Systems, methods, and other embodiments associated with index-based optimization of geometric figured-related queries are described. In one embodiment, a method includes receiving two points selected from a corpus of spatial data. A hierarchical index on the data is accessed to choose candidate nodes. The index is a hierarchical arrangement of nodes arranged in paths from root node entries to leaf node entries such that each node is contained in all nodes in a path leading to the node. The method includes determining a spatial relationship between the two points and the candidate nodes in the index. The candidate nodes are a proper subset of the nodes in the index, such that the spatial relationship is not determined between the two points and some non-candidate nodes. A candidate node is selected based on the determined angles for processing related to construction of a geometric figure describing the spatial data.