Bound states in the continuum (BICs) enable strong light confinement and enhanced light–matter interactions, yet how lattice deformation governs their momentum-space evolution remains unclear. Here, we develop a lattice-engineering framework for silicon photonic crystal slabs by investigating the continuous evolution from a square lattice to rectangular and monoclinic lattices. A symmetry-constrained far-field expansion shows that rectangular deformation lifts the degeneracy between two orthogonal BIC branches, while the preserved mirror symmetries pin their trajectories to the principal axes. Near the merging point, $k_{\mathrm{BIC}}^2$ varies linearly with the aspect-ratio detuning. Monoclinic shear removes these mirror constraints and enables coupling between orthogonal momentum components, steering the BICs along off-axis trajectories. The slab thickness provides an additional degree of freedom to shift the BICs along these symmetry-allowed trajectories and drive their charge-conserving merging at the $\mathrm{\Gamma }\mathrm{point}$. Further breaking the in-plane $C_2$ symmetry of the unit cell splits integer-charge BICs into circular-polarization points carrying half-integer topological charges, accompanied by extended regions of high ellipticity. These results show how lattice symmetry constrains BIC trajectories and geometric tuning controls their positions, providing a route to engineering BIC merging and polarization singularities.

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• Bound states in the continuum
• Metasurfaces
• Photonic crystals