Terrain and 3D Modeling

At the heart of 3D analysis is the Digital Elevation Model (DEM). A DEM is a raster grid where every pixel contains a single value representing the height ($Z$) above sea level. The quality of your analysis depends on spatial resolution; a 30m resolution DEM means each pixel covers a $30 \times 30$ meter area. From this simple grid, we can derive complex surface characteristics. By calculating the relationship between a cell and its eight neighbors, GIS software determines the 'lay of the land.' This process is the starting point for understanding water runoff, solar exposure, and construction feasibility.

A Viewshed Analysis determines what areas are visible (or invisible) from a specific observation point. The algorithm uses Line-of-Sight (LoS) logic, drawing a 3D vector from the observer's eye to every other cell in the DEM. If the terrain (or a building) rises above this vector, the target cell is marked 'hidden.' This is critical for placing cell towers, wind turbines, or fire lookouts. We can also factor in the Observer Height ($O_h$) to account for the height of a person or a tower, effectively 'lifting' the viewpoint above the ground surface.

In urban GIS, we move beyond natural terrain to volumetric modeling. Extrusion is the process of taking a 2D polygon (like a building footprint) and stretching it into a 3D object. This is usually driven by an attribute in the data table, such as 'Number of Floors' or 'Height in Meters.' If a building has a height $H$, the GIS creates a vertical volume from the ground elevation $Z$ to $Z + H$. This allows planners to perform Shadow Analysis, determining how a new skyscraper might block sunlight for neighboring parks.