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Limn must have some way to relate the discrete curve made from the original bitmap to the continuous spline being fitted to that curve. This is done by associating another number, traditionally called t, with each point on the curve.
Imagine moving along the spline through the points on the curve. Then t for a point p corresponds to how far along the spline you have traveled to get to p. In practice, of course, the spline does not perfectly fit all the points, and so Limn adjusts the t values to improve the fit (see section 10.1.5.4 Reparameterization). (It also adjusts the spline itself, as mentioned above.)
Limn initializes the t value for each point on the curve using a method called chord-length parameterization. The details of how this works do not affect how you use the program, so we will omit them here. (See the Plass & Stone article cited in `limn/README' if you're curious about them.)