# Nonlinear Design. Curvature range

Curvature range |

esides being visually multifarious, Bezier curves are capable
of expressing a surprisingly wide range of The fact is, Bezier's simplicity is deceptive. Such a curve may look graphically obvious, but even from the mathematical viewpoint, four points and a third order equation that define a Bezier curve are considerably more complex than what is used in plain and bloodless geometric primitives. However, if we don't happen to be mathematicians, do we have any method to sensibly classify the curves we use, to figure out what defines a curve's aesthetic impact, and to get any idea of what sort of curve to use and when? The very word "curve" suggests that the concept of |

Fig. 3:
Extending the curvature range: from calm to storm |

Those interested in mathematics might notice that, if we regard the
curve as a function graph, its curvature range is roughly equivalent to
the maximum value of that function's third derivative. Indeed,
the first derivative represents the slant of the line in each point, the
second corresponds to curvature, and the third is the rate of change
(i.e. velocity of increasing or decreasing) of the line's curvature. The
wider is the range of curvature changes, the higher the value that
the third derivative can achieve. |

Revised: Feb. 12, 1999

URL: http://www.webreference.com/dlab/9902/curvature.html