Generalizing the LoD transition space for continuous multi-scale representation using straight skeletons

Abstract Continuous multi-scale representation enables geographic features to evolve smoothly across Levels of Detail, avoiding abrupt transitions between independently generalized datasets. However, existing approaches provide limited support for complex transformations involving different geometric and topological configurations. This study generalizes the LoD Transition Space framework to represent continuous transformations between polygons, polylines, and points. The proposed approach uses straight-skeleton-based geometric primitives to construct continuous 2D + 1D transition volumes and decomposes complex transformations into localized LoD Transition Regions. The framework supports polygon-to-boundary-polyline, polyline-to-polyline, polygon-to-polygon, and N-to-M polygon transformations, including aggregation, merging, splitting, simplification, and collapsing. Horizontal slicing of the resulting 3D model generates intermediate representations at arbitrary Levels of Detail while maintaining geometric continuity and topological consistency. The approach was evaluated using real-world datasets from OpenStreetMap, NUTS, ATKIS, and Polish administrative and BDOT10k data. The experiments demonstrate that the framework can represent both regular and irregular multi-scale transformations, including cases where source and target geometries have complex spatial relationships or identical target extents. The proposed 3D model provides a unified representation for continuous map generalization and supports the generation of consistent intermediate representations across scales.