While computational geometers might like to see GIS as an instance of the practical implementation of computational geometry, this is not historically accurate. The GIS and CG communities have, for the most part, developed their understanding of geometric computation independently. In some key instances (``topological structure'' for storing planar subdivisions, and ``TINs''-triangulated terrains, interpolation properties of the Voronoi and Delaunay), development in GIS has preceded that in CG.
Computer cartography emerged in the 1960s. Many basic concepts (map layers, topological structure, TINs) can be traced back to work done in the The Land Inventory branch of the Canadian government or the Harvard Lab for Computer Graphics and Spatial Analysis. ESRI's ARC/INFO, which is the most popular commercial GIS system, got its start with Harvard Lab technology.
Interaction between CG and GIS has increased in recent years. CG papers at the biennial International Symposium on Spatial Data Handling have been generally well received. ESRI, Caliper Corp., and other companies have been hiring from the computational geometry community and taking in research results (including, for example, nearest-neighbor properties of Delaunay triangulations, and the use of Voronoi diagrams of line segments to assist in ``buffering'' (offsetting) operations). A common complaint has been that publication delays and the lack of textbooks in CG hampers the adoption of research results by other fields such as GIS.