Circle Catacaustic

Consider a unit circle and a radiant point located at . There are four different regimes of caustics, illustrated above.

For radiant point at , the catacaustic is the nephroid

			(1)
			(2)

(Trott 2004, p. 17, mistakenly states that the catacaustic for parallel light falling on any concave mirror is a nephroid.)

For radiant point a finite distance , the catacaustic is the curve

			(3)
			(4)

which is apparently incorrectly described as a limaçon by Lawrence (1972, p. 207).

For radiant point on the circumference of the circle (), the catacaustic is the cardioid

			(5)
			(6)

with Cartesian equation

(7)

For radiant point inside the circle, the catacaustic is a discontinuous two-part curve.

If the radiant point is the origin, then the catacaustic degenerates to a single point at the origin since all rays reflect upon themselves back through the origin.