Perspective View of a Circle is an Ellipse

Howard Vie

Architectural Illustrator - Applied Geometry

This proof was prepared in response to a letter in the August Issue of the Artist magazine. The correspondant Jeff Hughes asked for the name of the curve of the perspective view of a circle in a square. Because the perspective view of a circle is a trapezium he assumed it would be a complicated curve. In fact it is an ellipse. Any difficulty is resolved by noting that the major axis of the ellipse does not correspond with perspective view of the diameter of the circle.

I belive that all perspective views of circles in any orientation are ellipses. The axes of the ellipse do not usually correspond either in position or angle with the horizontal or vertical diameters of the circle. My proof covers the relatively simple case of a horizontal circle seen in central (one point) perspective. I have verified the algebra with figures in an spreadsheet.

Note that geometry is a special interest of mine, I like making my architectural drawings freehand on site.

©Howard Vie 2005

Updated August 2005

mail @ hvie.co.uk