All physical processes can be described, at a fundamental level, through interactions of elementary particles. The Standard Model of particle physics (SM) describes three of the four known fundamental forces and all of the known elementary particles. The accuracy of the predictions made using this theory has been experimentally established over a wide range of processes. Physicists endeavour to extend the SM to cover those phenomena, observed or hypothesised, that are currently beyond its scope. To develop these extensions, it is useful to identify processes involving SM particles where SM predictions differ from what is measured in nature. The fact that flavour-changing neutral currents (FCNC) processes are forbidden at tree level in the SM makes them a promising laboratory for precision measurements that can show effects of physics beyond the SM: New Physics (NP) at energy scales higher than those of an FCNC process can nevertheless indirectly affect it to a potentially measurable extent. This work realises one such precision measurement. It concerns the polarisation of the photon in b -> s gamma transitions. Due to the chiral nature of the weak interaction, which is the only SM interaction that mediates FCNC processes, the photon is almost entirely left-handed in decays that proceed through a b -> s gamma transition. NP with a chiral structure that is different from that of the weak interaction could enhance the right-handed component of the photon. The photon polarisation in b -> s gamma transitions is experimentally constrained through measurements of the inclusive branching fraction B -> X_s gamma and other measurements of radiative decays of b hadrons, as well as from B0 -> K*0 e+ e- decays at low q2. It has been directly measured in Lambda_b -> Lambda gamma decays. The experimental results are consistent with SM predictions. An up-down measurement of B+ -> K+ pi- pi+ gamma decays has shown that the photon in these decays is polarised, but the value of the polarisation parameter lambda_gamma could not be extracted from this measurement. In this work, an amplitude analysis of B+ -> K+ pi- pi+ gamma decays recorded at the LHCb experiment during Run 1 and Run 2 of the LHC is performed, and a model of the B+ -> K+ pi- pi+ gamma decay, including the value of lambda_gamma, is defined. This measurement further constrains the photon polarisation in b -> s gamma transitions and thus contributes to the identification of promising avenues for extending the SM. The reconstruction of charged particle momenta at LHCb requires a precise knowledge of the magnetic field that bends the particles' trajectories. A new map of the magnetic field of the LHCb dipole was developed for use in Run 3 of the LHC. This map and its development is also discussed in this work.