow depth around it, is an effect of Indirect Light treatment.

With the casting of light, comes the Cast Shadow. Cast shadows are the areas of a drawing where your subject matter interferes with the direction of light, and that interruption shows on another plane in the form of a shadow. The shadow you see of yourself on the ground on a bright day is a Cast Shadow. This is different than the type of shadow called Shading; ie. how lights and darks fall on an object, as discussed previously. Although one could consider the Shading on the dark side of the moon, to be a shadow which is cast by its lit side, such reasoning only confuses the issue. It is better to think of Cast Shadows as those shadows which an object throws onto another plane or object.

Cast Shadows: the interruption of light caused by an object, translated as darker value, appearing on a secondary object.
Shading: the translation of how light falls on a specific form, related to that form’s general shape.

When representing Cast Shadows, the artist must consider 3 factors. These factors are as follows:

position of light source
angle of light
the Vanishing Point (VP) of the shadow on the horizon.

Each of these three must be understood in order to place a Cast Shadow convincingly within the context of the scene an artist is attempting to represent. Loomis shows us how to do it. He indicates the best way to cast the shadow properly is to alter the plane of your subject matter which is facing the light to a square. Draw this square properly extending to the VP. Then, using the line the light falls at, project a central line and lines from the corners to the angle of ground you have your subject matter sitting on. This will show you how a square casts a shadow.

Example.

Here are the steps.

Contour draw your actual subject matter with light pencil. Decide where the light is hitting the object and the angle it is coming at.
Draw a line of the light direction, and approximate the “Illustrator’s Bump” (see last post) which will show at the transition from light to half tones. The line of light will bisect the Bump.
Draw a flat square shape, representing a simplification of the plane of your subject matter which is facing the light. Set the square to the VP which your actual subject matter is related to. Cast diagonals from corner to corner of your new square to reveal the centre. I do this on a separate layer to keep the original artwork clean. NB> the line of light is not related to the perspective lines. They are at separate angles.
Project the edge of the square onto the ground at the angle you imagine your subject matter to be sitting at. This angle goes to the horizon again, at a secondary point, where the VP of the shadow points.
Cast a line parallel to your light line off of the top near corner of the square. Let it cross the angle line you drew in step 4.
From the bottom near corner, send a line to the VP. Likewise do the same from the point where the top light line from step 5 bisects your ground angle. Lines to VP are pink, Light lines are green. The pink perspective lines show you the top of the projected square.
Use the points of the square to draw the other side of the projected square, bisecting the top perspective line you just drew. Aim this line to the VP of the shadow used in step 4. This line will establish the mostly hidden other side of the projected square. The yellow line represents the opposide edge of the projected square.
On another layer, draw lines from corner to corner on the projected square, and where they cross, draw a third dotted line parallel to either side. That dotted line is the centre of your projected square. These guides will help you draw the projected shadow of your original subject matter.
Using this information you worked out, go back to your original contour drawing of the shape, and add the proper modelling of form in light, as well as the Cast Shadow laying on the ground beside. Don’t forget the Illustrator’s Bump, where the shaded side meets the lit side.

Next week, we will continue with some more information on how to use Cast Shadows in perspective. Thank you very much for reading.

Variable Perspectival Spaces within a Single Block

On page 43 of Successful Drawing, Andrew Loomis shows a very useful mechanic for artists to know in order to convincingly draw architectural details or features on mechanical objects in perspective. This example demonstrates how to project a sequence of repeating sections, found within a whole, using a vertical and a horizontal scale. This is similar to previous lessons, but it expands the skill set so that the artist can draw repeating sections which are varied in sequence. For example, imagine a condominium building in perspective. The viewer can see the front of the building going off down the block. This viewed side features a set of 4 windows, followed by a portico with a double entryway in the middle, then another set of 4 windows. Each of the openings of the windows need to be identical in size; but naturally, of a different dimension than the portico, which again is different than the two sets of double doors within. This then is an example of Variable Perspective Space, Within a Single Block.

Let us begin.

Suppose you are an illustrator, and you are asked to draw the Egyptian temples at Abu Simbel. Let us say that you are drawing the small temple, and you have (for whatever reason) a restriction as to the perspective you must use. You search through the internet for reference, and let us say that there is nothing in the correct perspective which you need. Short of traveling to Nubia, you cannot get a reference shot of the correct perspective. This is how it is done.

Here is the small temple at Abu Simbel tumblr_nrqdlqhwMT1tkairwo1_1280

Lay out the image in the angle you want, establishing the horizon and the perspective which you need to draw the site at. This can be done with any angle of perspective that you wish.
At the wide edge, establish the vertical and horizontal planes which will be used as your measuring lines. (see last posting for further use of the horizontal and vertical lines as measurement guides)
Mark the VP and a new point, called the Measuring Point, just to the left or the right of the vertical scale. The MP can be on either side, but it must be close to the vertical line.
Now, looking at the reference shot of Abu Simbel, one can see that there are 5 different sections in the sequence of Variable Spaces. They are as follows:
- Green Bracket: we will call these the FRAMES
- Red Bracket: we will call these the NICHES
- White Bracket: we will call this the PORTICO
- Purple Bracket: we will call these the JAMBS
- Blue Bracket: we will call this the DOORWAY
Now, estimate the ratio of widths between the 5 spatial elements in the picture. For simplicity, let us say that the Frames to Niches are a 1:2 ratio in width, and the Jambs to Frames are also 1:2. (this means that the Niches are DOUBLE as wide as the Frames. So too is the relationship between the Jambs to the Frames; the Frames are DOUBLE as wide as the Jambs). Let us say the Jambs to the Doorway is 1:1.75. Once you have established a ratio of the sizes by eye, decide upon a base unit for the Frames (since most of the ratios refer to these). We shall say the Frames are 2 cm. Thus each section width is as follows:
- Frames: 2cm
- Niches: 4cm
- Portico: 3.75cm (two jambs + doorway)
- Jambs: 1cm
- Doorway: 1.75cm
Starting at the (0,0) point on the Vertical and Horizontal scale lines, lay out the measurements in the order that the sequence appears on the reference. The full sequence is not measured in this example, in order to accommodate the size of the image, and readability. In reality, one must layout the entire sequence on the horizontal Measuring Line.
Through the points on the Horizontal Measuring Line, cast new lines of measurement to the MP (Measuring Point)
The points where the cyan coloured Measuring Lines cross the bottom Perspectival Line will be the Variable Spaces on the monument, projected into perspective. A secondary (red) line of perspective is cast to accommodate for the sloping nature of the temple’s face, i.e. it is not 90°.
Erase the guidelines and the new temple is drawn in the new perspective. Finish it to the level of detail that you desire.

In closing, I would like to apologize for not posting this on Sunday as per usual. I hope you are able to use this technique of projecting Variable Spaces within a Single Block. I also hope to see you next week.

Drawing To Scale

It is amazing how much information Andrew Loomis packs into each of the pages of his books. His method of instruction is to constantly expand the uses of techniques outlined on previous pages. In so doing, he also expands the learner’s set of drawing mechanics in a straightforward way. For example, on page 39 of Successful Drawing, the method of depth by diagonal is elaborated upon, and here Loomis shows the reader how to use the technique in order to execute a scale drawing. He says:

Every artist should know how to draw to a scale. Scale drawings require the division of vertical and horizontal planes into square feet or square units.

Let us then examine the method.

We must first establish a vertical and horizontal measuring line, like an X and Y axis, where the lines touch at right angles at point zero. Both lines must have equal division of unit, which represent feet in the drawing. The size of the unit which you use is done by eye. A horizon line is established and the measuring lines are placed upon the scene.
From each of the ends of the measuring lines, and from point zero, lines are drawn to the VP. Set the VP where you want by eye.
Now, a fourth Line of Perspective is cast to the VP, this time from the mid point (at the 5) of the vertical line. This line is represented as a black and white dotted line in the example below. We shall call this line the Halfway Line.
Next, gauge by eye the optional depth of the first foot of measurement along the low Line of Perspective going from the zero point to the VP.
When the first unit is established, cast a Line of Perspective from point one on the vertical scale (yellow checker in this sample), as well as a second vertical line at the point where the first unit terminates (red checker in this sample). This first square unit will represent one foot.
Ascending diagonally from the low near corner (point 0, 0), cast a diagonal measurement line (cyan coloured in this sample). Make sure it crosses exactly through the upper furthest corner of the first square foot.
Where this diagonal measurement line (cyan coloured) crosses the top Line of Perspective, draw another vertical down to the bottom Line of Perspective. This is 10 feet deep into the image from point 0,0. Cast Lines of Perspective (yellow here) from each remaining vertical measurement points to the VP. Where the diagonal (cyan coloured) measurement line crosses the many interior Lines of Perspective (yellow), additional vertical lines are drawn. These represent 1 foot sections receding into the distance.
Next, draw horizontal lines on the horizontal plane, each at 90 degrees from every incremental foot measurement determined in step 7. This divides the ground plane also into ten 1-foot sections in perspective.
As in last week’s posting, cast a descending diagonal line from the top near corner of the vertical plane, crossing through the far mid point delineated by the Halfway Line (black and white line) on the plane. This shows where the next ten foot wide plane will terminate.
Draw the vertical for the twenty foot mark, and then diagonally bisect this new plane, from corner to corner (purple diagonal in this sample). Where that diagonal line crosses the Halfway Line is the centre of the second vertical plane.
At the centre point where the newly drawn diagonal (purple diagonal in this) crosses the Halfway Line, draw a new vertical. This will show the point of 15 feet in depth, as it is exactly between the 10 foot and 20 foot markers.
Repeat this process of descending diagonals from upper near corner through the Halfway Line, and ascending from corner to corner to determine as much depth as needed. Each line that descends from top corner through the Halfway Line shows us 10 more feet in depth.
Now suppose we were asked to place these two men of different heights, on the field 20 feet away from each other. Furthermore, we want to place two Greek columns of equal height also on the plain, 30 feet away from each other. We want to place the tall black man beneath the near column, and the short white man 20 feet behind, and 9.5 feet over to the left of the black man . The black man is 6 feet tall, the white man is 5 feet tall, and the columns are 10 feet tall.
With this method of Drawing to Scale, the task is simple.
Erase the guide lines and add some shadows, and the task is complete. Notice how the short white man looks proportionately still like a short guy -even way back in the field. Because the perspective is correct, and our Intelligent Perception is so fine tuned to seeing people in distances, we can tell he is a small man even though he is not standing directly beside any reference point. This is the power of perspective.

Thank you for reading this week’s posting. I hope you will subscribe and learn more about Andrew Loomis by keeping up with this blog.

A More Precise Method

Previously in Understanding Loomis, I have shown several ways of determining depth by diagonals. The method explained today is another method of finding depth by diagonal, but this one is a more accurate method than those previously covered. Today’s method should be used when the illustrator is seeking to draw to scale; i.e. when he must divide the vertical and horizontal planes into square units for measurement in perspective. The previously outlined methods are fine when the illustrator is seeking to represent visually realistic perspective, but when mathematical precision is necessary -as in the cases of scale drawings- a more precise method is needed.

Today’s post will explain the method of laying out the precise division of vertical planes. How this is used in the creation of scale drawings will be covered in the next posting.

First establish the horizon and the V.P. for the first plane. Cast perspective lines back from the VP to establish the height of the plane. Determine height by eye.
Establish the First Unit depth also by eye. This establishes a Base Unit Plane, which will be cloned in perspective. Next, cast a new line from the centre point on the nearest edge of the Base Unit Plane to the VP. This will bisect the plane perfectly in half. We shall call this new line the Middle Line.
When the first unit is established, it is cloned by using diagonals. Create a Vertical Line by bisecting the horizon at the original VP. Make certain to draw the Vertical Line long enough to accommodate the diagonals which you will draw in the next step.
Cast the first diagonal (green in this example) from the near bottom corner through the far top corner to the Vertical Line (the pink line in this example). At the place where the (green) diagonal line crosses the (pink) vertical, make a secondary VP.
This step is where the method tightens up the measurement. Cast a downward diagonal (yellow in this example) from the top near corner of the plane, through the point where the bisecting Middle Line (from step 2) crosses the midpoint on the far edge of the plane. This line does not go corner to corner. Extend this downward diagonal far enough for it to meet the (pink) Vertical Line. Mark a tertiary VP at the low crossing point.
Again, as in step 4, cast a new ascending diagonal from the next bottom corner (where the next plane will be) up to the secondary VP marked on the Vertical Line in step 4.
Where the ascending diagonal (green) and the descending diagonal (yellow) both cross the original perspective lines (red), draw a vertical line to indicate the depth of the second plane. This will be a more accurate representation of the First Unit Plane’s width in perspective, than that which was shown in previous postings.
Repeat the procedure by casting ascending lines corner to corner, and descending lines from corner through the Centre Line to establish the further planar depths.
Erase the guide lines to reveal the four planes receding into the distance, with more precise perspectival depth.

Conclusion

Readers will have noticed that with the introduction of a secondary guiding point, i.e. the bisecting Middle Line, the illusion of correct perspective is tightened. For the sake of interest, compare the planes of today’s post with the divisions of depth created with the earlier methods in previous postings. You will be able to see the subtle difference by eye, and how this method creates a more accurate representation of repeating planar depth in perspective. This is especially true in the perspectival plane sections which are shown far off in distance. The previous methods tend to shorten the depth incrementally, such that the distant planar sections become much too close together.

Next week, we will investigate how to use this method of depth by diagonal to set up for the creating of scale drawings.

A Specialized Method of using Diagonals

This week’s posting will be a very straight forward one. Andrew Loomis’ third example in this section of Successful Drawing shows how the artist can use diagonals to create a checkerboard pattern in perspective. This is useful for drawing repeating windows of uniform size, or bricks on a wall receding into the distance. The example I will use is of a brick wall.

This is how it is done.

Create the perspectival plane which will be the brick wall. Locate the Vanishing Point. Use any angle that you wish.
Divide the near vertical edge of the wall into equal separations. The size you choose will represent how tall each brick will be.
Cast lines to the V.P. from the points indicated by the vertical spacing you created with the brick heights in step 2. We shall call these lines the Brick Height Lines.
Here is where the diagonal comes in. Cast a diagonal line from corner to corner on the face of the wall you are drawing. The diagonal can go up or down.
Where the diagonal (blue line in this example) crosses each of the multiple Brick Height Lines, draw a 90 degree vertical from the bottom of the wall to its top.
Repeat this at each crossing point, and the wall plane will be divided perfectly in perspective.
Erase the guide lines to reveal the wall.

Uses

This method can be used for drawing multiple series of drawers, such as in a morgue or a bank vault, architectural or vehicular designs, it can be used as a grid for aiding the placement lettering or imagery on signage, or as a way of drawing bricks and checkers.

The diagonal is the key to being able to measure the depth of the sections. Next week, I will explain how the diagonal can help in measuring, and thus correctly drawing a repeating panel section in perspective.

Thanks for reading, and I hope to see you next posting.

Depth by Diagonals: method II

As discussed last week, the current section of the book Successful Drawing which I am reviewing, deals with some of the drafting rules for determining the depth of an object by casting diagonal lines. Last week we covered the first method, and this posting then will explain Loomis’ second method which is outlined in the text.

The use of the bisecting vertical

This method is very similar to the one outlined in the previous posting, but here, Loomis introduces a few more ‘controls’ to make certain that the placement of receding points are accurate. He advocates for the use of a bisecting vertical to be placed along the horizon line, to keep everything accurate. I find this method to be very useful for drawing buildings, with repeating surface features, such as windows, facade details, or columns on ancient buildings. Let’s get into it.

First, let us consider that you are trying to draw a building, with a series of columns located in regular intervals along the side of it, going off into the distance. First, create the near corner height of the plane you wish to decorate, and sight the V.P.
Now, the artist must place the ending of the facade plane at what Loomis calls the optional depth. This is the most unscientific part of his instruction, because it leaves the artist to place the second line by eyeball. He uses the word optional not in the sense that one may draw it or not draw it, but instead Loomis means where the line is drawn is optional, i.e. it is up to you. Once the visual depth chosen pleases the artist’s eye, he has created a section. The second line drawn is called the Terminus Line, as it delineates where the section terminates. This section is now easily cloned in perspective.
Now, the next step is the technical part of the procedure. The artist casts lines diagonally through the section, starting at the near top and bottom corners and extending through their diagonally opposing corners. Following that, a vertical line must be drawn bisecting the horizon perpendicularly, through the V.P. The diagonal lines must extend far enough to reach the point where the new vertical line delineates. Mark the points where the diagonals cross the vertical. Let us call the new high and low points, the Vertical Points.
This X of diagonal lines shows the centre of the section, and sets the artist up to clone the depth for the following section.
To find the depth of the second section, the artist again casts new diagonals, but this time he must start from the top and bottom of the newly drawn Terminus Line of the established section. These lines are cast diagonally up and down to both the high and low Vertical Points, This will create another X within the Lines of Perspective.
A new Terminus Line is drawn vertically where the diagonals cross the Perspective Lines, and a second section is established.
Repeat from step 5, casting diagonals to the Vertical Points. The sections will be drawn in their proper visual depth as per the laws of perspective.
These sections could delineate where a repeating surface feature is found on a building, such as a column or any regular repeating element, including doors, windows and other architectural features. This method is even useful for drawing a series of parked cars along the sidewalk, since many cars are relatively the same length, the sections can represent the cars’ body length. Any anomalies of vehicular type can be adjusted for as needed.

This concludes our posting of Understanding Loomis. Next week’s post will again unpack another of Andrew Loomis’ methods of finding depth by diagonals. Stay tuned.

Finding Equal Spacing using Diagonals

In this posting of Understanding Loomis, I will explain the primary method Andrew Loomis outlines in what he calls ‘depth by diagonals’. This is a rule of drafting which accurately represents depth in a subject matter featuring a repeated pattern, or a repeated spacing of surface feature. This particular treatment is useful for illustrating a sidewalk receding into the distance, or a tiled floor going off down a hall, or a train track with ties crossing the rails, traveling away to a vanishing point. It is a very useful mechanic to know.

To emphasize why knowing this mechanic of perspective is important, I will describe a scenario where such knowledge would save the artist painstaking hours of ineffective trial and error, or unconvincing guesswork. Consider; you as an illustrator have been given the task of drawing a rural road, where small trees and shrubs are growing along the side. Also standing along the road at regular intervals of 30 feet, are a series of 6 telephone poles on the shoulder. The image is to be drawn with the vanishing point of the road in the centre of the horizon, as if the viewer were standing at the head of the road, looking off to where it fades into the distance.

Drawing the simple one-point perspective of the road is no problem, and the shrubs/trees needn’t be precisely drawn on account of their being organic and irregular in nature, hence their placement is not a problem either. The telephone poles on the other hand are man-made, and erected with a constant distance of 30 feet between each of the pole bases. To be able to accurately place each pole as they recede into distance, is a baffling task to those unaware of technical perspective. Many artists would rely of approximate placement of the poles, by ‘eye-balling’ the spacing. This may be acceptable in some cases, but where approximation is not acceptable, a technical solution is necessary.

This then is how it is done.

Depth by Diagonal

(For the sake of these perspective lessons, crude sample drawings which were done in Photoshop in a matter of a few seconds, will be used forthwith. Proper, elegant drawings will be used as examples where actual drawing matters are being considered)

First represent the road and the bushes in one point perspective. Bushes and trees are organic, and can be represented by eye without difficulty. The rules of perspective still apply, but the artist can be a little sloppy in representing their relative size, since trees and shrubs are not regular.
Next place your first pole. Use the relative size of the trees around it for its height.
Next find the Vanishing point of the road on the horizon line.
Now, draw a diagonal line from the near corner of one of the Lines of Perspective, through the base of the first pole to a secondary point on the horizon line. Let us call this new point on the horizon Point One.
Next, draw a horizontal line (i.e. parallel to the horizon line – natch!) from the base of the pole, crossing through both Lines of Perspective.
From where this horizontal line meets the opposite Line of Perspective, draw another diagonal line to the secondary point you drew in step 4, which we called Point One.
Cast lines to the actual VP from the top and bottom of the telephone pole, and pay attention to where the bottom line crosses the diagonal which you drew in step six.
At the crossing point, draw your second telephone pole. The top line will show you how tall to make it.
Repeat the process, and erase your guidelines. The end result will show the poles moving off in correct perspective, spaced evenly apart.
Work in reverse to fill in any posts which should appear before the initial one you drew.

The Uses of Depth by Diagonal

Shown below is a sample of the nuts and bolts of the Depth by Diagonal mechanic. This example is shown stripped of any context in order to help the student imagine the uses of this rule of perspective. Some ways I have used this method of representing perspective in drawing comics are as follows:

representing regular sized plates of steel, clad on the hull of a ship
drawing the separation lines of ceiling panels on a t-bar drop-ceiling in an office
sidewalks, with contraction joints showing in the concrete
patterned carpet expanses
windows, or other architectural features on buildings
any regularly spaced series of object, such as telephone poles, the cars of a train, the ties between train track rails, the broken lines on a road which indicate a passing lane etc.

dbydiagonal

Next week, we will examine a variation on this method of finding Depth by Diagonals. I hope you will join me.

Imagining the Geometric Shape

Previously, I went at some lengths to explain a concrete method of drawing a laying square at any perspective. The reason this was done was in order to establish a groundwork for the student to begin to visualize the square as the base of a cube. A cube can me made from the laying square by drawing vertical lines up from the corners, and by adding an identical laying square as the lid. Alter the height and width dimensions, and one can easily draw various Rectangular Prisms in perspective.

The Rectangular Prism in 3-Dimensional space is the primary shape Loomis encourages us to become familiar with from any angle. The reason being, is that this shape will enclose any other shape which exists. Even the perfect sphere will fit in the perfect cube. Some shapes are long, some tall, many are irregular; but when one visualizes a Rectangular Prism bounding what one is trying to draw around the object, the artist takes the first step to being able to draw that object with mass and perspective.

If one does not use a beginning framework of Rectangular Prisms to work out the perspective of the various objects within a composition, the shortcomings will be evident to viewers on account of, again, ‘Intelligent Perception’. Stated differently, there is no way to “fake” correct perspective, so it does one best to work it out properly at the beginning.

Setting up a a geometric shape as a shorthand for an organic shaped object has further uses beyond perspective and understanding mass. An additional use is in aid of the artist seeking to establish values. When an artist is trying to work out his values (lights and darks) within a picture, it is much easier -and more appealing visually- if the gradation of light to dark is done in a series of planes, rather than rendered as one continuous blend. The ability to see form as a series of interconnected geometric shapes is essential to rendering transition of values in planes. This treatment of light and dark creates an aesthetic which the photograph cannot duplicate, and thus, it remains the domain of visual artists.

male-9 — The Male Figure rendered in planes

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