  Solar filament eruptions often show complex and dramatic geometric
deformation that is highly relevant to the underlying physical mechanism
triggering the eruptions. It has been well known that the writhe of filament
axes is a key parameter characterizing its global geometric deformation, but a
quantitative investigation of the development of writhe during its eruption is
still lacking. Here we introduce the Writhe Application Toolkit (WAT) which can
be used to characterize accurately the topology of filament axes. This
characterization is achieved based on the reconstruction and writhe number
computation of three-dimensional paths of the filament axes from
dual-perspective observations. We apply this toolkit to four dextral filaments
located in the northern hemisphere with a counterclockwise (CCW) rotation
during their eruptions. Initially, all these filaments possess a small writhe
number (=<0.20) indicating a weak helical deformation of the axes. As the CCW
rotation kicks in, their writhe numbers begin to decrease and reach large
negative values. Combined with the extended C\u{a}lug\u{a}reanu theorem, the
absolute value of twist is deduced to decrease during the rotation. Such a
quantitative analysis strongly indicates a consequence of the conversion of
twist into writhe for the studied events.
