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The relationship between B-field orientation and density structure in molecular clouds is often assessed using the histogram of relative orientations (HRO). We perform a plane-of-the-sky geometrical analysis of projected B-fields, by interpreting HROs in dense, spheroidal, pre-stellar, and protostellar cores. We use James Clerk Maxwell Telescope POL-2 850 |$\mu$| m polarization maps and Herschel column density maps to study dense cores in the Ophiuchus molecular cloud complex. We construct two-dimensional core models, assuming Plummer column density profiles and modelling both linear and hourglass B-fields. We find that high-aspect ratio ellipsoidal cores produce strong HRO signals, as measured using the shape parameter |$\xi$|⁠. Cores with linear fields oriented |$<\!\! 45 ^{\circ }$| from their minor axis produce constant HROs with |$-1 \lt \xi \lt 0$|⁠ , indicating that fields are preferentially parallel to column density gradients. Fields parallel to the core minor axis produce the most negative value of |$\xi$|⁠. For low-aspect ratio cores, |$\xi \approx 0$| for linear fields. Hourglass fields produce a minimum in |$\xi$| at intermediate densities in all cases, converging to the minor-axis-parallel linear field value at high and low column densities. We create HROs for six dense cores in Ophiuchus. |$\rho$| Oph A and IRAS 16293 have high aspect ratios and preferentially negative HROs, consistent with moderately strong field behaviour. |$\rho$| Oph C, L1689A, and L1689B have low aspect ratios, and |$\xi \approx 0$|⁠. |$\rho$| Oph B is too complex to be modelled using a simple spheroidal field geometry. We see no signature of hourglass fields, agreeing with previous findings that dense cores generally exhibit linear fields on these size scales. [ABSTRACT FROM AUTHOR]