Modeling the markets with Bezier curves by Mark Angel
The Bezier curve, also known as a B-curve, is a mathematical construct for tracing a smooth path between a series of key support and resistance points. B-curves, which were created as an industrial engineering method, are also a powerful new tool for understanding and predicting commodity markets.
A quick glance at a price chart reveals a tortuous winding path of bars pulled first in one direction and then another by unseen forces. The march of prices is rarely linear. Frequently, the market appears to steer a meandering course between floors of support and ceilings of resistance. On occasion, however, prices gravitate relentlessly in one direction.
Technical analysis exists to impose order on this chaos. The idea is to create a mathematical model or simulation of the market. Whether this predictive model is simple or complex, the goal of the technician is to separate the meaningless movement of prices from the profound. The moving average crossover approach, for example, ignores changes in price until the point at which a close passes under or over the current average is reached. This particular price movement is considered meaningful, and so a trading position is triggered. All technical systems filter price fluctuations to discern the market's "true" direction.