Anatomy of an
ellipse: When we view a circle at an angle we see an ellipse.
We refer to this viewing angle as the degree of the ellipse. A perfect
circle is viewed at 90 degrees and at angles less than that we see various
degree ellipses on the way down to a zero degree ellipse (a straight
line). Understanding the mechanics of drawing ellipses is not difficult,
mastering the drawing of ellipses is. An ellipse has two axes we need to
know about, the minor axis and the major axis. The minor axis divides the
ellipse into two equal halves across its narrow dimension. The major axis
divides the ellipse across its long dimension into two equal halves. The
minor and major axes cross each other at a 90 degree angle. See drawing
e1.
How you can use these axes for
drawing:
If we look at the
drawing in e2 we can see that I have drawn a square around our ellipse.
After I draw the square I draw an “X” across it to find its center in
perspective. When you observe the minor and major axes of the ellipse we
see that the minor axis goes through the center of the square while the
major axis does not. We also observe that the ellipse touches tangent
exactly in the middle of each side of the square, exactly where we would
expect it to. This is a bit of a mind bender. We have taken a symmetrical
shape, the ellipse, and dropped it into perspective. This always works if
you do your drawing within the allowable limits of distortion. Regardless
of whether your ellipse is rolling on the ground or resting on it, as we
see in drawing e3, the construction result remains the same. Learning
from this observation and now knowing where the minor and major axes of
our ellipse should be is the single greatest help in drawing ellipses
properly. Since the ellipse minor axis always goes through the center of
our square this is something we can use to help us draw it. Conversely the
major axis references nothing that can help us in locating it in our
perspective square. This is why I do not recommend using the major axis
when drawing ellipses.
Practice drawing ellipses without worrying about locating
them in perspective. Here are a few examples of my rusty arm trying to
draw some ellipses for this tutorial this morning. Draw various sizes and
differing degrees. After you draw the ellipse identify its minor axis by
drawing a line across its narrow dimension that divides each side
equally.
I find
it helpful if you imagine that you are going to fold your ellipse along
this line. You want it to fold along this line and land exactly back on
itself. If your minor axis is incorrect we can see what happens in drawing
e4.
After
you are feeling good about how your ellipses are looking and you are
confident you can locate the minor axis of each properly you are ready to
start trying to locate your ellipses within perspective constructions.
Start with something simple like drawing a straight line that represents
the minor axis of your ellipse and then try and draw ellipses of various
sizes and degrees on that line. This is a little harder than drawing the
ellipse first and then drawing the minor axis. After you nail that
exercise try drawing two converging straight lines and drawing ellipses
that touch tangent to each line. This is harder still. One of the most
difficult exercises is to draw a page of cubes and then draw an ellipse on
each face that touches tangent to the side of each square as we observed
in drawings e2 and e3. Drawing concentric ellipses are also good
practice.
You
can use ellipse guides to straighten up your ellipses but do not try to
sketch with them. I have yet to see this done efficiently. You are much
better off to do all of your perspective layout work freehand and then
break out the sweeps and ellipse guides to tighten things up if you need
to. Once you have practiced enough you will find that you can do very
competent drawings entirely freehand. There is a great sense of
satisfaction that comes from achieving nice line quality and proper
perspective in a freehand sketch.
How to check
if your ellipse is correctly drawn. It is important to
understand the mechanics of ellipses so you can make adjustments to them
after you have drawn them. Basically there are only two things that make
an ellipse either properly drawn in perspective or not.
Minor axis and
your vanishing points. The first thing to check is whether
your minor axis is correct. In the case of putting wheels on cars the
minor axis is always common to the axle of the wheel. Most of the time
this axle is also perpendicular to the centerline of your car. So it
follows that the minor axes of your ellipses (wheels) are also
perpendicular to this centerline. There are cases such as when the front
wheels are turned or the wheels have been set up with extreme camber that
they are no longer perpendicular to the centerline of your vehicle.
Another easy example for us to visualize is that the minor axis of a
propeller on an airplane is parallel to the centerline of the fuselage and
therefore they go to the same vanishing point. Remember when perspective
drawing that “all parallel lines go to the same vanishing point”.
Degree of your ellipse. Assuming
the minor axis of your ellipse is correct and your ellipse still looks
wrong it can be only one thing, the degree. Before trying to adjust the
degree of an ellipse the minor axis must be correct. No amount of
adjustment to the degree can make up for an incorrect minor axis. Checking
the degree is a simple perspective construction.
Step 1: Draw
a box around and tangent on each side to your ellipse. Be sure to follow
your perspective guidelines when doing this.
Step 2: Observe
where your drawn ellipse contacts the box you have drawn around it. If
your ellipse does not touch in the middle of each side of the box then the
degree is wrong. Adjust the degree of your ellipse by making it wider or
narrower until you can draw a box around it that touches exactly in the
middle of each side. When you have done this you will have a properly
drawn ellipse at the correct degree.
Here are a few more
sketches I quickly put perspective guidelines on top of to help you see
the minor axes of the ellipses within the drawings.
Congratulations you are now master of the
ellipse!
