How to Draw Ellipses in Perspective: Circles, Cylinders and Wheels

A circle in perspective is an ellipse, and everyone knows it; the trouble is that an ellipse has a size, a degree and a direction, and a drawing goes wrong when any of the three is off. This lesson is about ellipses in perspective with all three under control: the degree rule that says how round the ellipse is, the axis rule that says which way it tips, and the centre rule that says where the object actually sits inside it. Then cylinders, which are two ellipses and two lines, and wheels, which are the case that catches most people.

The degree rule: distance from eye level

Take a horizontal circle, a cup's rim. If the rim is exactly at your eye level you see it as a straight line. Lower the cup and the rim opens into a thin ellipse; lower it further and the ellipse gets rounder; put it on the floor and it is quite fat. Raise it above your eye level and the same happens in the other direction, with the ellipse opening the other way. The rule: the degree of a horizontal ellipse grows with its distance from the horizon. Every horizontal ellipse in a picture obeys it, which gives you an instant check: two rims at the same height in the same picture must have the same degree; a rim lower in the picture must be rounder than one higher up (below the horizon).

Vertical circles, a wheel or a clock on a wall, obey the same rule sideways: the degree grows with distance from the vanishing point of the circle's axis. A wheel whose axle points straight at you is a circle; a wheel far to the side of that direction is a thin ellipse.

For a cylinder standing on a table below eye level, this means the bottom ellipse is always rounder than the top. Draw them the same and the cylinder looks like a paper tube seen through a lens with no perspective. The perspective box generator draws cylinders with correct ellipses at any height and camera; change the camera height and watch the degrees change.

The axis rule: the minor axis follows the cylinder

The second rule sets the tilt. The minor axis of the ellipse lies along the axis of the cylinder. For a can standing upright the cylinder's axis is vertical, so the minor axis is vertical and the ellipse sits level: its major axis is horizontal, regardless of where the can is in the picture. This surprises people who expect the rim to tilt toward the vanishing point. It does not; the enclosing square tilts, but the ellipse inside it is level.

For a cylinder lying down (a pipe, a rolling pin, an axle) the axis runs to a vanishing point, and so does the minor axis of every ellipse along it. The ellipses tip: their major axes are at right angles to the line running to the vanishing point, not vertical. Wheels are this case; see below.

Drawn the wrong way, the tilt is what makes a cylinder look bent or a wheel look like it is falling off. Draw the axis line first, every time, and hang the ellipses on it with their minor axes along it.

The centre rule: the true centre is behind the middle

An ellipse is symmetrical about both its axes, but the circle it represents is not seen symmetrically: the near half is closer and appears larger. So the true centre of the circle (where a spoke would be fixed, where a straw stands in a glass) is not at the geometric centre of the ellipse but a little toward the far side. Find it properly by drawing the circle's enclosing square in perspective and crossing its diagonals: the crossing is the true centre, and the ellipse touches the square at the midpoints of its four sides, which are themselves found by lines from the diagonal crossing to the vanishing points.

The offset is small for distant or small circles and can be ignored for a coin across the room. It matters for a near wheel, a bowl seen from above, a clock face at arm's length, a table top: the middle of a round table is behind the middle of its ellipse, which is where the vase goes.

Constructing an ellipse in a square

When the ellipse has to be right (a wheel, a tower, a dome), construct it:

1. Draw the square the circle fits in, in perspective, on the plane the circle lies in: the ground for a horizontal circle, a wall for a vertical one. Its edges go to the vanishing points.
2. Cross the diagonals to find the true centre. From the centre, draw lines to the vanishing points to divide the square into quarters; where they meet the sides are the four points where the circle touches the square.
3. The circle also passes through the diagonals at about 0.71 of the way from the centre to each corner (√2/2). Mark those four points by eye or by measuring the near diagonal and transferring.
4. Draw a smooth curve through the eight points, keeping the minor axis along the cylinder's axis and the curve symmetrical about it.

For freehand work an ellipse template or a practised wrist is faster, and the construction is the check: draw the square, drop the ellipse in with a template at the degree the square suggests, and look for the touching points.

Cylinders

A cylinder is two ellipses on one axis, joined by two straight lines tangent to both. The steps:

Draw the axis line: vertical for a standing cylinder, a line to a vanishing point for a lying one. Mark the two ends. At each end draw an ellipse with its minor axis on the axis line, the far one thinner if the cylinder is nearer the eye level at that end. Join them with the two tangent lines. For a standing cylinder the tangents are vertical (or converge to the third vanishing point in a tilted view); for a lying one they run to the same vanishing point as the axis.

Cones, bottles, cups and wheels are cylinders with a change of radius, and the same construction with a different ellipse size at each station along the axis. A bottle is a stack of ellipses of different widths all on one vertical axis, all level, the lower ones fatter than the upper.

Wheels

A car's wheels defeat more drawings than anything else in this lesson, and the reason is the axis rule. The axle is a horizontal cylinder running across the car, so it goes to a vanishing point; each wheel is a circle on that axle, so each wheel's minor axis lies along the axle line, tipped, not vertical. The wheel on the near side is a higher degree than the wheel on the far side, because the near one is further from the axle's vanishing point. And since the car's axles are parallel, all four wheels have minor axes aiming at the same vanishing point.

Draw a car's wheels by drawing the two axles as lines to the vanishing point first, marking where each wheel sits on them, then drawing each ellipse with its minor axis on the line. Give each wheel thickness with a second ellipse a little further along the axle toward the vanishing point, and connect the two with short tangent lines. The tyre's tread sits between them. The how to draw a car in perspective lesson builds the whole vehicle this way.

Common mistakes

Pointy ends. An ellipse is round everywhere; there are no corners at the ends of the major axis. Draw it as one continuous curve, or rotate the paper and draw it in two strokes that overlap.

Tilted rims on upright cylinders. The rim of a standing can is level. If it tips, the can is falling over.

Same degree top and bottom. A cylinder below eye level is rounder at the bottom. Two identical ellipses read as no perspective.

Vertical wheels. Wheels seen from a three-quarter view have tipped minor axes along the axle. Vertical minor axes belong only to a car seen exactly from the side.

Objects centred in the ellipse. The vase, the straw, the hub go at the true centre, toward the far side, not at the middle of the ellipse.

Practice

Set the box generator camera to 1.2 m and add three cylinders of different heights. Draw them; then move the camera to 0.5 m and draw them again, watching the degrees change. Then draw a car body as a box, put two axle lines to the vanishing point through it, and hang four wheels on them.

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How to draw a car in perspective · how to draw perspective · figures in perspective · perspective box generator