In this paper, we present a software framework, S$pi$RITROOT, which is capable of track reconstruction and analysis of heavy-ion collision events recorded with the S$pi$RIT time projection chamber. The track-fitting toolkit GENFIT and the vertex reconstruction toolkit RAVE are applied to a box-type detector system. A pattern recognition algorithm which performs helix track finding and handles overlapping pulses is described. The performance of the software is investigated using experimental data obtained at the Radioactive Isotope Beam Facility (RIBF) at RIKEN. This work focuses on data from $^{132}$Sn + $^{124}$Sn collision events with beam energy of 270 AMeV. Particle identification is established using $left<dE/dxright>$ and magnetic rigidity, with pions, hydrogen isotopes, and helium isotopes.
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