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 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.