I was intrigued by a tutorial I found on artist Scott Robertson's web site drawthrough.com on how to freehand draw ellpses. I found it extremely educational, and wanted to play around in 3D with what I learned there.
His first main assertion, which I see a lot of people get wrong, is that when a circle in 3D space projects into 2D as an ellipse, the center of the circle and the center of the ellipse are not the same point. That much I already knew.
His second assertion, which I found particularly interesting, is that in such a situation, the minor axis of the 2D ellipse is the same as (or is at least parallel to?) the normal axis of the original 3D circle. In the case of a car, the minor axis of the 2D ellipses is parallel to the axle of the car. In the case of an airplane, the minor axis of the propeller's ellipse in parallel to the drive shaft.
I like to test things. Here's what I got when I did.
My results agree pretty closely with his predictions. Close enough that I think I'll be mindful of whether or not I'm following his suggestions when I draw.
The results of my experiment didn't look "dead-on," however. My own inaccuracy orienting the red axis along a vertical line and in hand placing the 2D test ellipses might be one source of the error.
Another source might be in the way in which the original tutorial depicts objects in perspective. Even when Robertson draws the X- and Z-axes of an object in perspective, he maintains the Y-axis perfectly vertical, as if he were using a view camera, or a kind of draftsman's perspective not produced by typical cameras.
UPDATE 3/21/2009
Based on a recent comment I took another look.
I am an architect with better than average drawing skills both intuitive and technical and have recently/finally endulged myself at 60 with a couple of years off and enrolled fulltime in art school. Nobody ever taught me to draw a circle in perspective, I just worked it out using the x and y axes exactly as per your diagrams, probably at about 10 years old. In the simplest sense a quick drawing of the circle is made up from 2 steep curves and two shallow ones, each slightly different. I remember trying to use a plastic ellipse template as a quick solution but found it simply did not produce a convincing shape. So, today my arrogant beligerent drawing tutor chose to teach me how to draw a circle in perspective, and while I bit my lip he explained that it will be a pure ellipse. I came away convinced he was wrong and Google showed me I was not alone and your contribution is elegantly succinct. I must admit to being surprised by how close the ellipse is in your examples, albeit tilted, but looking carefully at your overlays, it seems to be less than a perfect match. So ... is he correct or am I?
Nice tutorial. I linked it to my friend who asked me how to properly draw eclipses and it also helped him understand the concept a little bit better thanks mate
Thank you, although in this case I was mainly using 3D to follow along with the Scott Robertson tutorial that he used to post here:
http://www.drawthrough.com/tutorials/ellipses.html
So credit mainly to him. :)