Isometric Circles and Curves

Isometric Circles and Curves

A circle on any isometric face is an ellipse, because every face is inclined to the viewer. Grade 11 requires drawing them accurately rather than sketching them.

The four-centre method is the standard construction. Draw the isometric square (a rhombus) that would enclose the circle. Mark the midpoint of each side. From the two obtuse corners, draw lines to the midpoints of the two opposite sides — where these cross gives two centres, and the obtuse corners themselves are the other two. Swing the two large arcs from the obtuse corners and the two small arcs from the crossings.

Orientation matters. The ellipse's major axis always lies along the long diagonal of the enclosing rhombus, which changes depending on which of the three isometric faces the circle sits on. A learner who draws every ellipse the same way round will have two of the three faces wrong.

Worked example. A cylinder standing upright: the top face is a rhombus whose long diagonal runs left-to-right, so the ellipse is wide. The same cylinder lying on its side has the circular ends on a vertical face, and the ellipse turns with it.

Core checkpoint: Draw the enclosing rhombus first. Its long diagonal fixes the ellipse's orientation, and its midpoints give the tangent points.