2005F Fall 2005 
ARTS 102 Aesthetics of the Algorithmic Image 

Definition 
Caustic is a method of deriving a new curve based on a given curve and a point.  
Literal Meaning 
Caustics are complex patterns of shimmering light that can be seen on surfaces in presesnce of reflective or refractive objects such as those formed on the floor of a swimming pool in sunlight. Caustics occur when light rays from a source, such as the sun, get refracted, or reflected, and converge at a single point on a nonshiny surface, which creates the nonuniform distribution of bright and dark areas. The algorithm has the simplistic nature of shadow mapping, yet produces impressive results comparable to those created using offline rendering.  
Description 
Caustic is a method of developing a new curve based on a given curve and a point. A curve produced this way may also be called caustic. Given a curve x and a fixed point y, which is the light source, catacaustic is the envelope of light rays coming from the y and reflected from the curve. Diacaustic is the envelope of refracted rays. Light rays may also be parallel as when the light source is at infinity.  
History 
Caustics were first introduced and studied by Tschirnhausen in 1682. Other contributors were Huygens, Quetelet, Langrange, and Cayley.  
Caustics 
Shown below are some example of curve relations by caustics, formulas, and caustics.
The catacaustic of a cardioid
Catacaustic of sinusoid
Catacaustic of an ellipse 

The Curve Relations by Caustics 


Links 
http://mathworld.wolfram.com/TschirnhausenCubic.html 

