Let's have a curve C. Vary two tangents to the
curve in such a way that the angle between the two lines is a constant. Then the
intersections of the tangents form the isoptic of C.
The sinusoidal spiral is the curve for which the
isoptic is also a sinusoidal spiral.
Some isoptic curves are the following:
When the constant angle between the tangents has the value π/2,
the curve is called an orthoptic.
For the logarithmic spiral its orthoptic is equal to itself.
Some other orthoptic curves are:
La Hire (1704) was the first to mention the curve.
Another curve with isoptic properties is the isoptic cubic.