Iso-Optic Curve of the Ellipse

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This Demonstration shows an ellipse (red), and two other curves (blue), from which the ellipse subtends the angles (further from the ellipse) and (closer to the ellipse).

Contributed by: Géza Csima, Jenő Szirmai, and János Tóth (December 2008)
Open content licensed under CC BY-NC-SA



Given an ellipse with semi-major and semi-minor axes and , we look for viewpoints from which the ellipse subtends the angle . We start from the point on the ellipse; this will be one of the tangent points. Next we calculate the two possible viewpoints , ; from one of them the ellipse subtends the angle , from the other one the ellipse subtends the angle . As the parameter goes from 0 to we get the set of viewpoints for those two angles, which form the two iso-optic curves of the ellipse.

You can set the ellipse parameters and to between 1 and 10, and between 5° and 90°. The first snapshot shows the iso‐optic curve in general. From the second snapshot you can see that if is small, the curve looks like a circle. In the third snapshot, , so the curve is a circle.

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