## 3 Proposed Procedure
### Vector-Based 3D Object Generation Procedure
#### 3.1.3 Generation of Vector-Based 3D Objects  
This study generates LoD1-level 3D objects through triangular mesh generation and elevation value assignment based on 2D spatial information data. This process focuses on representing urban terrain and structures in 3D while ensuring mesh structure precision and elevation value accuracy. Triangular Mesh Generation: this stage constructs the geometric structure of objects based on 2D vector data, utilizing a constrained Delaunay triangulation algorithm for precise and stable triangular mesh generation, as shown in Figure 3.  
To ensure spatial accuracy and realism in the 3D modeling process, several geometric principles were applied during triangular mesh generation. First, terrain continuity was preserved by maintaining seamless connections between adjacent terrain surfaces and spatial objects. This approach prevents spatial discontinuities and geometric distortion during rendering and analysis. In addition, the mesh division density was dynamically adjusted in areas with significant elevation variation to accurately reflect terrain curvature. This adaptive meshing strategy helps capture subtle elevation changes and ensures topographic fidelity. Furthermore, in urban regions containing artificial structures such as buildings and roads, triangular meshes were generated while maintaining geometric consistency with existing spatial data. This ensured that the 3D representations of urban elements remained structurally coherent and aligned with the original 2D datasets. Figure 3: Constrained Delaunay triangulation and spatial partitioning. Following the generation of the triangular mesh, elevation values (Z-values) were assigned to each mesh vertex using numerical terrain data derived from the DEM. This mapping process allowed the 3D objects to accurately represent terrain height variations, contributing to a more realistic three-dimensional representation of the spatial environment. To enhance the visual and structural continuity of the terrain, interpolation techniques were applied within each triangular region, resulting in smoother and more natural elevation transitions across the surface. In cases where the resolution of the DEM data was lower than that of the generated triangular mesh, bilinear interpolation was employed to estimate intermediate elevation values. This technique ensured that the elevation data were seamlessly integrated into the finer mesh structure by calculating interpolated heights based on the surrounding four DEM grid points. As a result, discrepancies caused by resolution differences were effectively minimized, thereby improving the overall precision and continuity of the terrain representation within the 3D model, as shown in Figure 4.  
Bilinear interpolation estimates the elevation \(f(x,y)\) at an arbitrary point \(f(x,y)\) based on the surrounding four DEM grid points, \((x_{1},y_{1}),(x_{2},y_{1}),(x_{1},y_{2}),(x_{2},y_{2})\), where each point has a known elevation value. The interpolation formula is expressed as follows:  
\[f(x,y)=f(x_{1}y_{1})\cdot(1-\alpha)(1-\beta)+f(x_{2},y_{1})\cdot\alpha(1-\beta )+f(x_{1},y_{2})\cdot(1-\alpha)\beta+f(x_{2},y_{2})\cdot\alpha\beta\]  
To ensure structural accuracy and semantic consistency, elevation assignment was adjusted based on object type. For fixed structures such as buildings, a constant Z-value was applied to each object in order to prevent distortion caused by terrain undulations. In contrast, continuous elements such as roads and natural terrain were processed using dynamic interpolation based on DEM data. This allowed these features to more accurately reflect the underlying topography, resulting in smoother and more realistic elevation transitions throughout the model. By applying this object-specific elevation adjustment strategy, the proposed 3D object generation procedure effectively balanced geometric precision and visual coherence, while also enhancing large-scale data processing efficiency and reducing memory consumption during rendering and analysis.