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Arc Length Parameterization

  1. Given a spline path P(u) = [x(u),y(u),z(u)], compute the arclength of the spline as a function of u: s = A(u).
  2. Find the inverse of A(u): .
  3. Substitute into P(u) to find a motion path parameterized by arclength, s: .
Note that u (and thus s) should be global parameters, extending across all segments of the original spline.

CS488/688: Introduction to Interactive Computer Graphics
University of Waterloo
Computer Graphics Lab