Studied by Huygens and Tschirnhausen about 1679 in connection with the theory of caustics . Jacques Bernoulli in 1692 showed that the nephroid is the catacaustic of a cardioid for a luminous cusp. Double generation was first discovered by Daniel Bernoulli in 1725. The latter is known as double generation. Figure on the right shows the coordination of both methods.
P is the tracing point.
D is the point of contact. PDH are colinear. We call the line from cusp to cusp the diameter of the nephroid. Properties Catacaustic of a Circle or Cardioid Nephroid is the catacaustic of a circle with parallel rays. Nephroid is the catacaustic of a cardioid with lightsource at the cusp.