Galactic bars are ubiquitous in the Local Universe and play an important role in the secular evolution of disc galaxies, facilitating the outwards transport of angular momentum. By driving gas into central regions, they encourage the growth of supermassive black holes. However, the exact connection between bars and physical properties of their host galaxies, for example, the effect of a bar on the bulge mass — black hole mass scaling relation, is not very well understood. We present a new orbit superposition code for potentials with figure rotation. Extensively testing our code on mock data generated from a suite of N-body models of barred galaxies, we recover their 3D bar shapes, pattern speeds and black hole masses. We show that even in the face-on case, there is enough information in the line-of-sight velocity data to determine the pattern speed. Given that we are now able to model barred galaxies, we intend to carry out a systematic study of their scaling relations and "large-scale" properties, such as bar orientation angles, dark halo parameters and mass-to-light ratios, using upcoming Euclid photometry and presently available IFU data.