Theory on Ellipses

Questions from Xuan, Drawing Academy student

Hello Vladimir,

Thank you for the excellent video lessons. I very much enjoy them.

You mention that the ellipse (representing a circle in perspective) is distorted, with its front portion larger than the back portion, so that it becomes an oval with only one axis of symmetry.

I think, a circle always appears as an ellipse from a linear perspective. While it is true that the closer half of the circle is larger in perspective, the resulting shape that we see is still a perfect ellipse. However, the horizontal line that bisects the circle does not intersect the ellipse at its widest point.

I have made an image to illustrate this:

I modelled a cylinder in perspective using a 3D modelling tool and then overlaid the ellipse outline and its major axis.

As you can see, the darker half of the circular face of the cylinder indeed takes up larger than half the area. However, the 2D projection of the circle in perspective is still an ellipse and the major axis of the ellipse is not the same line as the line that bisects the circular face.

Can you please give your point of view on this subject?

Best regards,
Xuan

Feedback from Vladimir London, Drawing Academy tutor

Dear Xuan,

Many thanks for your question and drawing.

I am very glad that you are thoughtfully reviewing the topics, presented in the drawing course, with an analytical approach.

You are correct, perspective is not a straight-forward subject.

The main challenge is that it is impossible to represent three-dimensional objects, drawing on a flat surface, without distortion. The best method is to use a type of perspective that will minimize distortions.

Sometimes, artists use “incorrect” proportions or geometry to give a viewer a natural feel of objects instead of choosing “geometrically perfect” solutions.

In this painting, Paul Cézanne depicted mountains in the background proportionally larger than in real life. This approach allows the human brain to process the image in a more balanced manner.

You might have such an experience when photographing far-away objects without a zoom function. You may believe that objects in the background would appear larger than they actually do on a photograph.

The same applies to a circle in perspective. Sometimes, you need to step away from a geometrical approach as it would not solve the challenge of drawing without distortion.

It is better to create an “illusion” of a realistic-looking object than to make it geometrically perfect, but looking less natural.

In regard to the 3-D modelling tool, you need to remember that it is done by software calculations. The program has the same difficulties in depicting the real three-dimensional world on the flat surface of a screen.

Developers of the tool used approximations (this is the answer to your question regarding the way 3D and 2D ovals overlap perfectly).

It is great that you ask such questions as it shows you are thinking in a similar manner as great artists of the past.

To your creative success,
Vladimir

Response from Xuan, Drawing Academy student

Dear Vladimir,

Thank you for your kind words and your quick response.

I found a better illustration of what I was trying to say in my previous email.

The widest part of the 2D ellipse does not correspond to the widest part of the circle. In geometric terms, the tangent line where the ellipse intersects the quadrilateral should not be vertical, but should always follow the line that leads to the vanishing point.

You are absolutely correct that there will always be distortion when transferring from 3D to 2D, and it becomes apparent when using a camera.

Anyway, if we draw objects in linear perspective (which is different from how a camera would view them) because it appears to be realistic to our minds, then does it not mean we should follow the rules of linear perspective (e.g., circles becoming ellipses in perspective) to make the objects look believable?

I tested what would happen if I did not follow the rules of linear perspective, but instead used a camera to incorporate some distortion (I am an engineer, after all =]). The result was still an almost perfect ellipse.

This tells me that we should depict circles, in perspective, as ellipses (even if we are approximating) to create the most “natural” look in a picture.

Thank you for helping me think so deep about perspective.

Best regards,
Xuan

Feedback from Vladimir London, Drawing Academy tutor

Hi Xuan,

Many thanks for your response. I really enjoyed you answer and I am very pleased that you are taking questions of perspective seriously. I understand your point and agree with your views.

Regarding this image:

1. The square would be less distorted if a two-point perspective is used;

2. As the result of one-point orthogonal perspective, the oval is tilted, which would not be the case in real life. See the image below.

When drawing ovals, you can rely on your eye (and you should train your eyes to recognize proportions and dimensions) or you can “calculate” it graphically.

If you want to practice this task, you can use this template of a cube with circles (right-click the link and save this file to your computer). You can print it on A3 size paper, cut out the contour, fold along dashed lines, and glue the planes together. Next, place it in various positions and draw it in perspective.

You should use visual measurements. With time and practice, you will learn how to judge proportions by eye, and when in doubt, you can always double check them by measuring with a pencil.

Do not over-complicate this question in your artwork.

There are just a few main rules that will help you draw ovals:

1. Every circle located horizontally will have its main axis parallel to the horizon line.

2. The further away the circle is from the horizon, the fuller the oval will appear; the closer to the horizon, the slimmer it will become.

3. When a horizontal circle coincides with the horizon line, the oval will become a straight line.

4. A non-horizontal circle (like in a vase lying on its sides) will have its main axis perpendicular to the vase’s main axis of symmetry (its central vertical line).

5. An oval will never have pointed edges (or a tuna shape); all sides of an oval will be rounded.

The question of how to realistically depict ovals has bothered fine artists for centuries.

I have seen many paintings and drawings by artists of the past where ovals are depicted with obvious mistakes.

However, it does not diminish these artworks’ artistic values.

I hope this helps.

Kind regards,
Vladimir