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There are some nasty problems with the arc-length parameterization approach:
- The arc-length s = A(u) is given by the integral
which 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
CS488/688: Introduction to Interactive Computer Graphics
University of Waterloo
Computer Graphics Lab