Anais do IX SIBGRAPI'96 (1996), 143150
Approximate Arc Length Parametrization
Marcelo Walter e Alain Fournier
Dept. of Computer Science  The University of British Columbia
marcelow@cs.ubc.ca
 Abstract:

Current approaches to compute the arc length of a parametric curve
rely on table lookup schemes. We present an approximate closedform
solution to the problem of computing an arc length parametrization for
any given parametric curve. Our solution outputs a one or twospan
Bezier curve which relates the length of the curve to the parametric
variable. The main advantage of our approach is that we obtain a
simple continuous function relating the length of the curve and the
parametric variable. This allows the length to be easily computed
given the parametric values. Tests with our algorithm show that the
maximum error in our approximation is 8.7% and that the average of
maximum errors is 1.9%. Our algorithm is fast enough to compute the
closedform solution in a fraction of a second. After that a user can
interactively get an approximation of the arc length for an arbitrary
parameter value.
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