Polarization singularities, such as bound states in the continuum (BICs) and circular polarization points ($C$ points), are central to advanced light manipulation in photonic systems. Although the evolution and splitting of these singularities have been widely studied, the underlying dynamics of the polarization nodal lines that dictate their birth, motion, and annihilation remain inadequately explored. Here, using polarization graphs, we reveal that two families of closed nodal lines with orthogonal orientations successively emanate from the Γ point in Dirac semimetal slabs and expand outward. Their rich interlacing configurations—intersection, tangency, separation, and concentric contraction—fully govern the trajectories of accidental BICs and the generation, merging, and topological charge conversion of general BICs. These intricate configurations can be achieved not only through conventional geometric adjustments, but also through active Fermi-energy tuning of Dirac semimetal, enabling dynamic reconfiguration of general BICs and their topological charges. Under mirror-symmetry breaking, we identify two distinct mechanisms—polarization nodal-line generation and splitting/anticrossing—that govern $C$-point formation. These mechanisms are also observed in two-dimensional Dirac semimetal systems. We further reveal that $k$-space loops encircling $C$-point pairs exhibit sharply different coverage patterns on the Poincaré sphere—broad for nodal-line generation and confined for splitting—offering promising avenues for polarization manipulation. Our findings provide insights into the dynamics of polarization singularities, with potential applications in chiral photonics, nonlinear optics, and tunable light-matter interactions.

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• Bound states in the continuum
• Photonic crystals
• Photonics
• Waveguides
• Polarization