Abstract: Quadrilateral mesh generation based on medial-axis partitioning of interior-point-free triangular meshes preserves sharp-angle features with a simple and efficient workflow, yet existing methods still suffer from irregular partitions, unstable singularity placement, and element flips in concave, chamfered, or highly varying regions. This work develops an optimized medial-axis-based framework. By examining the link between singularity distribution and the topology of interior-point-free triangular meshes, the analysis reveals a correspondence between boundary singularities and the number of adjacent type-Ⅲ triangles. Two preprocessing strategies and edge-swapping refinement schemes are introduced to improve partition regularity and control boundary-singularity valence. Integrated with boundary-first flattening and integer programming, the approach forms a complete quadrilateral-mesh generation pipeline for complex CAD models. Experiments on planar, curved, and feature-constrained CAD models, together with comparisons against mainstream techniques, report consistently improved mesh quality in metrics such as scaled Jacobians and minimum angles, confirming the effectiveness of the method.