This paper discusses the representation of the scale dimension using tGAP/SSC-DHE, emphasizing its role in creating vario-scale representations. It outlines the process of integrating the scale dimension as the third dimension in a 2D map before transitioning to 3D or 4D maps. DHE is introduced as an effective data structure for this approach, maintaining crucial connections across different levels of detail and offering enhanced topology. Its strength lies in the ability to modify specific parts of the model while retaining a clear structure, thanks to well-defined operators such as Euler operators. This method provides a versatile framework for representing complex spatial data, allowing for detailed analysis while preserving overall coherence and it updates the shape and structure of the model at the same time through local modifications. Through practical implementation, it demonstrates the potential for improved visualization and understanding of multi-dimensional spatial relationships. Also, the DHE data structure supports slicing by either a horizontal plane to produce a map at a specific scale (depending on the height of the horizontal plane) and tilted planes to produce perspective views with mixed scales.@en

Scaling factor is one of the most crucial aspect in 2D and 3D models especially in computer graphics, CAD, GIS, and games. Different user or/and application need different scale models during various stages of the use of data, including visualization and interaction. There are some arisen issues on 3D data model especially to meet GIS requirements while minimize the redundancy of the datasets. In GIS modelling, various data structures and data models have been proposed to support variety of applications and dimensionalities, but only a few in scale dimension. Some of them have succeeded in modelling scale such as in Space-Scale Cube (SSC) model. The recently implemented Dual Half-Edge (DHE) data structure within the PostgreSQL database is suitable for any valid 3D spatial model; not yet being explored for other dimensional such as scale environment. Using the same vario-scale approach, the DHE data model is also capable to implement a variable Level of Detail (LoD) representation such as SSC model. Some advantages of the DHE are described in this paper such as the dynamic property (valid updates based on Euler operations) and topology approach in comparison with other existing data structures. The last section of this paper describes capability of the DHE data structure to provide a better platform for GIS integrated space-scale data model.@en