There are some nasty problems with the arc-length parameterization approach:

- The arc-length
*s*=*A*(*u*) is given by the integralwhich has no analytic solution if the motion path is a cubic spline.

- Since
*A*(*u*) has no analytic form, has no analytic form.

We have to use numerical techniques:

- Find
*A*(*u*) with numerical quadrature. Precompute some values of*s*, at least at the boundaries of segments, to make this easier. - Since
*s*is a monotonic function of*u*, for a given we can find the solution to by bisection (binary search).

CS488/688: Introduction to Interactive Computer Graphics

University of Waterloo

Computer Graphics Lab