Topologically Consistent Line Simplification with the Douglas-Peucker Algorithm

Abstract

We examine key properties of the Douglas-Peucker polyline simplification algorithm which are shared with many similar "vertex sub-sampling" algorithms. We examine how the Douglas-Peucker algorithm and similar algorithms can fail to maintain consistent or correct topological relations among features. We then prove that a simple test added to the stopping condition of Douglas-Peucker-like algorithms can guarantee that the resulting simplified polyline is topologically consistent with itself and with all of its neighboring features, and is correctly situated topologically with respect to all other features. We describe how a dynamically updated convex hull data structure may be used to efficiently detect and remove potential topological conflicts of the polyline with itself and with other features in that polyline's neighborhood.