Inclined Planes on a Roof

Good day,

It has been a very long while since my last posting.  I intend on posting again weekly on Sundays as before.

Let us get underway.

On page 57 of Successful Drawing, there is a very useful tip which Andrew Loomis gives his readers.  Any illustrator will encounter this problem, and unfortunately, very few know how to properly solve it.  This is the problem of how to draw the sloping pitch of a roof, in perspective.

First establish the horizon.Screen Shot 2018-01-21 at 5.14.19 PM

Since a single point perspective is a very unnatural point of view, you must now establish 2 Vanishing Points on the horizon line.  Below, I have added a red VP on the left and a green on on the right.

Screen Shot 2018-01-28 at 2.22.37 PM

Third, use the Vanishing Points to establish the main walls and roof of your 2 point perspective structure.  In this case we will draw a simple barn.  Screen Shot 2018-01-28 at 2.26.49 PM

Our fourth step is to locate the point on the facing side of the barn,  mid-way between the left and right walls, at the top.  From this point, draw a 90 degree vertical line up to the apex point of the roof line (drawn in the previous step).  This will help us establish the pitch of the roof correctly.

Screen Shot 2018-01-28 at 2.29.25 PM

Fifth, draw two vertical lines through the left and right VPs, and make the lines rather long.  These lines are displayed in a a cyan colour in the image below.Screen Shot 2018-01-28 at 2.36.44 PM

The sixth step is to now draw lines for the pitch of the roof.  These lines are drawn from the near corner of the wall and where the roof will be, up diagonally through the apex point established in step 4.  Make a Vertical Vanishing Point (VVP) on the vertical line (cyan) where the new diagonal line crosses.  Screen Shot 2018-01-28 at 2.41.16 PM

Seventh, draw a line back down from your newly established VVP, diagonally through the far corner of barn’s near wall.  Erase anything beyond where this line bisects the original roof line.  These new lines will be the correct pitch of the roof, in proper perspective.  Many artists do not know how to do this. Screen Shot 2018-01-28 at 2.45.35 PM

Step eight is to repeat the process for the opposite side of the roof.  Cast the horizontal lines downward this time to a VVP that is below the horizon line.    You can see below the orange lines show the pitch through the transparent house where the opposite roof would lay. It looks proper to our eyes.

Screen Shot 2018-01-28 at 2.48.04 PM

Here is the barn with a simple amount of finish applied to the image, and a simplistic setting.  The construction lines remain to show the workings of the perspective.Screen Shot 2018-01-28 at 2.50.16 PM

Lastly, remove the construction lines for the finished image.  Although this is a very simple example, the theory holds true even when representing buildings of various type within a single image.

Screen Shot 2018-01-28 at 2.54.14 PM

The tip Loomis gives us again uses the Vertical Vanishing Point method.  The VVP is an essential tool for establishing correct perspective.  We shall see it again.

Thank you for reading, and please check out the other internet media I am producing.  – my illustration website   – my youtube channel.

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 Simbeltumblr_nrqdlqhwMT1tkairwo1_1280

  1. 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.  2
  2. 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)3
  3. 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.real4
  4. 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 DOORWAY5spaces
  5. 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
  6. 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.real5
  7. Through the points on the Horizontal Measuring Line, cast new lines of measurement to the MP (Measuring Point)6real
  8. 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°. 8
  9. Erase the guidelines and the new temple is drawn in the new perspective. Finish it to the level of detail that you desire.1inal

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.

  1. 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.1
  2. 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.2
  3. 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.3
  4. 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.  4
  5. 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. 5
  6. 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.6
  7. 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.8
  8. 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. 9
  9. 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.  10
  10. 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.   12
  11. 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. 13
  12. 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.  15
  13. 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.  Frontier
  14. With this method of Drawing to Scale, the task is simple.16
  15. 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.  17

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.

  1. 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.2 precise
  2. 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. 3 precise
  3. 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.  4 precise
  4.  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 VP5 precise
  5. 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.  6 precise
  6. 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 4.7 precise
  7. 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. 8 precise
  8. 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. 9 precise
  9. Erase the guide lines to reveal the four planes receding into the distance, with more precise perspectival depth.10 precise


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.

  1. Create the perspectival plane which will be the brick wall.  Locate the Vanishing Point. Use any angle that you wish.1
  2. Divide the near vertical edge of the wall into equal separations.  The size you choose will represent how tall each brick will be.2
  3. 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.3
  4. 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. 4
  5. 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.5
  6. Repeat this at each crossing point, and the wall plane will be divided perfectly in perspective.6
  7. Erase the guide lines to reveal the wall.7


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.

  1. 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.per2
  2. 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.per3
  3. 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.per6
  4. This X of diagonal lines shows the centre of the section, and sets the artist up to clone the depth for the following section.per7
  5. 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.  per9
  6. A new Terminus Line is drawn vertically where the diagonals cross the Perspective Lines, and a second section is established.per10
  7. 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. per11
  8. 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. per12

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)
  1. 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.road1
  2. Next place your first pole.  Use the relative size of the trees around it for its height. road2
  3. Next find the Vanishing point of the road on the horizon line.road3
  4.  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. road5
  5. 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.road6
  6. 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.road7
  7. 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.road8
  8. At the crossing point, draw your second telephone pole.  The top line will show you how tall to make it.  road9
  9. Repeat the process, and erase your guidelines.  The end result will show the poles moving off in correct perspective, spaced evenly apart.  road10
  10. Work in reverse  to fill in any posts which should appear before the initial one you drew.road11

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.


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

Drawing the Perspectival Ellipse, or the ‘Laying Circle’

To conclude the written section on perspective, Andrew Loomis gives us some rules to remember as well as a few reminders of some familiar points he has elaborated on in previous sections.  Consider these to be Loomis Axioms, as they are each gems in their own right.  In rapid succession, here are the highlights from the end of the written section on perspective:

  • To know is to save time, and the more you lean on your ‘crutches’ the more your strength will ebb
  • be more concerned with geometric shape and light/dark than with little muscular ‘lumps and bumps’ when figure drawing
  • photos with several light sources -which is the norm for most modern photography- defy every principle of good drawing
  • art chooses to elevate a subject above the multiplicity of nature
  • since we as humans cannot do otherwise than live with nature and her laws, art cannot either
  • deeper knowledge of reality will bring the artist added power
  • Caravaggio had it harder than we do, and he was better
  • use the wrist for your strokes, not your fingers
  • avoid scratchy, small, thin-lined strokes for greys and blacks

Perspective the Artist Should Know

The following section consists of several examples of concrete perspective rules.    These are concepts derived from drafting, and methods of solving perspective problems which are not well-known amongst artists unfamiliar with the mathematics of representing reality.

A few postings ago, I explained the methodology of drawing what I termed ‘the Laying Square’, that is a square drawn in a specific perspective so that it appears to lay on the ground.  I also mentioned how Andrew Loomis outlines the principle of using a rectangular prism as a temporary enclosing box, around whatever subject the artist is trying to represent.  As a rectangular prism is easy to imagine in perspective, this temporary shape drawn in place of the actual subject, helps the artist visualize the mass and perspective of what he is actually trying to draw*.  We shall proceed then, from this point.

*Please refer to the previous 2 postings for elaborations on this concept.

Drawing the Ellipse

Being able to draw an ellipse is very important.  The ellipse is a fancy word for an oval, and the oval is how we perceive circles in perspective.  There have been many instances where I’ve needed to draw a circle correctly in perspective in my professional art career; I can’t seem to get away from them! So many things from the man-made world are circular.  Here are a few I have already needed to draw in my career as a comic artist.

  • tires of cars
  • dinner plates and mouths of cups
  • the bases of columns
  • warrior shields
  • flying saucers(!)

There are certainly countless more examples.  Since there are so many circular things which an illustrator may be called upon to draw in perspective, it is essential to understand how it is done.

If any object can be conceived of as being bounded within a rectangular prism, then the drawing of the Laying Square is essential to begin with, in order to draw an ellipse.  Once the Laying Square is drawn correctly to the horizon, and in the correct perspective to your other scenic objects, the next step is to divide the Laying Square.

In the following examples, I will use a regular square, not drawn in perspective. This is done so that the steps I am outlining are in their easiest form to comprehend.  The rules are the same for a Laying Square, though it may be slightly harder for some to draw.

Step one: Draw your Laying Square in the perspective you want. (here represented in flat-on perspective)

drawn square Step two: find the centre of the square by drawing diagonal lines from each of the 4 corners to their opposite. This will create an X sign.

corner to corner

Step three: Draw lines from the centre of each of the sides, crossing through the middle point of the square, to a point on the middle of the opposing side. This will create a + sign.

side to side

Step four: Using the side to side lines as a guide, draw a new square, turned at 45 degrees to the original square, inside of it.

divide with lines

Here is what you should have with the square actually in perspective.loomis laying square

Step 5: Mark points A and B as shown in the example on  the side/corner of the 2 squares you have drawn.  You will need to do this for each of the sides/corners.loomis laying square points ab

Step 6: Mark the halfway point on the line between point A and point B.

loomis laying square points ab halfway

Step 6: Draw an arc just shy of the halfway point, spanning from the two corners of the inner, 45 degree square.

loomis laying circle

Step 7: Do this for each of the sides of the inner, 45 degree square. This will produce an ellipse, which will be the accurate representation of a circle were it laying in the perspective you have chosen.  We can call this the Laying Circle, or a perspectival ellipse.

loomis laying circle Red

This is how the artist can accurately draw columnar shapes in consistent perspective with other shapes in a picture.  All that is needed to be done is to draw verticals from the sides of the Laying Circle, and a secondary Laying Circle (derived from a Laying Square) as the cap.loomis laying circle column

Beyond this example, Andrew Loomis indicates to us a few facts about drawing the Laying Square and hence the Laying Circle.  He states that when drawing small objects (thus small Laying Squares), it is best to place the two Vanishing Points far apart from one another.  If the object you are drawing is big (thus the Laying Square will be big), place the two Vanishing Points closer together.  If one doesn’t adjust the V.Ps this way, distortion will occur in the drafting.  He concludes by saying that your eye will see the error right away, and most artists will make this “closer/further apart” adjustment naturally.

My upcoming several posts of Understanding Loomis will each concern a single one of Loomis’ perspective examples, as well as my explanation.

See you in seven.



Concerning Rendering of the Geometric Shape

My last post introduced the reader to Andrew Loomis’ concept of imagining any object primarily as a geometric shape, prior to attempting to draw it.  After one is able to conceptualize subject matter as a series of three-dimensional geometric shapes, Loomis reminds the reader that:

Every plane must have its relative values correctly rendered, or the entire image will fail to convince.

It is appropriate at this time to therfore indicate how one correctly renders the five essential, three-dimensional geometric shapes.  To do this we will perforce need to leave Andrew Loomis for a short while.

The essential shapes, if the reader recalls, are

  1. the Cylinder
  2. the Cone
  3. the Sphere
  4. the Torus
  5. the Rectangular Prism

All other geometric shapes are derivatives of these primaries.

Rendering the Shapes

Each of the above 5 shapes show their dimensionality and mass in predictable and easily memorized  patterns of rendering. To help the student, the patterns of value can be remembered as “value shapes”, in that the lights and darks will take on a recognizable geometric form when laying upon the larger three-dimensional shape being represented.  These rules should be memorized in order for the artist to properly represent the shapes. (each of the rendering examples are from this site by Bill Martin)

  • The Cylinder:  rendering the cylinder is done in bands of value, laying lengthwise along the body of the shape; i.e.  if the cylinder is sitting upright, as does a soup can in your cupboard, the bands of value will be vertical.  Should the cylinder be laying down, as does a felled tree or a log, the bands of value will run horizontally (or at whichever angle the log lays at). Below is a representation of a cylinder, as well as an example of how the bands of value will fall.  The “value shape” is essentially rectangular.
  •  The Cone:  when rendering the cone, the values take on a basically triangular shape, with the vertex of each  triangular “value shape” corresponding to the vertex of the cone.  The bases of the “value shapes” are slightly curved to follow the curvature of the cone’s base.


  • The Sphere: to render light and dark on the sphere, the artist must look to create two sections of “value shapes”.  Primarily, an oval shape, which will form on the section of the sphere where the highlight is, and the corresponding darker values in crescent shapes, nearer to the edges of the sphere
  • The Torus:  the torus is somewhat complicated in that it’s “value shape” bears the qualities of both the cylinder and the sphere.  To render the torus, some sections of the “value shape” need to be treated as one does the cylinder; i.e. it will be basically rectangular, whereas other sections of the shape is more like the sphere’s crescent.  The rectangular, band-like aspect of the torus’ “value shape” are found within the length , whereas the crescent aspects  are found at the extreme right and left of the shape, relative to the viewer.
  • The Rectangular Prism:  this shape, though likely being the most familiar to the artist, is actually the most complex to render.  This is because of the necessary lack of curvature on the Rectangular Prism’s 6 planes.  The flatness of the planes necessitates a gradation effect to be represented on their faces. The Rectangular Prism therefore has no “value shape” to look for when rendering its planes; each of the shape’s sides will feature a gradation. The key factor to remember when rendering the Rectangular Prism is that the gradation on the planes are in opposition to one another, i.e. that the darkest value of any plane will meet on an edge  with the lightest value of the adjacent plane. Correspondingly, the values of each other section of plane will meet on an edge with their opposite value on adjacent planes.


Next time, we will return to Andrew Loomis and his final considerations of geometric shapes, their use in figure drawing, and his closing thoughts to this section of the book, Successful Drawing.

Of interest to my readers, I would like to inform you that I will be now posting new entries for Understanding Loomis every Sunday, in order to complete my synthesis of Andrew Loomis’ writing in a more timely manner.

See you in 7 days.

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.

The Male Figure rendered in planes