Abstract.Arc length parametrization can be thought of as the most natural among all possible parameterizations of a given curve. Beyond having several nice mathematical properties, this parametrization is useful for computer graphics applications: drawing a curve given in this form and computing its length, are particularly easy. Unfortunately, for the curves used mostly in computer graphics, namely cubic splines, the arc length parametrization cannot, in general, be expressed as any elementary function. As a result, practitioners are forced into employing approximate numerical methods which are in many cases complex, computationally intensive, and susceptible to error accumulation due to their iterative nature.

This paper explores the following new direction to this problem. Instead of the traditional classes of curves, such as polynomials and rational functions, we promote the usage of a new class of curves which are all given in an explicit arc length parametrization form. On a par with polynomials, it is possible to select a subclass of curves which has any desired number of degrees of freedom. Our results show that several important settings of the general interpolation problem can be solved using curves from this class.

Received: August 13, 2006

AMS Subject Classification: 26B15, 51M25

Key Words and Phrases: arc length, length parametrization

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 31
Issue: 3