Circles in 3D
Circles can be easily drawn with a compass. But you can also draw a freehand circle by using your hand as the compass as indicated in the bottom pictures. Place your thumb on the paper. Hold the pen so it touches the paper. Then rotateyour paper 360° to complete your circle.

It can be shown mathematically that a circle in perspective is a true geometric ellipse. An ellipse has a major and a minor axis at right angles to each other, it’s also symmetrical about both axes so that each half of each axis is the same length. When an ellipse is viewed as a circle in perspective, the axis of rotation of that circle coincides with the minor axis. If you have trouble drawing freehand ellipses, turn the paper so that the minor axis is vertical on the paper and the major axis is horizontal. To help understand a circle in perspective draw a square. Construct the diagonals and connect the mids of the opposing sides. Create another inscribed square as indicated. Divide the line between the outer and inner square in two. The ellipse must go trough these points. Although this is just indication and may differ a little bit. Above all it’s important to have a clean ellipse. So construction is just an aid and reference.

To truly see what circles look like in perspective we’ll place them in a cube. First find the center of all visible planes by drawing the diagonals. Do the same with the opposing mid-points. Construct the inner-scribed squares. Divide the lines between the squares in two and start constructing the ellipses, It tends to go better if you turn your page when you go along. What is most noticeable is the skew-effect that occurs in the tow vertical planes. This is important to keep in mind when free-sketching. It will give the sketch that extra credibility and flair.

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