GIS research has a continuing thread devoted to classifying the operations performed by analytical software. Prior efforts to classify GIS operations have limitations and inconsistencies, often arising from an attempt to establish overly direct links between geographic procedures and arithmetical operations. The transformational view of cartography provides a more solid basis for classifying GIS operations. This paper presents a new scheme for geographical transformations based on measurement frameworks as the principal distinction. Transformations between measurement frameworks can be summarized in terms of a spatial neighbourhood and a rule to process attribute information. This scheme organizes most analytical GIS operations by their geometric and attribute assumptions.