# 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.

### 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)

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.

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.

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.

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

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.

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

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

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.

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.

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.