Ellipse with equal height and width reveals error in shape when rotated

Question

Take an ellipse, make a copy rotate it 45 degrees from the Main Menu > Window > Transform. Transform it from the center. Follow the path around the circle and you will see the paths do not match.

Another option is to draw a circle and do Main menu > Effects > Distrort & Transform > Transform, rotate it 15 degrees and make 20 copies and then expand the appearance. You will see the multiple paths do not match.

You can use the rotate tool and the paths also do not match.

Jacob Bugge · Answer

John,

You are looking at the inherent inaccuracy of a Bezier circle with 4 Anchor Points.

A Bezier circle created with 4 Anchor Points is created to have the exact diameter at every 45 degrees, in other words vertical and horizontal and midway in between, and is inherently bulging in between (in between).

Circumference ratio when compared with true circle is about 1.000014, in other words a deviation of about 0.000014 or about 14 in a million too long.

Bulging rate (relative radius/diameter) at 22.5 degrees compared with true circle is about 1.000262, in other words a deviation of about 0.000262 or about 262 in a million too wide.

If needed and applicable you can rotate a circle to have the right diameter at some other angle.

And if needed, a circle with more Anchor Points can be used.

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