Question 12 of 15: Discrete objects versus continuous fields

Question 12: Discrete objects versus continuous fields (5 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

These are the two fundamental ways of conceptualizing geographic phenomena before choosing a data model. The discrete-object view treats the world as populated by distinct, countable, bounded entities that have identity and exist between empty space — for example roads, parcels, wells, buildings and lakes. Each object has a clear boundary, can be counted, and carries its own attributes; the world is "empty" except where an object is present. This view maps naturally onto the vector model (points, lines, polygons) and object/feature databases, where each feature is a record with a unique identifier. The continuous-field view treats the world as a set of properties that vary continuously over space, with a value defined at every location — for example elevation, temperature, rainfall, soil pH or slope. There are no objects to count; instead there is a function z = f(x, y) sampled across the area. This view maps naturally onto the raster (grid) model, or onto TINs and contour representations. The distinction matters for database design and analysis: discrete objects are queried by identity and topology ("which parcels touch this road?"), whereas fields are queried by location and value ("what is the elevation here?", map algebra). Some phenomena can be seen either way (a forest as discrete stands or as a continuous canopy-density field), and the chosen conceptualization drives the data model, storage and the operations that are meaningful.