Abstract: Quadrilateral mesh generation based on the medial axis partitions on planar triangular meshes without interior points naturally preserves right-angle features while remaining simple and efficient. How ever, existing algorithms still face challenges in handling concave corners, chamfers, and regions with drastic area variations, often leading to irregular partitions, poorly controlled singularities, and element inversion. This paper analyzes the relationship between singularity distribution and triangular mesh topology, revealing an intrinsic connection between boundary singularities and the number of type-III triangles adjacent to boundary vertices. Based on this observation, we introduce two preprocessing schemes and a medi al-axis-based partition optimization method using edge-swap operations, which improve partition regularity and enhance controllability of singularity placement. Furthermore, by integrating boundary-first flattening with integer programming, we develop a quadrilateral meshing pipeline suitable for complex CAD models. Experimental results on multi-boundary planar domains, curved surfaces, and feature-constrained CAD models demonstrate that the proposed method consistently produces high-quality quadrilateral meshes, val idating its effectiveness.