A measure of the writhing of a curve is introduced and is used to extend the Călugăreanu decomposition for closed curves, as well as the polar decomposition for curves bound between planes. The new writhe measure is also shown to be able to assess changes in linking due to belt-trick and knotting type deformations, and further its utility is illustrated on examples taken from elastic rod parameter-continuation studies. Finally C++ and mathematica codes are made available and shown to be faster than existing algorithms for the numerical computation of the writhe.
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