How to Draw an Ellipse? Ellipse Construction.

What Is an Ellipse?

When a cylinder or cone is cut by a plane inclined to its base, the outline of the resulting cross-section is an ellipse. The outline of the cross-section formed when a cylinder or cone is cut by a plane inclined to its base is called an ellipse.

An ellipse is a closed curve and cannot be drawn with a compass. An ellipse drawn with a compass is only an approximate ellipse.

How Is an Ellipse Drawn?

Even though drawing an ellipse in technical drawing today can be done with a single click using software like AutoCAD, traditional ellipse-drawing methods can still be needed. In case you don’t have a computer/software on hand that can do this job, we’ve prepared this topic for those wondering how to draw an ellipse.

How to Draw an Ellipse with String? (Gardener’s Ellipse)

Drawing an ellipse with string is also one of the ellipse-drawing methods.

Given that 2a, 2b, and the focal points F1, F2 are known; mark the horizontal and vertical axes. Mark F1, F2 on the horizontal axis.

Tie a nail to the end of a string of length 2a. Drive the nails into the focal points F1, F2.
Keeping the string taut with a pencil, trace around the perimeter. This drawn curve forms the “gardener’s ellipse” used to lay out pools in gardens.

How to Draw an Ellipse Given Its Axes?

Circles are drawn centered at O with diameters equal to the ellipse’s axes. Any line passing through O is drawn, and its intersection points with these circles, P and P’, are found.

The intersection point M of the lines drawn from these points parallel to the ellipse’s axes is a point on the ellipse. By finding enough points this way and joining them appropriately, the ellipse is drawn.

Drawing an Ellipse with the Rectangle Method

A rectangle is drawn formed by lines passing through the ends of the ellipse’s axes. The short sides of the rectangle and the ellipse’s major axis are each divided into the desired number of equal parts and numbered as shown in the figure. These points are connected to the ends of the ellipse’s minor axis. The intersection point of the lines drawn from points with the same number is a point on the ellipse. The ellipse is drawn by finding enough points this way.

Drawing an Ellipse Inside a Parallelogram

A semicircle is drawn with one side of the parallelogram as its diameter. This circle’s radius DE and the ellipse’s half-axes MD and MC are each divided into the desired number of equal parts and numbered as shown in the figure. The intersection points 1′, 2’… of lines drawn from the points on DE, parallel to the parallelogram’s side, with the circle are found. From these points, the intersection points 1″, 2″… of lines drawn parallel to DE with the ellipse’s axis are determined.

The intersection points of the lines drawn parallel to CD from points 1″, 2″… with the lines drawn parallel to AB from the same-numbered points on CD are points on the ellipse

drawing an ellipse inside a parallelogram

The ellipse drawing is completed by finding enough points.

Drawing an Ellipse Using Focal Points (Major and Minor Diameters Known)

– Draw the horizontal and vertical axes. Mark points A, B, and C, D.
– Open the compass to AB/2 and, centered at D, draw an arc to find the focal points F1, F2.
Mark a few points (such as 1 and 2) between F1 and M.

Center the compass at A, open it to point 1, then center it at F1 and draw an arc.
Center the compass at B, open it to point 2, then center it at F2 and draw an arc, intersecting it with the previously drawn arc. This gives point E.
Continue the same process for point 1 as before. This completes 1/4 of the ellipse.

Finding the Curvature Circles at the Vertices of an Ellipse Given Its Axes

Lines parallel to the axes are drawn from the ellipse’s vertices to find point E. A perpendicular is dropped from this point to line BC, and the intersection points O1 and O2 with the ellipse’s axes are determined.

O1 and O2 are the centers of the curvature circles, and O1B and O2C are their radii. When drawing an ellipse by any method, it’s useful to make use of curvature circles at the ellipse’s vertices.

Finding the Axes of a Given Ellipse

Finding the axes of an ellipse whose center is known.

Any circle centered at M is drawn. The intersection points of this circle with the ellipse are the corners of a rectangle. The lines joining the midpoints of the opposite sides of this rectangle are the ellipse’s axes.

In this article, we covered how to draw an ellipse. We explained ellipse-drawing methods with illustrations. We gave information about ways to draw an ellipse. We hope it’s useful.