This paper presents the CAGE (Continuity-Aware edgeGE) network, a powerful framework for directly reconstructing vector floor plans from point cloud density maps. To address the sensitivity of existing corner-based polygonal representations to noise and incomplete observations, as well as their difficulty in recovering fine geometric details, we propose an edge-centric formulation that models each wall segment as a geometrically continuous, directed edge. This representation infers a consistent floor plan structure, improves robustness, and reduces artifacts. To achieve this, CAGE develops a dual-query transformer decoder that stabilizes optimization and accelerates convergence. Experimental results on Structured3D and SceneCAD demonstrate that CAGE achieves state-of-the-art performance, achieving F1 scores of 99.1% (rooms), 91.7% (corners), and 89.3% (angles). It also demonstrates strong cross-dataset generalization.
