CAUSTIC CURVE : Summary

If you have worked through the caustic curve constructions, you will have discovered the results in the following table. We have only listed the cases where the caustic curve is known or of interest. It is a little disppointing that more of our curves are not generated in this way. On the other hand, we might suggest that many of these caustic curves are new curves worthy of study!

CURVES AND THEIR CAUSTIC CURVES
Original curve 
Rays
Caustic curve
Circle
From point on circle
Cardioid

Circle

Parallel
Nephroid

Cycloidal arch

Perpendicular to base

Two cycloidal arches

Deltoid
Parallel (any direction)
Astroid
Parabola
Perpendicular to axis
Tschirnhausen’s cubic