In GIS, there are two main perspectives on spatial data and how it should be represented. These two perspectives are topology and geometry, each with different roles and purposes depending on what is being analyzed or visualized.
Source: Jiang & Slocum (2020:4)
The geometric perspective in GIS focuses on geometric details and accuracy. This includes aspects like location, size, and direction. These geometric details are represented in GIS systems through geometric primitives such as pixels, lines, points, and polygons (Jiang 2019: 14). This perspective is concerned with describing the exact positions, sizes, shapes, and directions of objects in space. For example, a line may represent a road, and the road's length, direction, and precise position in relation to other objects are captured. Geometry is essential when precision is required, such as when determining the exact location of a building or specifying the distance between two points on a map.
Source: Jiang &Slocum (2020:12)
Another key perspective on spatial objects in GIS is topology, which, according to Jiang (2019: 14), refers to the relationships between geometric entities. Topology does not focus on the exact geometric shape or size of an object; rather, it emphasizes the relationships and connections between objects. As Jiang (2019: 14) points out, it is more about an entity's importance or meaningfulness than its geometric details. The topological perspective thus concerns how objects are connected or related, regardless of their exact positions, shapes, or directions. For instance, the topology of a road network describes which roads are connected to each other, without considering their actual length or shape. The topological perspective, as noted by Jiang (2014: 8), is also often crucial in cognitive mapping, as it provides a more intuitive way to visualize the importance or prominence of geometric entities.
References:
Jiang B. and Slocum T. (2020), A map is a living structure with the recurring notion of far more smalls than larges, ISPRS International Journal of Geo-Information, 9(6), 388. Reprinted as the cover story in the magazine Coordinates, August issue, 6–17, 2020.
Jiang B. (2019), New paradigm in mapping: A critique on Cartography and GIS, Cartographica, 54(3), 183–205. Reprinted as the cover story in the magazine Coordinates, October issue, 9–21.