 
Summary: ArcLength Parameterized Spline Curves
for RealTime Simulation
Hongling Wang, Joseph Kearney, and Kendall Atkinson
Abstract. Parametric curves are frequently used in computer an
imation and virtual environments to control the movements of syn
thetic objects. In many of these applications it is essential to effi
ciently relate parameter values to the arc length of the curve. Cur
rent approaches to compute arc length or to construct an arclength
parameterized curve are impractical to use in realtime applications.
This paper presents a simple and efficient technique to generate ap
proximately arclength parameterized spline curves that closely match
spline curves typically used to model roads in highfidelity driving sim
ulators.
§1. Introduction
Parametric cubic splines are the curves of choice for many applications
of computer graphics. They are widely used in computer animation and
virtual environments to define motion paths [6]. As the parameter vari
able ranges over the interval of definition, the computed position traces
a smooth curve in space. Naively, one might compute position using the
parameter variable directly. However, it is difficult to regulate the speed
