Abstract Testing Shortcuts to Maintain Simplicity in Subdivision Simplification

Cartographers collect more data than they need,and so must simplify coastlines,boundaries,and other linear features to display a map at a given scale. Many simplification methods,however,can introduce intersections that were not originally present,corrupting the features. Kulik suggests a simple shortcut operation for polygonal lines: remove a point pi and connect its former neighbors pi−1 and pi+1 directly,but only if the triangle △pi−1pipi+1 is empty of other points. We show geodesic triangulations support shortcut operations and triangle tests in O � log 2 n � time for connected subdivisions of size n. This can be integrated into simplification methods that support cartographic preferences so that they can also avoid self-intersection.