2D to 1D and 2D to 0D Geometry Generalization Based on the Straight Skeleton by the Dual-Half Edge Structure

Abstract. Efficient vario-scale representation is important in Geographic Information Systems (GIS) and cartographic generalization, particularly when transitioning 2D features into 1D or 0D representations. Traditional approaches often introduce topological inconsistencies and abrupt transitions between scales. This paper presents a novel method for vario-scale representation by integrating the Straight Skeleton Network (SSN), Dual Half-Edge (DHE) structure, and Space-Scale Cube (SSC). The straight skeleton enables hierarchical polygon decomposition, ensuring smooth feature transitions across scales. The DHE structure maintains topological consistency, supports dynamic updates, and allows structured connectivity between spatial features. The SSC framework organizes these transformations within a volumetric model, ensuring seamless scale transitions. The proposed approach is tested on various polygonal configurations, demonstrating its effectiveness in preserving spatial coherence, feature continuity, and structural integrity. This research contributes to multi-scale GIS modeling, automated map generalization, and spatial data structuring.